Priority Schemes for Life Extension and Data Delivery in

Research ArticlePriority Schemes for Life Extension and DataDelivery in Body Area Wireless Sensor Networkswith Cognitive Radio Capabilities

Sergio M Mart-nez Chaacutevez 1 Mario E Rivero-Angeles 2

Laura I Garay-Jimeacutenez1 and Issis C Romero Ibarra1

1Seccion de Estudios de Posgrado e Investigacion Unidad Profesional Interdisciplinaria en Ingenierıa y Tecnologıas AvanzadasIPN Av Instituto Politecnico Nacional 2580 Barrio La Laguna Ticoman Gustavo A Madero 07738 Mexico City Mexico2Networks and Data Science Laboratory Centro de Investigacion en Computacion del Instituto Politecnico NacionalAv Juan de Dios Batiz Esq Miguel Othon de Mendizabal SN Nueva Industrial Vallejo 07738 Mexico City Mexico

Correspondence should be addressed to Mario E Rivero-Angeles mriveroaipnmx

Received 7 January 2019 Revised 22 April 2019 Accepted 9 May 2019 Published 29 May 2019

Academic Editor Jesus Fontecha

Copyright copy 2019 Sergio M Martınez Chavez et al This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Wireless sensor networks have recently been used to monitor bioelectric signals generated by the human body However sincethe dimensions and capabilities of the network nodes are small and limited a problem is generated inherently by the energyconsumption and radioelectric interference In view of this we propose two priority schemes to improve the performance of thenetwork In the first one we aim at increasing the system lifetime by reducing the number of transmissions of nodes with lowenergy levels In the second scheme we aim at conveying priority data to the sink node as fast and efficient as possible In theformer scheme users can be monitored for long time periods considering a low data generation On the other hand the latterscheme allows expediting transmission of important data when energy efficiency is not relevant In this article we mathematicallymodel analyze and study the performance of the system for both priority schemes considering cognitive radio capabilities to makeefficient use of resources and limit the radioelectric interference when the network transmits both continuousmonitoring and eventdetection information Numerical results provided in this work allow a careful parameter selection for practical implementation ofBANETs

1 Introduction

The evolution of technologies in recent years has causedthe dimensions of the devices to tend to decrease whiletheir processing capacity tends to increase The advances inelectronics and solid-state technologies have also allowedworking with wireless devices that provide the facility to usethem remotely without the need for connections or wires Inpractical terms technology has also been used in medicalapplications from the assistance of surgical procedures totaking vital signs to prosthetics and remotely monitoringdifferent biosignals Such recent applications have given riseto the e-health research area It should be noted that wireless

and ambulatory applications have relevant importance asthey allow the patient to move without the need to berestricted to a specific area or to take extreme caution dueto devices disconnection [1] Within e-health the area ofbody monitoring is contemplated where the sensing of thesignals that are constantly created by the organs is required fordiseases detection recovery assessment and effort supportamong othersTherefore tools are required to efficiently cap-ture transmit store and analyze electrical signals generatedby the human organs (these studies are known as bioelectricor biopotential) [2]

There are different solutions that have been proposedin the literature for monitoring biosignals including wired

HindawiWireless Communications and Mobile ComputingVolume 2019 Article ID 2637830 22 pageshttpsdoiorg10115520192637830

2 Wireless Communications and Mobile Computing

and wireless approaches The cabled option approach has nointerference among nodes but patients are not comfortablewith wires around their body for long periods of timeand the nodes disconnection is highly probable For thesecond approach wireless sensor networks (WSN) constitutea functional and practical alternative [3] where each sensoris composed of electrodes battery and a processing moduleto allow the transmission of the information to a sink nodeTherefore the wireless option is advisable in order to allowpatients to have full mobility with the recording equipmentin ambulatory monitoring However WSNs face an inherentconflict with energy consumption since despite technologi-cal advances several authors have reported that the lifetimebattery of nodes in this type of systems is compromised bythe network dimensions (number of nodes) and data ratetransmission Consequently the system lifetime is usuallylower than that in wired networks or when nonambulatorynodes with higher dimensions are used [4 5] even in hospitalenvironments as analyzed by Sodagary in [6] In this contextenergy efficiency is one of the main research topics that havebeen recently studied

Based on the above we propose and develop amathemat-ical analysis that models the main dynamics of the system inorder to calculate energy consumption and packet loss proba-bilitiesNumerical results obtained through themathematicalmodel show that the system lifetime is greatly extended whendata transmission is limited On the other hand when mostdata is required at the sink node the energy consumed toachieve it tends to be higher reducing the operation timeof the network In view of this inherent compromise amongdata transmission and energy consumption we propose twopriority schemes to enhance either system duration or datagathering described as follows

(i) In the energy-efficient approach nodes limit datatransmission in order to extend the system lifetimeFurthermore nodes with lower residual energy per-form fewer transmissions to the sink node whilenodes with their full batteries can make more trans-missions without affecting the operation of the net-work In this scheme less information is transmitted(manydata packets are dropped to reduce energy con-sumption) since the main objective of this scheme isto gather just enough information from the patient tohave insight into his health but not critic illness thatrequires prompt medical attention

(ii) In the data gathering efficient approach we assumedifferent packets types effectively assigning prioritylevels to packet data Building on this the priorityscheme enables the expediting transmission of highpriority data over low priority data reducing packetdropping probability and reducing packet delayHowever in this approach energy consumption ishigher reducing the operation time of the network

These schemes are intended to work under differentconditions in ambulatory systems For instance consider apatient in stable conditions where his medical team hasthe need to monitor him for long periods of time but no

emergency events are expected (eg an elderly person invacations or a business trip for a highly stressed corporateworker) where different biopotential signals are of interestbut there are no ongoing urgent medical procedures In thesecases the system is required to gather as much informationregarding the patient as possible but the main interest is thatthe monitoring network lasts as long as the trip (or intervalbetween medical visits) lasts On the other hand there arepeople with specific affections that require immediate med-ical attention As an example in the case of cardiac diseasepatients medical staff can monitor the electrical activity inthe patientrsquos heart while allowing such patients to have asmuch normal life as possible with no need to spend countlesshours in the hospital However in case of a tachycardiathe patient can be taken to the hospital and the attendingmedic can retrieve all information regarding such episodeIn both schemes it is difficult to establish the adequateparameter values to guarantee the performance required foreach case Therefore the derived mathematical analysis isof great relevance to learning about the performance of theBANET for different systemparameters Based on thismodelthe system can be finely tuned to achieve a specific use

With the aim of reducing energy consumption andinterference into the system we propose the use of CognitiveRatio (CR) capabilities There are several examples of thepotential benefits from this technology in computer networks[7ndash10] In CR two systems are considered the primarysystem (PS) consists of users that have the right and licenseto use the radio-frequency resources and in the secondarysystem (SS) nodes transmit in available channels only if theyare not being used by primary users (PUs) ie users of thePS Secondary users (SUs) have to be constantly monitoringthe availability of the channel to identify empty slots (radio-frequency resources not being used by any PU) in order toavoid any negative impact on the service provided to PUs

As such PUs are not affected by the operation of theSS and their service is not degraded Building on this wemake use of such CR capabilities by allowing continuousmonitoring data to be transmitted as the primary systemwhile event-related reports are transmitted as a secondarysystem making use of empty spaces in the PS

Furthermore we propose an ONOFF scheme for pri-mary nodes in order to generate empty spaces to be usedby secondary nodes In the OFF mode primary nodesdo not report data and energy consumption is reducedallowing event-related data to be transmitted in the systemAccurateness of the data is not affected by nodes in theOFF mode since we use an oversampling procedure to allowmultiple biopotential signals to be transmitted in a single timeframe [11] This issue is explained in detail in Section 2

The main contributions of this work can be described asfollows

(i) A body area network (BANET) for both continuousmonitoring and event reporting with CR capabilitiesis proposed analyzed and studied using MarkovChains in order to provide clear guidelines for thedesign and parameter selection in practical e-healthmonitoring ambulatory systems

Wireless Communications and Mobile Computing 3

(ii) Two priority schemes (energy-focused and data-focused) are developed and mathematically analyzedin order to study the capabilities limits and perfor-mance of each scheme

(iii) We propose design and study the ONOFF mecha-nism for primary nodes in order to have empty spacesand reduce energy consumption

(iv) Numerical results for different system conditions areobtained in order to provide relevant insights into theoperation of the system

(v) The mathematical model is validated through the useof discrete event algorithmic simulations

The rest of the paper is organized as follows In Section 2a brief discussion on related works previously published inthe literature is presented Then in Sections 3 and 4 wedescribe in detail the proposed communication protocol andmain assumptions of this workWe present the mathematicalanalysis in Section 5 battery and hardware specificationsin Section 6 and finally relevant numerical results anddiscussion on the performance of the system in Section 7We conclude with important remarks and future works in thearea

2 Related Work

Biosignals (also called bioelectric studies) are measurementsof electrical voltages between two points in living cellstissues and organisms The study of such signals allowsmonitoring the status and health of organs muscles or bodyparts Bioelectric studies can be evaluated in the area ofe-health in charge of the use of technological resourcesto improve the quality of life of the patients and generalpopulation [12]

Most of the time these studies are made through spe-cialized wired instrumentation however at present (LTEsystems) and future (considering the full potential of theInternet of Things IoT in 5G systems) wireless optionsare an accessible and fully functional resource [13] For thisreason there are a wide variety of tools that can assist inthe measurement of biopotential signals wirelessly [14] Forinstance we can consider the implementation of biopotentialsignal monitoring with ZigBee (a set of protocols that makeup a wireless technology for signal acquisition) prepared by[15ndash17] (all three casesmeasure the heart status) or embeddedECG (electrocardiogram) systems adaptable to commercialdevices [18] orWiFi-basedECG systems like [19]However inthese investigations the authors themselves indicate that theyare limited by the particular specifications that the protocolsdescribe energy consumption levels are already establishedand there is not a clear proposal for life extension in datadelivery for WSNs

An alternative to these standardized applications iscustom-design wireless sensor networks whose use hasincreased due to their versatility and functionality inmultipleimplementation areas [20] Specifically e-health networkshave a broad applications spectrum The literature presentsseveral protocols that can be implemented in Wireless Body

Area Sensor Network (WBASN) where efficiency and energyconsumption are evaluated and in most cases to extend theaverage node duration it is required to include additionalhardware or to include software for analysis and networktopological balancing [21] To illustrate this we can seethe work by Sivakumara [22] His proposal consists of thestudy and evaluation of energy consumption for wirelesssensor networks applying conventional protocol models withtheir respective programming we can also go to the workof Kan et al in [23] he makes an efficient study of aWSN (without including cognitive radio and neglecting thepossible interferences that can be generated with highlyspecialized medical equipment) for ECG nodes LikewiseSaleh [24] also proposes an architecture for each sensor of aWSN where the maximum energy efficiency in the system iscontemplated without including the cognitive radio concept

There are also works like that by Chavez [25] whichmakes a proposal of the bases of implementation of cognitiveradio in weareble networks but does not develop an energyconsumption analysis but rather focuses its developmenton compatibility with the devices and reduction of interfer-ences Mamoon in [26] also defines the implementation ofCognitive Radio Network (CRN) in hospitals but withoutspecifying the energy consumption over WSN

As it can be seen there are several works focused on thenetwork implementation for the monitoring of biosignals inpatients with noninvasive nodes [27]Their proposed systemsare analyzed in a theoretical and practical way using variousprotocols and tools proposed to contemplate the networkenergetic performance However it is very important to notethatmost of the reported works for life extension of the nodesand analysis of energy consumption do not usually includethe conceptualization of cognitive radio in their development(or specifically cognitive radio is used for the decreaseof radioelectric interference and bandwidth but ignoringthe analysis of the energy performance of the network) Incontrast our work presents a general flexible mathematicalframework to evaluate the performance of the body areanetwork (BANET)

To further expand the cognitive radio capabilities wedevelop the analysis for each scheme that is network config-urations that allow a greater efficiency to be generated withrespect to what the users may require Two general schemesare contemplated a configuration to extend the networklifetime (such as the one used by Al in [28] which describes indetail the energy behavior of the network but only focusingon one scheme and a single study) and another to providea better resolution in the medical studies (like the oneproposed by Jenq in [29] which performs a development of anefficient high-resolution scheme but just like the previousexample does not mention any other scheme for the samenetwork) It should be noted that there are researches such asthose by Pramanick [30] or Tamanna [31] that contemplatemultiple schemes but focus on the nodes routing withoutthe respective mathematical analysis Therefore two priorityschemes are proposed to enhance the system performance Inaddition to this the mathematical model allows parametersto be adjusted in order to configure the network and havean approximate performance to what is specifically required


This is not considered in many commercial products such asMobita [32] As such if the user requires a 2-hour study it ispossible to estimate the performance of the system in termsof energy consumption and the final resolution of the study(since it is associated with the packet loss probability)

3 System Design

In this section we present the main assumptions madethroughout the paper and explain the overall operation of thesystem

A WSN is composed by a set of autonomous devicesthat allow sensing processing and communication betweenother nodes of the network [33] On the other hand abiopotential study refers to the representation of ionic fluxthrough the cell membrane that can be measured invasivelyor noninvasively (invasive indicates that it is placed insidethe body while noninvasive means it is placed superficiallyon the person) [34] The studies considered for the networkdesign are presented in Table 1 however other studies can beincluded in future applications

The proposed BANET consists of a set of noninvasivesensors organized as a low-range transmission WSN thatobtain a bioelectric measurement of signals assuming thatthey are placed on a standalone person (We assume thatthe probability of finding multiple patients with the samemonitoring system in such ambulatory network is relativelylow) The intercommunication distance between the nodesis less than or equal to forty inches so sensors operateon body area networks [35] with e-health applications Thesystem functionality considers the actual medical applica-tions described below but different studies may use differentparameters to measure the specific aura or symptoms foreach individual patient and medical team It is important toindicate that heart rate variability (HRV) is a study associatedwith electrocardiogram (ECG) but this is not limited to theHRV That is why the frequency of 250 Hz is considered forthe ECG In this work we consider a Time Division MultipleAccess (TDMA) protocol where each sensor node from thePS transmits in a previously assigned time slot and nodesbelonging to the secondary network transmit in case of anevent detection in an empty slot (time slot not being used bya PU)

In Figure 1 we can observe that the primary nodesare continuously transmitting their information and eachsensor (with its electrode) has a predesignated slot avoidingcollisions As nodes become activeinactive certain slots areleft unused allowing secondary nodes to send event-relatedinformation

In order to maintain control of the electrodes that aresending informationwe add redundancy sending control bitsbetween the sensors and the sink The packet headers areincluded at the beginning of each of the frames composed by119889 bits Initial bits are equal to the number of primary systemsensors and indicate whether a sensor transmits (1) or doesnot transmit (0) The remaining bits are equal to the numberof SS or secondary system nodes and they indicate whetherthey transmit or not This can be visualized in Figure 2

To exemplify this process let us suppose that we have10 sensors in PS and 4 in SS In addition to the frame thatcontains the information of the signals 14 bits are included10 of them to indicate which electrodes of the PS are activeand 4 indicate how many and which electrodes of the SSwill transmit in the frame It is important to indicate thatwhen all the nodes of the secondary network have the sametransmission probability and there are limited slots the eventnodes that gain access to the channel are the first ones thatdetected the event As such a FIFO (First In First Out) eventqueue is assumed

In order to obtain the frame and slot duration for thebiosignals indicated inTable 1 the following sampling processhas to be considered The biopotential study which requiresthe highest sample rate is electrocardiogram Specifically thesampling frequency of ECG can be calculated as 1(2)(250) =2 ms Hence the frame duration is set at 119879119891119903119886119898119890 = 2 msie the time between each data point for the ECG and therest of the biopotential signals is also set at 2 ms Note thatby assuring a high sampling rate the rest of the signals areoversampled which allows the correct reconstruction of allsignals in the sink node according to the Nyquist theorem[36]

This oversampling (which is required in order to havemultiple biopotential signals in the same frame) also entailshaving much more information than needed For instanceconsider the case of the EEG (electroencephalogram) signalswhich require a sampling frequency of 1(2)(150) = 33 mswhich generates 300 samples per second ie 300 data packetsper second for the EEG study However since the data frameis set at 2 ms the number of data packets for all biosignals isaround 500 per second As such there are 200 additional datapackets per second for the EEG study

We take advantage of this fact in order to design theBANET protocol as follows We consider the nodes mon-itoring the EEG signals as the primary users ie nodesreporting the biopotential signals from the electric activity ofthe brain as the primary system transmitting in a continuousmonitoring fashion Due to the oversampling of this signalwe propose to turn ON and OFF such nodes in order togenerate empty spaces that can be used by the rest of thenodes which transmit in an event-driven basis As suchnodes in the secondary network (nodes monitoring the ECGHRV EGG EOG and ERG signals) only transmit data in caseof an abnormal activity is detected from these signals andsuch transmissions occur by searching empty spaces left bynodes in the OFF mode of primary nodes (EEG nodes)

Conversely primary nodes in the ON state transmit adata packet each frame In this work we model this ONOFFprocess by considering that nodes have probability 119875119874119873 tobecome active in a given frame Hence nodes go to the OFFmode with probability 1 minus 119875119874119873 As such nodes can becomeactive (inactive) at each frame independently of the statein the previous frame Based on the mathematical analysispresented below we are able to establish the adequate valueof 119875119874119873 to attain an adequate performance of the proposednetwork From this the slot duration can be computed by119879119904119897119900119905 = 2119873119888 + 119905119889 119898119904 as depicted in [40] where 119873119888 isthe number of nodes that report continuous monitoring


Table 1 Considered studies to measure biopotential signals in the WSN [37ndash39]

Study Description Voltage FrequencyECGEKG Electrocardiogram Electrical signals of heart depiction 05 - 4 mV 001 - 250 HzHRV Heart rate variability 05 - 4 mV 50 HzEEG Electroencephalogram Representation of brain electrical signals 5 - 300 120583V 150 HzEGG Electrogastrogram Depiction of stomach electrical signals 10 120583V - 1 mV 1 HzERG Electroretinography Representation of retina electrical signals 0 - 900 120583V 50 HzEOG Electrooculogram Representation of ocular electrical signals 0 - 3500 120583V 100 Hz

information and 119905119889 is the time derived from the 119889 controlbits discussed above It is important to note that by usingsuch ONOFF scheme and enabling the CR technique weeffectively reduce the frame from119873119888+119873119890 time slots to119872 timeslots where119873119890 is the number of nodes reporting in the event-driven regime and 119872 lt 119873119888 + 119873119890 which reduces the data raterequired from nodes allowing lowering the implementationcost of the system and making a more efficient use of theradioelectric frequencies

Building on this specific values are proposed to exemplifythe system design development There are pathologies dis-eases and preventive analyses that requiremultiple biosignalsoperating at the same time An example is polysomnographya particular sleep study to diagnose disorders such as sleepapnea syndromes of periodic legmovements andnarcolepsyamong others that needs the diagnosis of the signals [41]One way to monitor polysomnography is a 20-channel EEGand 4-channel EOG study [42] Since the EEG requiresconstant monitoring it is selected as the primary systemnetwork On the other hand the retina movement occurs inparticular dream phases (for example rapid eye movementor REM) [43] therefore it is necessary to monitor EOG onlyunder certain circumstances assigning it as the SS

It must be taken into account that the polysomnographyis a possible application case but the user can set the networkaccording to the specific need as long as the sensor samplingrate is not higher than the studies presented in Table 1 Asmentioned before we consider the case where the PS isdedicated to the data gathering of an electroencephalogramcomposed of 20 electrodes (primary nodes) The secondarynetwork is assumed to be a 4-channel EOG From this weset 119872 = 119873119888 = 20 nodes 119873119890 = 4 event detection monitoringelectrodes (secondary network nodes) and 119889 = 24 controlbits

Energy consumption in the nodes forming the BANET isas follows

(i) In the ON mode The PS electrodes in the ON stateconsume 119864119905119909 energy units per packet transmission

(ii) In the OFF mode The PS can be switched OFF andconsequently do not transmit their respective EEGinformation and consume119864119904 energy units where119864119904 =01119864119905119909 This relationship can be adjusted according tospecific commercial node used in the study

The use of energy units allows a general mathematicalmodel that can be used for any commercial or noncommer-cial nodes Indeed each electronic device that can be selected

to be used as a node has its own specific parameters of energyconsumption that depend on the electronic characteristics ofthe node As such these values can be directly substituted onthe analytical expressions derived later in this work to obtainperformance metrics for such particular nodes

Additionally in the system model we consider the casewhere sensor nodes do not detect the ongoing event Thisoccurs with a nonnegligible probability in BANETs due tothe movement of the patient and the displacement of nodesin direct contact with the skin As such we consider thatan event-driven node successfully detects an event withprobability 120598 (Nodes do not detect an event with probability1 minus 120598)

Finally it is important to mention that data packets canbe dropped or lost for different reasons

(i) Not enough empty channels are availableThis occurswhen the number of nodes that detect an event ishigher than the number of empty channels (unusedchannels from the primary users) In the case ofpolysomnography suppose that the 4 EOG channelsneed to transmit but there are only three unusedchannels in the PS Based on this we would have onelost packet

(ii) False Negative This occurs when an event occurs inthe system but nodes fail to detect it

(iii) Nontransmission This occurs due to the use of thepriority schemes as some nodes have priority overother nodes to convey their information some event-driven nodes that correctly detect an event and findenough empty channels to transmit may choose not totransmit in order to prioritize some data over other asexplained in detail in the following section

4 Priority Schemes

In this section we explain in detail the proposed priorityschemes to improve the system performance In the firstscheme (energy-centered scheme) nodes with low energymake fewer transmissions than high energy nodes effectivelyextending the system lifetime In the second scheme (data-centered scheme) nodes with important event packets havepriority over nodes with data from less important events

41 Energy-Centered Priority Scheme The main objective ofthis scheme is to extend the system lifetime This is doneby reducing the number of transmissions Hence in this


Slot

PS Sensor

SS Sensor

Slot

PS Sensor

SS Sensor

PS Sensor no transmitting

Slot

PS Sensor

SS Sensor


PS Frame (０ = 1)

PS Frame (０ = 1)

PS Frame (０ = 1)

Figure 1 TDMA frame construction for the communication system with ONOFF process

scheme data resolution is reduced which also reduces energyconsumption As we show in the Numerical Results datatransmissions cannot be reduced arbitrarily since this wouldlead to poor system performance Instead we propose a fine-tuning of the system by selecting the appropriate valuesBuilding on this it is clear that this scheme is not intended

for applications where themain objective is to gather asmuchinformation as possible Rather it is aimed at situationswherethe patient may be far from the hospital or medical staff forlong periods of time and only general information regardinghis particular health is required for instance for elderlypeople or patients with chronic disease or to evaluate a brain


hellip hellip

Disposition fornode transmission PS

Disposition fornode transmission

SS

Data segment (information for each node)

Frame (d redundant bits + M slots)

d bits

０３1 ０３2 ０３－３３1 ３３2 ３３Ｃ

Figure 2 TDMA frame with control bits

behavior between different impulses throughout a day oreven for sportsmen or women interested in monitoring theirhealth status Returning to the case of polysomnography thisscheme can be useful when the medical staff requires themonitoring of a patient while he is at home and needs toanalyze long sleep periods

Considering this we propose the following transmissionprobability for all nodes in the network Specifically eventreporting nodes with information to be relayed ie nodesthat detected an event in the previous frame (with probability120598) transmit with probability 120588 described as

120588119894 = 120574119890minus1198640119864119877 (1)

where

120588119894 is the transmission probability for node 119894120574 is the control parameter1198640 is the initial battery energy119864119877 is the residual battery energy

It can be seen that by using this transmission probabilitynodes with higher residual energy transmit with higherprobability while nodes with low residual energy levelstransmit sporadically

42 Data-Centered Priority Scheme Contrary to the previousscheme where system lifetime is extended by reducing thenumber of transmissions of low energy nodes in this priorityscheme we intend to expedite highly important packets overless important packets regardless of energy consumptionThis is due to the fact that in e-health applications thereare situations where the information of one sensor is moreimportant than others For instance in an EGG study somepatients who have diabetes present arrhythmias in specificstomach areasTherefore a schemewhere gastric informationis delivered more efficiently than other event data is of majorinterest in certain patients In the case of sleep problemsthis priority scheme would work best when the user is at thehospital and themedical teamneeds to analyzemainly a brainhemisphere that is more active than another through eyemovements In this way the sensors of one eye have greaterimportance than the other nodes To differentiate low prioritynodes from high priority nodes we preassign the prioritylevel at the system setup

From this transmission probabilities are set as follows

(i) High priority nodes transmit with probability 120588119867(ii) Low priority nodes transmit with probability 120588119871In Table 2 we present the main system design parameters

and probabilities in order to simplify the further sections

5 Mathematical Analysis

In this section we develop theMarkov Chain that models themain system dynamics Specifically this analysis considersON andOFF transitions of the continuousmonitoring nodesevent detection probabilities event packet transmissionsaccording to two priority schemes and ON and OFF tran-sitions of event reporting nodes

We propose a Discrete Time Markov Chain where tran-sitions occur at the beginning of each frame as shown inFigure 3

The system state is defined as Ω 119899119860119872119862 119890(1198781)1 119890(1198782)2 119890(119878119899)119899 0 le 119899119860119872119862 le 119872 0 le 119890(119878119894)119894 le 1198640 1 le 119894 le 119873119890V where 119899119860119872119862is the number of active nodes in the continuous monitoringregime ie continuous monitoring nodes in the ON state119872 is the total number of continuous monitoring nodes 119890(119878119894)119894is the residual energy of the 119894119905ℎ event reporting node 119873119890V isthe total number of event reporting nodes and 119878119894 representsthe state of the event reporting node and it is given by thefollowing

119878119894 = 0 if event node 119894 does not detects an event

1 if event node 119894 detects an event(2)

As stated before event reporting nodes detect an eventat each time frame with probability 120598 and such nodes withdata to convey to the sink node have to search for emptychannels in the primary system Once an empty channel isdetected event node 119894 transmits with probability 120588119894 At eachframe nodes consume a certain amount of energy due to thetransmission reception or sleep activities

Hence when nodes deplete all their energy the networkis considered to be useless For this reason system lifetimecorresponds to the time from the initial operation of theBANET (when all nodes have their batteries at the maximumenergy level 1198640) until all nodes have depleted their energyAs such the final state of the system corresponds to state(119899119860119872119862 0 0 0) Hence the proposed Discrete Time Markov


Table 2 System design parameters and probabilities

Parameter Description119875119874119873 Probability that a PS node is active in the current frame120598 Probability that an SS node successfully detects an event120588 Node transmission probability120588119867 High priority node transmission probability120588119871 Low priority node transmission probability119872 Total slots for each frame119873119890 Number of nodes reporting in SS119873119888 Number of nodes reporting in PS120574 Control parameter1198640 Initial battery energy119864119877 Residual battery energy119864119905119909 Energy units consumed by transmitting nodes119864119903119909 Energy units consumed by non-transmitting nodes119864119904 Energy units in sleep mode node

N(A)MC e

S11 e

S22 e

S33 eSn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

Figure 3 Transitory Markov Chain for the complete system dynamics


Chain (DTMC) is a Transitory Markov Chain and state(119899119860119872119862 0 0 0) is an absorbing state Figure 3 depicts statetransitions from the aforementioned DTMC when there areenough resources for event reporting nodes to convey all theirinformation ie sum119899119894=1 119878119894 le 119872 minus 119862 As such no event packetsare lost due to lack of resources in the primary channel

At each time frame the system evolves in the followingframe to states where nodes consume energy according tothe specific operation of each node Specifically continuousmonitoring nodes can

(i) switch from the ON state to the OFF state(ii) switch from the OFF state to the ON state

And event reporting nodes can

(i) transmit in this case 119864119905119909 energy units are consumedby such nodes

(ii) not transmit in which case 119864119904 energy units areconsumed by such nodes

(iii) go from the ON (OFF) state to the OFF (ON) statethis is represented by 119878119894 since 119878119894 is a binary variableAs such if 119878119894 = 0 (119878119894 = 1) then 119878119894 = 1 (119878119894 = 0)

(iv) remain in sleepmode

From this the number of active continuous monitoringnodes is 119862 which represents the final number of activenodes after some of them have become active while someothers have become inactive Similarly some event reportingnodes become activeinactive in the following frame withthe residual energy at the beginning of the frame minus thecorresponding energy units used in such frame Since thestate depicted in Figure 3 corresponds to a general statewe represent such energy consumption as Δ 119894 Note thatin case that the event reporting node is in the OFF state(inactive) then the energy consumption is 119864119904 Hence energyconsumption of node 119894 is given as follows

Δ 119894

=

119864119905119909 if 119878119894 = 1 transmits with 120588119894119864119904 if 119878119894 = 1 and do not transmit with 1 minus 120588119894119864119904 if 119878119894 = 0

(3)

Now we consider energy consumption in terms of energyunits where 119864119905119909 gt 119864119904 Indeed in most commercial devicespacket transmissions consume more energy than nodes insleep mode which are considered to be in low energy con-sumption mode but still consume small amounts of energy

For generality sake we consider arbitrary values of suchenergy units in the mathematical model in order to allow theuse of the specific values of any commercial device As suchpractical implementation is straightforward by substitutingthese values in themodel However in theNumerical Resultswe use practical values from our specific nodes developed inour laboratory

In Figure 4 we show transition probabilities from thegeneral state (119899119860119872119862 119890(1198781)1 119890(1198782)2 119890(119878119899)119899 ) to any other valid

state In order to simplify the numerical solution of theDTMC we derive all transition probabilities to have a generalform described by

119875119899119860119872119862119890(1198781)

1 119890(1198782)

2 119890(119878119899)119899

= (119873119872119862119862 ) 119875119862119874119873 (1 minus 119875119874119873)119873119872119862minus119862

sdot [ 119899prod119894=1

119878119894119875119894 + 1198680] [ 119899prod119894=1

119896119894](4)

where 119875119874119873 is the probability that a continuous monitoringnode is active in the current frame (Evidently a continuousmonitoring node is inactive with probability (1 minus 119875119874119873))119878119894 is defined in (3) 119875119894 is the probability of transmittingor receiving independently of the state of the node Sincetransmissionreception probabilities are multiplied by thestate of the node (119878119894) in case that 119878119894 = 0 the value of 119875119894 isirrelevant In order to maintain the general form presented in(4) we defined it as follows

119875119894 = 120588119894 if node 119894 transmits

1 minus 120588119894 if node 119894 does not transmit(5)

Since all nodes can be inactive in a given time frame ie119878119894 = 0 for all values of 119894 we have to add an indicator function1198680 to avoid having zero transition probabilities when in factsuch probabilities are nonzero

From this 1198680 is defined as follows

1198680 =

0 if119899prod119894=1

119878119894119875119894 gt 01 if

119899prod119894=1

119878119894119875119894 = 0 (6)

Finally 119896119894 is the probability that an event reporting nodesdetects or not an ongoing event Specifically for node 119894 (1 le119894 le 119899)

119896119894 = 120598 if node 119894 detects and 119878119894 = 11 minus 120598 if node 119894 does not detect or 119878119894 = 0 (7)

Using the general expression for the transition probabil-ities depicted in Figure 3 it is straightforward to find thenumerical value of such probability from any state to anyother valid state as shown in Figure 4

It is important to note that not all event-related packetsare successfully conveyed to the sink node Indeed theprevious system description considered that sum119899119894=1 119878119894 le 119872 minus119862 where 119872 is the total number of time slots and 119862 is thenumber of channels being used by primary users (continuousmonitoring nodes) Now consider the case when sum119899119894=1 119878119894 gt119872 minus 119862 In this case the number of event-related packets ishigher than the number of empty spaces in the time frameHence not all event packets can be transmitted This case isshown in Figure 5

In this case the number of event-related packets that canbe successfully transmitted is 119872 minus 119862 and sum119899119894=1 119878119894 minus (119872 minus


C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

N(A)MC e

S11 e

S22 e

S33 eSn

[(NMC

C) PON(1 minus PON)NminusC [(prodn

i=1 SiPi) + I0] [prodni=1 ki]

[(NMC



[(NMC



[(NMC



[(NMC


i=1 SiPi) + I0] [prodni=1 ki] Si =

01

Node is OFFNode is ON

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

k1 =

k2 =

ki =

1 minus

1 minus

1 minus

S = 1S = 0

k3 = 1 minus

S = 1S = 0

S = 1S = 0

S = 1S = 0

i = 234 n

ki = 1 minus S = 1

S = 0 i = 134 n

ki = 1 minus S = 1

S = 0 i = 124 n

Figure 4 Description of Markov Chain in the initial state

sum4i=1 S

i gt M minus C

N(A)MC e

S11 e

S22 e

S33 e

S44

Available slots = (sum4i=1 Si ) minus (M minus C)

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

S44 minus Δ 4

ki = 1 minus

Si = 0

Si = 1 and Remaining available slots i = 1234

(NMC

C) PON(1minus PON)NminusC[(prod4

i=1 SiPi) + I0][prod4i=1 ki[ ]

Figure 5 Markov Chain analysis for case sum119899119894=1 1198781015840119894 gt 119872 minus 119862


119862) event-related packets cannot be transmitted Building onthis nodes that cannot transmit consume 119864119904 energy unitsinstead of 119864119905119909 or 119864119903119909 For clarity sake consider the followingexample Suppose that the number of event-related packetsthat cannot transmit is one and there are four event reportingnodesThen there are four possible events leading to the statetransition depicted in Figure 5 Specifically event nodes 1 2and 3 transmit and node 4 cannot transmit or event nodes1 2 and 4 transmit and node 3 cannot transmit or eventnodes 1 3 and 4 transmit and node 2 cannot transmit orevent nodes 2 3 and 4 transmit and node 1 cannot transmitThese possible transitions occur with the same probability119878119894 = 1 119896119894 = 120598 and 119875119894 = 120588119894 for 119894 = 1 2 3 4 As such evenif one node cannot transmit it still had a packet ready tosend but no available channel was found However energyconsumption for this node is different from the nodes thatactually transmitted

The aforementioned chain is numerically solved in orderto find the average number of time frames from initial state(119873119872119862 11986400 1198640011986400) to absorbing state (119899119860119872119862 0 00) denotedas V1198731198721198621198640 11986401198640 where V

11986211989011987811 11989011987822 119890119878119899119899

denotes the expectedabsorption time starting at state (119862 11989011987811 11989011987822 119890119878119899119899 ) of the chainThese conditional expectations are computed by solving thelinear system

V11986211989011987811 11989011987822 119890119878119899119899

= 1 + sumforall119862

sumforall11989011987811

sumforall11989011987822

sdot sdot sdot sumforall119890119878119899119899

11987511986211989011987811 11989011987822 119890119878119899119899V11986211989011987811 11989011987822 119890119878119899119899

(8)

where the transition probabilities11987511986211989011987811 11989011987822 119890119878119899119899are given by (4)

Now the average packet loss 119871 is calculated Based onthe lack of available resources in the primary network theaverage number of packets lost in state (119862 11989011987811 11989011987822 119890119878119899119899 ) isgiven by

11987111986211989011987811 11989011987822 119890119878119899119899

=

0 if119899sum119894=1

119878119894 le (119872 minus 119862)119899sum119894=1

119878119894 minus (119872 minus 119862) if119899sum119894=1

119878119894 gt (119872 minus 119862)(9)

which can be expressed as

11987111986211989011987811 11989011987822 119890119878119899119899

= max0 119899sum119894=1

119878119894 minus (119872 minus 119862) (10)

and the average number of packets lost in the system isderived as follows

119871= sumforall119862

sumforall11989011987811

sumforall11989011987822


(119871 (119862 11989011987811 11989011987822 119890119878119899119899 )) V11986211989011987811 11989011987822 119890119878119899119899

(11)

Finally average energy consumption is now derived Ineach frame when the system is in state (119862 11989011987811 11989011987822 119890119878119899119899 ) thenumber of packets successfully transmitted is as follows

11987911987511986211989011987811 11989011987822 119890119878119899119899

=

119862 + 119899sum119894=1

119878119894120588119894 if119899sum119894=1

119878119894120588119894 le (119872 minus 119862)119872 if

119899sum119894=1

119878119894120588119894 gt (119872 minus 119862) (12)

Note that if there are enough available resources the numberof nodes that transmit is the number of continuous moni-toring nodes in the ON state 119862 and the number of eventreporting nodes that detected the event that is those beingactive and those transmittingwith probability 120588 On the otherhand if there are no available resources to transmit all theevent reporting nodes then all time slots are being used andthe number of transmitted packets is 119872 This can also beexpressed as follows

11987911987511986211989011987811 11989011987822 119890119878119899119899

= max119872 119862 + 119899sum119894=1

119878119894120588119894 (13)

Then the average number of transmitted packets fromstate (119862 11989011987811 11989011987822 119890119878119899119899 ) to the absorbing state V11987311987211986211986401198640 1198640 canbe calculated as

119879119875= sumforall119862

sumforall11989011987811


(119879119875 (119862 11989011987811 11989011987822 119890119878119899119899 )) V11986211989011987811 11989011987822 119890119878119899119899

(14)

and the for each transmitted packet 119864119905119909 energy units areconsumed active nodes that do not transmit consume 119864119903119909energy units and inactive nodes consume 119864119904 energy unitsHence average energy consumption can be expressed asfollows

119864119862 = sumforall119862

sumforall11989011987811


[(119879119875 (119862 11989011987811 11989011987822 119890119878119899119899 ) 119864119905119909)

+ ( 119899sum119894=1

119878119894 (1 minus 120588119894) 119864119903119909)

+ ((119872 minus 119862) + 119899sum119894=1

(1 minus 119878119894) 119864119904)] lowast V11986211989011987811 11989011987822 119890119878119899119899

(15)

6 Numerical Results

In this section we present some relevant numerical results forthe proposedWSN First we compare the performance evalu-ation obtained through the numerical solution of theMarkovChain described in the previous section to numerical resultsobtained through a homemade network simulator developedin C language For this software linear programming wasconsidered in a MacBook Pro (Processor Intel Core i5 24GHZ 8GB RAM Intel graphics Iris 1536MB 256 Hard DriveStorage) The general algorithm is described below


(i) Whole system initialization starts from the statewhere all the nodes are off and nothing is beingtransmitted

(ii) The simulation of the occurrence of an event is carriedout so that it can be transmitted through PS (primarysystem)

(iii) The frame sending is prepared indicating based on atime ON whether each of the nodes will transmit ornot in the PS

(iv) Randomly a study is recreated with a transmissionprobability 120598 for the SS (secondary system)The orderof transmitting-sensors is selected randomly (if it isthe energy-focused scheme) or a node is prioritized(if it is the data-oriented scheme)

(v) The transmission process is simulated the control ofhow many nodes of the PS and SS transmitted howmany packets were lost and how much energy wasconsumed in the frame is generated

(vi) This process is repeated for each frame calculating thepackets loss energy consumed and energy consumedending until the initial system energy reaches zero

This is described in the diagram presented in Figure 6This comparison allows us to verify the validity of the

mathematical model and identify the system conditionswhere the assumptions of the model are accurate For theresults presented in this section we consider a system withfour event reporting nodes and 20 continuous monitoringnodes as required for the polysomnography study

First we focus on the data-efficient priority scheme Weshow the accuracy of themathematicalmodel for the differentperformance metrics of the system comparing the discreteevent simulation results to the Markov Chain numericalresults as shown in Figures 7ndash10

For these results we set the system with one high priorityevent reporting node and three low priority event reportingnodes These figures show a good match between the mathe-matical model and simulation results mainly for the centralpart of the figures The main reason for the discrepanciesbetween these results (analytical and simulation) is that thetime unit of the Markov model is the time frame As suchwe consider that ONOFF transitions and event occurrencesonly happen at the beginning of the time frame

However in the simulation we consider that these eventscan occur at any time during the simulation and not only atthe beginning of the time frame As such in themathematicalmodel events in the middle of the frame are not consideredHowever we can see that the mathematical model caneffectively describe the performance of the system withrelatively small errors compared to the simulations Alsoconsider that a more accurate mathematical model wouldrequire considering a time slot basis system which couldfurther complicate the analysis

In Figures 7 and 8 we present the average energyconsumption for active primary nodes and inactive primarynodes respectively

As continuous monitoring nodes remain longer timesin the active mode (119875119874119873 997888rarr 1) active nodes consume

more energy since they transmitreceive more data packetsbut inactive nodes consume less energy In these figureswe can clearly see the prime tradeoff between system life-time and data fathering accuracy Specifically if the systemadministrator (treating medical team) requires strict medicalfollowing of the continuous monitoring nodes a high valueof 119875119874119873 should be used However this entails high energyconsumption which reduces the system lifetime Even if thisobservationmay soundobvious themerit of thiswork residesin the fact that we provide hard numerical values for bothtradeoff parameters

As such using the mathematical model it is possible tocalculate both energy consumption and reporting efficiencyin such a way as to carefully select the system parametersto achieve adequate performance for each individual patientNote that data gathering is directly related to the value of119875119874119873 If the system requires that continuousmonitoring nodesreport 70 of their data then119875119874119873 has to be set at 07 Anotherimportant observation is that the value of the probabilityto detect an event 120598 has no major impact on the resultspresented in Figures 7 and 8 simply because in these figuresthe energy consumption of the primary nodes is depictedwhich is not impacted by the event reporting activities exceptfor high values of 120598

Indeed for 120598 997888rarr 1 secondary nodes have moreprobability of occupying the systemrsquos resources As such if aprimary node becomes active in the middle of the frame itcannot use such channels and no packet transmission occursThis explains the energy reduction of primary nodes (thatcould not transmit) for high values of 120598

Figure 9 shows the average energy consumption ofsecondary nodes Here the value of 120598 has a major impact onthe system performance since higher values of this variableimply a higher number of event data transmissions

Note that this value cannot be modified or selected bythe network administrator since it is proper for the systemenvironment As such 120598 reflects the dynamics of the patientin the sense that it models how many events occurr for thisparticular patient and how efficient the nodes are at detectingsuch events Building on this we argue that the medicalteam may not have strict knowledge of the value of 120598 at thebeginning of the system operation However as a few daysof operation go by the medical team can have more accuratevalues for this parameter which in turn allows a better energyconsumption calculation

Also from this figure we can see that as 119875119874119873 increasesprimary nodes make more intensive use of the systemresources which leaves a very low number of empty spacesfor the secondary nodes to use which in turn reduces theenergy consumption of secondary nodes This observation isfurther validated by the high packet loss probability as shownin Figure 10

Furthermore these results bring up another importanttradeoff High continuous monitoring data gathering entailslow event monitoring data reports and vice versa Thenfor specific requirements of event-related-data the valueof 119875119874119873 has to be finely tuned to achieve a good systemperformance


Start

System configurationlowastE0 = Initial energy (taken from battery)lowast = SS detects successfully an eventlowastPon = Probability that PS node is activelowasti = i-th PS nodelowastj = j-th SS nodelowast= Random value for simulating onoff state orsimulating transmission Change in each block

Initial energy consumption for PS and SS iszero PS nodes are set OFF

E0gt0 Yesi = 0 lt ０ＩＨ

YesYes

No

i lt M

Node[i] is on

i++Node[i] is off

No

No

Yes slotavailable lt

Yes

No

lt ϱ

Yes

No

Node [j] transmits

End

j ++ Yes j lt Ne

Yes

No i ++

j = 0

Transmission probabilitycomputation based on thescheme (value of each ϱ)

Figure 6 Flow chart of the system simulation

15

10

5

0

times107

Ener

gy co

nsum

ptio

n (

ＮＲ)

02

04

06

08

0304

0506

07

０ＩＨ

Markov chain

Network simulation

Figure 7 Average energy consumption of the active primary nodes for the data-efficient priority scheme 1 high priority sensor and 3 lowpriority sensors


00204060811080604020

123

5

0

4

Markov chainNetwork simulation

Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107

Figure 8 Average energy consumption of the inactive primary nodes for the data-efficient priority scheme 1 high priority sensor and 3 lowpriority sensors

1

05

0010203040506070809

0

3

1

2


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107

Figure 9 Average energy consumption of the secondary network for the data-efficient priority scheme 1 high priority sensor and 3 lowpriority sensors

Now we focus on the energy-efficient priority schemeFor these results we use 120574 = 1 although in subsequentexperiments we use different values

Figures 11 and 12 show the average energy consumptionof active and inactive continuous monitoring nodes respec-tively As in the data-efficient case as 119875119874119873 increases theenergy consumption of primary nodes increases accordinglyas well as continuous monitoring data gathering Howeverthis leaves almost no empty spaces for the secondary nodesto report event-related packets as depicted in Figure 13 wherealmost no event packet can be successfully transmitted

Contrary to the data-efficient priority scheme in thisenergy-efficient scheme energy consumption does not dis-play an almost linear relation to neither 119875119874119873 nor 120598 Con-versely in this scheme nodes with high residual energy levelsperform more transmissions than low energy nodes averageenergy consumption is depicted in Figure 14

In this figure it is shown that for high values of 120598 wherenodes consume more energy for data transmissions energyconsumption is lower The rationale behind this is as followsIn such high event detection environment nodes consumemuch more energy in less time As such the transmissionprobability 120588119894 highly decreases effectively increasing thesystem lifetime From this it is clear that the proposedpriority schemes have different performance since they aredesigned to operate for different goals

Again it is important to note that the mathematicalmodel derived in this paper allows one to know in advance the

performance of the system in terms of continuousmonitoringpackets event-related packets and energy consumption ofboth primary and secondary nodes mainly finely selectingthe value of 119875119874119873 since the rest of the parameters cannot bedirectly selected

Now that the mathematical model has been validated wecompare both priority strategies using only analytical results

7 Battery and Hardware Specifications

In order to have practical values for the energy consumptionand for the sake of completeness we consider the followinghardware specifications to present results not only in energyunits but in amperehr

(i) Device specification for noncommercial sensornodes We call these nodes noncommercial sincethe sensor processor and transceptor are not builtfor specific wireless sensor network applicationsThese are general purpose modules that wereinterconnected for this specific application Thevalues shown below are associated with devicesused in our laboratory (not involving the networkimplementation but only the characteristics of theavailable devices)(a) Sensor In order to collect the measurements

generated by the electrode composing theBANET an integrated circuit that includes both



０ＩＨ

times106

1080604020108060402

10

0

15

5

0Pack

et lo

ss (P

acke

ts)

Figure 10 Average packet loss probability of event-related packets due to lack of resources for the data-efficient priority scheme 1 highpriority sensor and 3 low priority sensors

1

05

00908070605040302010

2

1


０ＩＨ

times106

Ener

gy co

nsum

ptio

n (

ＮＲ)

Figure 11 Average energy consumption of the active primary nodes for the energy-efficient priority scheme 120574 = 1

00204060811080604020

2

15

0

05

1


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105

Figure 12 Average energy consumption of the inactive primary nodes for the energy-efficient priority scheme 120574 = 1

1080604020108060402

005

015

01

00Pa

cket

loss

pro

babi

lity


０ＩＨ

Figure 13 Average packet loss probability of event-related packets due to lack of resources for the energy-efficient priority scheme 120574 = 1


0

05

1010203040506070809

10

32


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105

Figure 14 Average energy consumption of the secondary network for the energy-efficient priority scheme 120574 = 1

the electrode (transducer device that detectsbiopotential signals) and the digital signal pro-cessing is required For this the Texas ADS1299commercial sensor is used

(b) Processor We use an ATMEL ATMEGA328Pmicroprocessor that will be able to work withsignals retrieved from the ADS1299

(c) Low power transceiver ATmega128RFA1 whichallows the wireless biosignals transmission isused

(d) Batteries 3 Duracell MN2400 size AAA batter-ies are used given that they provide the elec-trical supply necessary to operate the completeWSN

Each ADS1299 consumes 60 119898119860ℎ in average (con-sidering specifications given in the datasheet) andeach one supports 8 electrodes The system occu-pies 3 of these generating 119868119860119863119878 = 180 119898119860ℎ AnATMEGA328P consumes 119868328119875 = 150 119898119860ℎ basedon the maximum circuit consumption Additionallya transceiver is required to send the information ofeachmicrocontroller In this case it is known from the128RFA1 datasheet that the device consumes 10 119898119860contributing 119868128119877119865 = 30 119898119860Therefore the demanded energy of the system is 119868119905 =119868119860119863119878 + 119868328119875 + 119868128119877119865 = 360 119898119860ℎBased on the battery datasheet it supports a currentof 320mAh for a duration of 4 hours with the voltageoccupied by the devices (45 V) Then the currentconsumed by each node is as follows

119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 360119898119860ℎ1800000ℎ = 02 120583119860 (16)

Hence each slot consumes 02 120583119860 and the system hasinitial energy of 1198640 = 128 119860 All the consideredvalues are an estimation since the temperature andother parameters can affect the hardware opera-tion In the case of the polysomnography study 20electroencephalogram nodes and 4 EOG nodes arerequired as mentioned in Table 2These circuits and devices were selected for a widevariety of biomedical studies already available in our

research group As such they may not be the mostsuited energy options However the mathematicalmodel can be adapted to any device

(ii) Device specifications for commercial nodes Wecalled these nodes commercial nodes because these areexplicitly built for WBANET applications and theirperformance is optimized for this usage Hence a sys-tem that occupies the ARM Cortex-M0 + processorbased on SoC is proposed as a second case of nodesthat entail different energy consumption valuesThesedevices are of particular interest since they havebeen tested and showed a very adequate behaviorfor WSN with ECG studies [44] they constitute asuitable option for embedded applications of smalldimensions of high energy efficiency Also sincethe rest of the bioelectric signals considered in ourstudy are oversampled with respect to the ECG thesenodes can operate in an effective way for the completesystem showing its behavior with commercial valuesIn this sense we take the practical values fromthe works of James [45 46] that have measured aconsumption of 2 mA (for each node) per cycle forthe processor with an ECG signal in such a way that119868119905 = 40119898119860 If battery specifications are taken againfrom the noncommercial nodes it supports a currentof 150 mAh for a duration of 24 hours with the 12 V(based on the datasheet curves) used by the system

119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 40119898119860ℎ1800000ℎ = 22 119899119860 (17)

Consequently each slot for this case consumes 22 119899119860and system initial energy is 1198640 = 128 119860 As we cansee the devices energy performance is much lowerthan the noncommercial nodes As such numericalresults show an increased system lifetime Howeverthe important contribution about these results isto show the versatility of the mathematical modelwhere any device can be used to derive the expectedperformance of the system

For the next set of results (considering both cases)we use practical commercial energy consumption in termsof amperes in order to show the flexibility of the derived


mathematical analysis by directly converting energy units toamperes

In Figure 15 we show the average energy consumption forsecondary nodes comparing both priority schemes namelythe energy-efficient and data-efficient schemes for the non-commercial nodes For these results we use the values of120574 = 01 10 as opposed to 1 to see the impact of thisadjustment parameter in the performance of the system Forthe data-efficient scheme we show energy consumption ofboth low and high priority nodes as well as the total energyconsumption for the complete scheme In these figures itcan be seen that low priority nodes always consume lessenergy than high priority nodes in the data-efficient schemesince low priority nodes transmit less information than highpriority nodes Furthermore low priority nodes consumeeven lower energy levels than nodes in the energy-efficientscheme at the expense of the number of reported packetsHowever when observing the total energy consumption inthe secondary network we can see that the residual energyscheme with 120574 = 01 consumes less energy than the data-efficient scheme The energy-efficient scheme with 120574 = 10consumes more energy than the other schemes for almostall system conditions Indeed low values of 120574 restrict thenumber of transmissions as observed in (1) Unlike the data-efficient scheme where all low priority nodes reduce theirtransmissions in the energy-efficient scheme only nodeswith low residual energy reduce the number of transmissionswhile nodes with high residual energy levels transmit almostall their data packets From these results it is clear thatselecting low values of 120574 entails longer system lifetimes at thecost of reducing the event reporting data when nodes beginto deplete their energy

Figure 16 shows the system performance when commer-cial nodes are used First we can observe a much lowerenergy consumption compared to the noncommercial nodesbecause the devices demand much less current and voltageHowever the behavior of both schemes is maintained in thesense that the energy-efficient scheme entails lower energyconsumption compared to the priority scheme

Now we observe the packet loss probability for bothpriority schemes in commercial and noncommercial nodesrespectively as seen in Figures 17 and 18 First note thatpacket loss probability is not affected by the type of nodebeing used since the specific node only affects energy con-sumption but the amount of information conveyed by thenetwork is the same Also it can be seen that in generalpacket loss probability is low (lower than 001) for 119875119874119873 le 06However when primary nodes are mostly active 119875119874119873 gt 06this packet loss probability increases to values lower than01 Hence less than 10 of the packets are lost due to theimplementation of these priority schemes The data-efficientpriority scheme and the energy-efficient scheme with 120574 = 01lose more packets than the rest However in the residualenergy scheme with 120574 = 10 packet loss probability is lowerthan that in the data-efficient scheme It is important to notethat high priority nodes losemore packets since they performmore transmissions than low priority nodes

In Figures 19 and 20 we compare the results of totalenergy consumption (PS and SS) and average packet loss

with the same network setup with and without the priorityschemes From these figures it is clear that the energy-efficient scheme consumes less energy than the priorityscheme and the system where no schemes are used Further-more we can also see that the data scheme also entails alower energy consumption than the system with no schemesAs such even if the main objective is to increase the datatransmission of high priority nodes ie energy consump-tion reduction is not the main priority the data-orientedscheme naturally reduces energy consumption in the systemcompared to the case where no transmission schemes areused The reason for this is that nonpriority data packetstransmit with lower transmission probability also reducingthe number of overall transmissions in the system

In order to havemore insights into the performance of thepriority schemeswe now show the packet loss probability dueto nonreporting events for both cases as shown in Figures 21and 22

It can be seen that the data-efficient scheme has ahigher reporting rate ie there is a lower nonreportingprobability compared to the energy-efficient scheme Sincein this scheme the objective is to report as many packetsas possible from high priority nodes we can see that thispriority scheme achieves its goal However this intensivedata transmission entails a higher energy consumption Thiscan be seen in Figure 23 (for noncommercial nodes) andFigure 24 (for commercial nodes) where the system lifetimeis presented

Conversely the energy-efficient strategy achieves longersystem lifetime since nodes transmit less packets as reflectedby the high packet loss probability due to nonreportedpackets seen in Figure 21 Certainly the fact of using devicesthat demand lower energy consumption also influences thefinal duration such as the maximum difference of hours thatcan be observed in Figures 23 and 24

8 Conclusion

This article developed a mathematical analysis using DiscreteTime Transitory Markov Chains to represent the energeticperformance of a hybrid (continuous monitoring and eventreporting) wireless sensor network oriented toward themonitoring of biopotential signals in ambulatory BANETsThe TDMA-based communication system allows performingmultiple medical studies such as EEG (electroencephalo-gram) ECG (electrocardiogram) EGG (electrogastrogram)ERG (electroretinogram) EOG (electrooculogram) andEMG (electromyography) interchangeably according to thespecific condition of a patient To this end we propose theuse of cognitive radio capabilities by assigning the use ofthe channels to primary nodes while secondary nodes makeopportunistic use of empty spaces Nodes in the primarysystem report their data packets according to a continu-ous monitoring regime while secondary nodes transmit inan event-driven fashion As such primary nodes becomeactive or inactive in order to release their channel reduc-ing both energy consumption and data gathering accuracyand generate opportunities (empty spaces) for secondarynodes


005

008

0706

0504

03

Ener

gy co

nsum

ptio

n(A

mpe

re)

08

06

04

02

Residual scheme = 01


Priority scheme total

Priority scheme (low priority)

Priority scheme (high priority)

０ＩＨ

Figure 15Average energy consumption of the secondary nodes for the energy-efficient anddata-efficient priority schemes for noncommercialnodes 120574 = 01 10 and 1 high priority sensor and 3 low priority sensors

005

10020406081Ener

gy co

nsum

ptio

n(A

mpe

re)

０ＩＨ

Residual scheme = 01Residual scheme = 100Priority scheme totalPriority scheme (low priority)Priority scheme (high priority)

10minus1

10minus2

10minus3

10minus4

Figure 16 Average energy consumption of the secondary nodes for the energy-efficient and data-efficient priority schemes for commercialnodes 120574 = 01 10 and 1 high priority sensor and 3 low priority sensors

1080604020108060402

005

0

01

0Pack

et lo

ss p

roba

bilit

y

０ＩＨ


Figure 17 Schemes comparison for busy channel packet loss for noncommercial nodes

Two priority schemes to improve the performance of thesystem are proposed studied developed andmathematicallyanalyzed In the first scheme nodes with low residual energylevels perform fewer transmissions in order to conserveenergy and increase system lifetime while the second schemeis aimed at increasing data gathering by assigning high

priority nodes with more opportunities to transmit than lowpriority nodes

Although it is evident that an ineluctable tradeoff betweenenergy consumption and data gathering efficiency is presentin most BANETs the proposed priority schemes are aimed atimproving one over the other Furthermore to the best of our


1080604020108060402

001002003004

00Pa

cket

loss

pro

babi

lity

０ＩＨ


Figure 18 Schemes comparison for busy channel packet loss for commercial nodes

1080604020108060402

03

02

01

00

(Am

pere

)En

ergy

cons

umpt

ion

Priority schemeWSN without scheme with = 1Residual scheme = 1

０ＩＨ

Figure 19 Total energy consumption (for noncommercial nodes) of energy-centered scheme data-centered scheme and the same systemwithout schemes 120574 = 1

1080604020108060402

004

002

0

006

0

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ

Figure 20 Total energy consumption (for commercial nodes) of energy-centered scheme data-centered scheme and the same systemwithoutschemes 120574 = 1

knowledge this is the first work that presents clear guidelinesfor the selection of the system parameters to achieve thedesired performance of the system for medical studies thatrequire either an extended network lifetime (at the cost oflosing a certain amount of data) or enhanced data gatheringcapabilities (at the cost of increasing energy consumption)Specifically through the mathematical model the systemadministrator can finely tune the system in terms of 119875119874119873 and

120588119894 to different system conditions given by the event detectionprobability 120598Data Availability

All data used in this work was obtained through the numer-ical solution of the Markov Chains and it can be available onrequest from the corresponding author


002040608102468100

002

006008

004

Pack

et lo

ss p

roba

bilit

yPriority schemeResidual scheme = 05

０ＩＨ

Figure 21 Comparison of nonreported packets for both data-efficient and energy-efficient priority schemes for noncommercial nodes

002040608102468

008

0

002

004

006

10Pack

et lo

ss p

roba

bilit

y

Priority schemeResidual scheme = 05

０ＩＨ

Figure 22 Comparison of nonreported packets for both data-efficient and energy-efficient priority schemes for commercial nodes

time [min]0 50 100 150

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20

Residual energy schemePriority scheme

Figure 23 System lifetime for both data-efficient and energy-efficient priority schemes for noncommercial nodes

time [min]0 200 400 600 800 1000 1200

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20


Figure 24 System lifetime for both data-efficient and energy-efficient priority schemes for commercial nodes


Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was partially supported by Instituto PolitecnicoNacional under SIP project 2018 [1970]References

[1] J Cabra D Castro J Colorado D Mendez and L TrujilloldquoAn IoT approach for wireless sensor networks applied to e-health environmental monitoringrdquo in Proceedings of the 2017IEEE International Conference on Internet of Things (iThings)and IEEE Green Computing and Communications (GreenCom)and IEEE Cyber Physical and Social Computing (CPSCom) andIEEE Smart Data (SmartData) pp 578ndash583 June 2017

[2] Y Jiang O Samuel X Liu et al ldquoEffective biopotential signalacquisition comparison of different shielded drive technolo-giesrdquo Applied Sciences vol 8 no 2 pp 276ndash305 2018

[3] J Aponte J Gımez F Gımez M Sınchez J Espigado andP Teixido ldquoAn efficient wireless sensor network for industrialmonitoring and controlrdquo Sensors vol 18 pp 3ndash15 2018

[4] H Salam and B Khan ldquoUse of wireless system in healthcare fordeveloping countriesrdquo Digital Communications and Networksvol 2 pp 35ndash46 2016

[5] S Pirbhulal H ZhangWWu L Xu and Y Ting Zhang ldquoAnal-ysis of efficient biometric index using heart rate variability forremote monitoring of obstructive sleep apneardquo Neuropsychia-try pp 788ndash795 2017

[6] S Sodagari B Bozorgchami and H Aghvami ldquoTechnologiesand challenges for cognitive radio enabled medical wirelessbody area networksrdquo IEEE Access vol 6 pp 29567ndash29586 2018

[7] J Agarkhed and V Gatate ldquoCognitive radio routing in wirelesssensor networks A comprehensive studyrdquo in Proceedings ofthe 2017 International Conference on Intelligent ComputingInstrumentation and Control Technologies ICICICT 2017 pp1434ndash1439 July 2017

[8] J Maisuria and S Mehta ldquoAn overview of medium accesscontrol protocols for cognitive radio sensor networksrdquo inProceedings of the 4th International Electronic Conference onSensors and Applications vol 2 pp 4963ndash4970

[9] H Alcalı M Rivero E Aguirre F Cruz S Castellanos and GHernandez ldquoPerformance analysis of a wireless sensor networkwith cognitive radio capabilities in structural healthmonitoringapplications A discrete modelrdquo International Journal of Dis-tributed Sensor Networks vol 14 pp 1ndash16 2018

[10] A Ahmad S Ahmad M H Rehmani and N U Hassan ldquoAsurvey on radio resource allocation in cognitive radio sensornetworksrdquo IEEE Communications Surveys amp Tutorials vol 17no 2 pp 888ndash917 2015

[11] S Martınez M E Rivero-Angeles and L Garay ldquoDesign ofhybrid wireless sensor network to monitor bioelectric signalsfocused on the study of epilepsyrdquo Research in ComputingScience Instituto Politıcnico Nacional vol 75 pp 43ndash49 2014

[12] V Jagadeeswari V Subramaniyaswamy R Logesh and VVijayakumar ldquoA study on medical internet of things and bigdata in personalized healthcare systemrdquo Health InformationScience and Systems Elsevier vol 6 no 1 2018

[13] C-T Lin M Prasad C-H Chung et al ldquoIoT-Based WirelessPolysomnography Intelligent System for Sleep MonitoringrdquoIEEE Access vol 6 pp 405ndash414 2017

[14] X Li and Y Sun ldquoDesign and evaluation of a non-contactwireless biopotential monitoring system with motion artifactsrdquoin Proceedings of the 4th IEEE EMBS International Conferenceon Biomedical and Health Informatics BHI 2017 pp 69ndash72Orlando FL USA February 2017

[15] M Nurdin S Hadiyoso and A Rizal ldquoA low-cost Internetof Things (IoT) system for multi-patient ECGs monitoringrdquoin International Conference on Control Electronics RenewableEnergy and Communications (ICCEREC pp 7ndash11 2016

[16] M A Reyna C I Lima R L Avitia and M E BravoldquoWireless transmission of ECG biopotentials using XBee tech-nologyrdquo in Proceedings of the 2016 Global Medical Engineer-ing Physics ExchangesPan American Health Care ExchangesGMEPEPAHCE 2016 pp 1ndash4 Madrid Spain April 2016

[17] X Meng P Lu and B Li ldquoHuman ECG data detection systembased on ZigBeerdquo in Proceedings of the 2017 Chinese AutomationCongress CAC 2017 pp 7265ndash7270 China October 2017

[18] R Trobec I Tomasic A RashkovskaM Depolli and V AvbeljldquoCommercial ECG systemsrdquo in Body Sensors and Electrocar-diography SpringerBriefs in Applied Sciences and TechnologySpringer Cham Switzerland 2018

[19] Z Yang Q Zhou L Lei K Zheng andW Xiang ldquoAn IoT-cloudbased wearable ecg monitoring system for smart healthcarerdquoJournal of Medical Systems vol 40 Article ID 286 2016

[20] S Ramson and D Jackuline ldquoApplications of wireless sensornetworks - A surveyrdquo in Proceedings of the2017 InternationalConference on Innovations in Electrical Electronics Instrumen-tation and Media Technology (ICEEIMT) pp 325ndash329 2017

[21] P Akila and U Maheswari ldquoA survey on recent techniquesfor energy efficient routing in WSNrdquo International Journal ofSensors and Sensor Networks vol 6 pp 8ndash15 2018

[22] P Sivakumara and M Radhikab ldquoPerformance Analysis ofLEACH-GA over LEACH and LEACH-C Kurukshetrardquo inProceedings of the 6th International Conference on Smart Com-puting and Communications ICSCC 2017 vol 125 pp 248ndash256Kurukshetra India 2017

[23] K Luo Z Cai K Du F Zou X Zhang and J Li ldquoA digitalcompressed sensing-based energy-efficient single-spot blue-tooth ecg noderdquo Journal of Healthcare Engineering vol 20182018

[24] N Saleh A Kassem and A M Haidar ldquoEnergy-efficient archi-tecture for wireless sensor networks in healthcare applicationsrdquoIEEE Access vol 6 pp 6478ndash6496 2018

[25] R Chıvez D Jankunas V Fomin and I Balasingham ldquoDual-band cognitive radio for wearable sensors in hospitalsrdquo in 8thInternational Symposium on Medical Information and Commu-nication Technology (ISMICT) pp 1ndash5 2014

[26] M Ishtiak I Muzahidul B Sabariah W Toshio and K ShozoldquoA priority aware cognitive radio based hospital system archi-tecture priority management and communication protocolsrdquoin 8th International Symposium on Medical Information andCommunication Technology (ISMICT pp 1ndash5 2014

[27] K Rahat and A Pathan ldquoThe state-of-arte wireless body areasensor network a surveyrdquo International Journal of DistributedSensor Network vol 14 pp 1ndash23 2018

[28] M AlMusallam and A Soudani ldquoEnergy-aware ECG sensingscheme for M-health applicationsrdquo in Proceedings of the 20165th International Conference on Electronic Devices Systems and


Applications (ICEDSA) pp 1ndash4 Ras Al Khaimah December2016

[29] J-S Leu T-H Chiang M-C Yu and K-W Su ldquoEnergy effi-cient clustering scheme for prolonging the lifetime of wirelesssensor network with isolated nodesrdquo IEEE CommunicationsLetters vol 19 no 2 pp 259ndash262 2015

[30] M Pramanick P Basak C Chowdhury and S Neogy ldquoAnalysisof energy efficient wireless sensor networks routing schemesrdquoin Proceedings of the 4th International Conference on EmergingApplications of Information Technology EAIT 2014 pp 379ndash384India December 2014

[31] T Puri R Challa and N Sehgal ldquoEnergy efficient QoSaware MAC layer time slot allocation scheme for WBASNrdquoin Proceedings of the International Conference on Advances inComputing Communications and Informatics ICACCI 2015 pp966ndash972 India August 2015

[32] Biopac systems Inc ldquoMobita Wearable Biopotentials 32CHEEG ECG EMG EOG EGG Biopac systemsrdquo httpswwwbiopaccomproduct-categoryresearchmobita-wearable-bio-potentials 2018

[33] S Santar andC Sharma ldquoA survey on research issues inwirelesssensor networksrdquoASurveyOnResearch Issues inWireless SensorNetworks vol 2 2015

[34] J Debashis and A Kumar ldquoDesign of low noise amplifier forsensor applicationsrdquo Devices for Integrated Circuit (DevIC) pp451ndash455 2017

[35] A Hassan F Shaikh S Pirbhulal and S Ali ldquoMedical-QoStelemedicine service selection using analytic hierarchy processrdquoin Handbook of Large-Scale Distributed Computing in SmartHealthcare Scalable Computing and Communications pp 589ndash610 Springer 2017

[36] S Benatti B Milosevic M Tomasini et al ldquoMultiple biopoten-tials acquisition system for wearable applicationsrdquo in Proceed-ings of the 8th International Conference onBiomedical Electronicsand Devices BIODEVICES 2015 pp 260ndash268 January 2015

[37] S Martınez M E Rivero-Angeles L Garay I Romero andS Martınez ldquoPriority data transmission schemes for a wire-less sensor network on ban research in computing sciencerdquoResearch in Computing Science Instituto Politıcnico Nacionalvol 138 pp 19ndash27 2017

[38] A Pal A Gautam and Y Singh ldquoEvaluation of bioelectric sig-nals for human recognitionrdquo in Proceedings of the InternationalConference on Computer Communication and ConvergenceICCC 2015 pp 747ndash753 India December 2014

[39] S Mahdiani V Jeyhani M Peltokangas and A VehkaojaldquoIs 50 Hz high enough ECG sampling frequency for accurateHRV analysisrdquo in Proceedings of the 37th Annual InternationalConference of the IEEE Engineering in Medicine and BiologySociety EMBC 2015 pp 5948ndash5951 Italy August 2015

[40] S M Martınez-Chavez M E Rivero-Angeles L I Garay-Jimenez and E F Ruiz-Ledesma ldquoCognitive radio systemfor interference reduction in BANETs focused on epilepsydiagnosisrdquo Computer Networks vol 134 pp 1ndash22 2018

[41] S Myllymaa A Muraja-Murro S Westeren-Punnonen etal ldquoAssessment of the suitability of using a forehead EEGelectrode set and chin EMG electrodes for sleep staging inpolysomnographyrdquo Journal of Sleep Research vol 25 no 6 pp636ndash645 2016

[42] B P Lucey J S Mcleland C D Toedebusch et al ldquoComparisonof a single-channel EEG sleep study to polysomnographyrdquoJournal of Sleep Research vol 25 no 6 pp 625ndash635 2016

[43] W Bukari W Daud and R Sudirman ldquoTime frequencyanalysis of electrooculograph (eog) signal of eye movementpotentials based on wavelet energy distributionrdquo in Proceedingsof the FifthAsiaModelling Symposium pp 81ndash86 Kuala Lumpur2011

[44] L C Keat A B Jambek andUHashim ldquoHeart ratemonitoringusing ARM soft core processor based system-on-chiprdquo Journalof Telecommunication Electronic and Computer Engineeringvol 10 no 1 pp 113ndash118 2018

[45] J Myers P Prabhat A Savanth S Yang and R GaddhldquoDesign challenges for near and sub-threshold operationA casestudy with an ARM Cortex-M0+ based WSN subsystemrdquo inProceedings of the 26th International Workshop on Power andTiming Modeling Optimization and Simulation PATMOS 2016pp 56ndash63 Germany September 2016

[46] J Myers A Savanth R Gaddh D Howard P Prabhat andD Flynn ldquoA subthreshold ARM cortex-M0+ subsystem in 65nm CMOS for WSN applications with 14 Power Domains 10TSRAM and integrated voltage regulatorrdquo IEEE Journal of Solid-State Circuits vol 51 no 1 pp 31ndash44 2016

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

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Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


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Journal of

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Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



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Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

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wwwhindawicom Volume 2018

Advances in

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Submit your manuscripts atwwwhindawicom


and wireless approaches The cabled option approach has nointerference among nodes but patients are not comfortablewith wires around their body for long periods of timeand the nodes disconnection is highly probable For thesecond approach wireless sensor networks (WSN) constitutea functional and practical alternative [3] where each sensoris composed of electrodes battery and a processing moduleto allow the transmission of the information to a sink nodeTherefore the wireless option is advisable in order to allowpatients to have full mobility with the recording equipmentin ambulatory monitoring However WSNs face an inherentconflict with energy consumption since despite technologi-cal advances several authors have reported that the lifetimebattery of nodes in this type of systems is compromised bythe network dimensions (number of nodes) and data ratetransmission Consequently the system lifetime is usuallylower than that in wired networks or when nonambulatorynodes with higher dimensions are used [4 5] even in hospitalenvironments as analyzed by Sodagary in [6] In this contextenergy efficiency is one of the main research topics that havebeen recently studied

Based on the above we propose and develop amathemat-ical analysis that models the main dynamics of the system inorder to calculate energy consumption and packet loss proba-bilitiesNumerical results obtained through themathematicalmodel show that the system lifetime is greatly extended whendata transmission is limited On the other hand when mostdata is required at the sink node the energy consumed toachieve it tends to be higher reducing the operation timeof the network In view of this inherent compromise amongdata transmission and energy consumption we propose twopriority schemes to enhance either system duration or datagathering described as follows

(i) In the energy-efficient approach nodes limit datatransmission in order to extend the system lifetimeFurthermore nodes with lower residual energy per-form fewer transmissions to the sink node whilenodes with their full batteries can make more trans-missions without affecting the operation of the net-work In this scheme less information is transmitted(manydata packets are dropped to reduce energy con-sumption) since the main objective of this scheme isto gather just enough information from the patient tohave insight into his health but not critic illness thatrequires prompt medical attention

(ii) In the data gathering efficient approach we assumedifferent packets types effectively assigning prioritylevels to packet data Building on this the priorityscheme enables the expediting transmission of highpriority data over low priority data reducing packetdropping probability and reducing packet delayHowever in this approach energy consumption ishigher reducing the operation time of the network

These schemes are intended to work under differentconditions in ambulatory systems For instance consider apatient in stable conditions where his medical team hasthe need to monitor him for long periods of time but no

emergency events are expected (eg an elderly person invacations or a business trip for a highly stressed corporateworker) where different biopotential signals are of interestbut there are no ongoing urgent medical procedures In thesecases the system is required to gather as much informationregarding the patient as possible but the main interest is thatthe monitoring network lasts as long as the trip (or intervalbetween medical visits) lasts On the other hand there arepeople with specific affections that require immediate med-ical attention As an example in the case of cardiac diseasepatients medical staff can monitor the electrical activity inthe patientrsquos heart while allowing such patients to have asmuch normal life as possible with no need to spend countlesshours in the hospital However in case of a tachycardiathe patient can be taken to the hospital and the attendingmedic can retrieve all information regarding such episodeIn both schemes it is difficult to establish the adequateparameter values to guarantee the performance required foreach case Therefore the derived mathematical analysis isof great relevance to learning about the performance of theBANET for different systemparameters Based on thismodelthe system can be finely tuned to achieve a specific use

With the aim of reducing energy consumption andinterference into the system we propose the use of CognitiveRatio (CR) capabilities There are several examples of thepotential benefits from this technology in computer networks[7ndash10] In CR two systems are considered the primarysystem (PS) consists of users that have the right and licenseto use the radio-frequency resources and in the secondarysystem (SS) nodes transmit in available channels only if theyare not being used by primary users (PUs) ie users of thePS Secondary users (SUs) have to be constantly monitoringthe availability of the channel to identify empty slots (radio-frequency resources not being used by any PU) in order toavoid any negative impact on the service provided to PUs

As such PUs are not affected by the operation of theSS and their service is not degraded Building on this wemake use of such CR capabilities by allowing continuousmonitoring data to be transmitted as the primary systemwhile event-related reports are transmitted as a secondarysystem making use of empty spaces in the PS

Furthermore we propose an ONOFF scheme for pri-mary nodes in order to generate empty spaces to be usedby secondary nodes In the OFF mode primary nodesdo not report data and energy consumption is reducedallowing event-related data to be transmitted in the systemAccurateness of the data is not affected by nodes in theOFF mode since we use an oversampling procedure to allowmultiple biopotential signals to be transmitted in a single timeframe [11] This issue is explained in detail in Section 2

The main contributions of this work can be described asfollows

(i) A body area network (BANET) for both continuousmonitoring and event reporting with CR capabilitiesis proposed analyzed and studied using MarkovChains in order to provide clear guidelines for thedesign and parameter selection in practical e-healthmonitoring ambulatory systems







2 Related Work










3 System Design



























4 Priority Schemes




Slot

PS Sensor

SS Sensor

Slot

PS Sensor

SS Sensor


Slot

PS Sensor

SS Sensor


PS Frame (０ = 1)

PS Frame (０ = 1)

PS Frame (０ = 1)





hellip hellip



SS



d bits

０３1 ０３2 ０３－３３1 ３３2 ３３Ｃ




120588119894 = 120574119890minus1198640119864119877 (1)

where


















N(A)MC e

S11 e

S22 e

S33 eSn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn












Δ 119894

=


(3)





119875119899119860119872119862119890(1198781)

1 119890(1198782)

2 119890(119878119899)119899

= (119873119872119862119862 ) 119875119862119874119873 (1 minus 119875119874119873)119873119872119862minus119862

sdot [ 119899prod119894=1

119878119894119875119894 + 1198680] [ 119899prod119894=1

119896119894](4)






1198680 =

0 if119899prod119894=1

119878119894119875119894 gt 01 if

119899prod119894=1

119878119894119875119894 = 0 (6)







C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

N(A)MC e

S11 e

S22 e

S33 eSn

[(NMC



[(NMC



[(NMC



[(NMC



[(NMC



01


C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

k1 =

k2 =

ki =

1 minus

1 minus

1 minus

S = 1S = 0

k3 = 1 minus

S = 1S = 0

S = 1S = 0

S = 1S = 0

i = 234 n

ki = 1 minus S = 1

S = 0 i = 134 n

ki = 1 minus S = 1

S = 0 i = 124 n


sum4i=1 S

i gt M minus C

N(A)MC e

S11 e

S22 e

S33 e

S44


C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

S44 minus Δ 4

ki = 1 minus

Si = 0


(NMC







11986211989011987811 11989011987822 119890119878119899119899


V11986211989011987811 11989011987822 119890119878119899119899


sumforall11989011987811

sumforall11989011987822


11987511986211989011987811 11989011987822 119890119878119899119899V11986211989011987811 11989011987822 119890119878119899119899

(8)



11987111986211989011987811 11989011987822 119890119878119899119899

=

0 if119899sum119894=1

119878119894 le (119872 minus 119862)119899sum119894=1


119878119894 gt (119872 minus 119862)(9)


11987111986211989011987811 11989011987822 119890119878119899119899

= max0 119899sum119894=1

119878119894 minus (119872 minus 119862) (10)


119871= sumforall119862

sumforall11989011987811

sumforall11989011987822


(119871 (119862 11989011987811 11989011987822 119890119878119899119899 )) V11986211989011987811 11989011987822 119890119878119899119899

(11)


11987911987511986211989011987811 11989011987822 119890119878119899119899

=

119862 + 119899sum119894=1

119878119894120588119894 if119899sum119894=1

119878119894120588119894 le (119872 minus 119862)119872 if

119899sum119894=1

119878119894120588119894 gt (119872 minus 119862) (12)


11987911987511986211989011987811 11989011987822 119890119878119899119899

= max119872 119862 + 119899sum119894=1

119878119894120588119894 (13)


119879119875= sumforall119862

sumforall11989011987811


(119879119875 (119862 11989011987811 11989011987822 119890119878119899119899 )) V11986211989011987811 11989011987822 119890119878119899119899

(14)


119864119862 = sumforall119862

sumforall11989011987811


[(119879119875 (119862 11989011987811 11989011987822 119890119878119899119899 ) 119864119905119909)

+ ( 119899sum119894=1

119878119894 (1 minus 120588119894) 119864119903119909)

+ ((119872 minus 119862) + 119899sum119894=1

(1 minus 119878119894) 119864119904)] lowast V11986211989011987811 11989011987822 119890119878119899119899

(15)

6 Numerical Results
























Start




YesYes

No

i lt M

Node[i] is on

i++Node[i] is off

No

No


Yes

No

lt ϱ

Yes

No

Node [j] transmits

End

j ++ Yes j lt Ne

Yes

No i ++

j = 0



15

10

5

0

times107

Ener

gy co

nsum

ptio

n (

ＮＲ)

02

04

06

08

0304

0506

07

０ＩＨ

Markov chain

Network simulation



00204060811080604020

123

5

0

4


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107


1

05

0010203040506070809

0

3

1

2


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107















０ＩＨ

times106

1080604020108060402

10

0

15

5

0Pack

et lo

ss (P

acke

ts)


1

05

00908070605040302010

2

1


０ＩＨ

times106

Ener

gy co

nsum

ptio

n (

ＮＲ)


00204060811080604020

2

15

0

05

1


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105


1080604020108060402

005

015

01

00Pa

cket

loss

pro

babi

lity


０ＩＨ



0

05

1010203040506070809

10

32


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105







119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 360119898119860ℎ1800000ℎ = 02 120583119860 (16)




119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 40119898119860ℎ1800000ℎ = 22 119899119860 (17)













8 Conclusion



005

008

0706

0504

03

Ener

gy co

nsum

ptio

n(A

mpe

re)

08

06

04

02






０ＩＨ


005

10020406081Ener

gy co

nsum

ptio

n(A

mpe

re)

０ＩＨ


10minus1

10minus2

10minus3

10minus4


1080604020108060402

005

0

01

0Pack

et lo

ss p

roba

bilit

y

０ＩＨ







1080604020108060402

001002003004

00Pa

cket

loss

pro

babi

lity

０ＩＨ



1080604020108060402

03

02

01

00

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ


1080604020108060402

004

002

0

006

0

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ






002040608102468100

002

006008

004

Pack

et lo

ss p

roba

bilit


０ＩＨ


002040608102468

008

0

002

004

006

10Pack

et lo

ss p

roba

bilit

y


０ＩＨ


time [min]0 50 100 150

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20



time [min]0 200 400 600 800 1000 1200

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20






Acknowledgments




















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








2 Related Work










3 System Design



























4 Priority Schemes




Slot

PS Sensor

SS Sensor

Slot

PS Sensor

SS Sensor


Slot

PS Sensor

SS Sensor


PS Frame (０ = 1)

PS Frame (０ = 1)

PS Frame (０ = 1)





hellip hellip



SS



d bits

０３1 ０３2 ０３－３３1 ３３2 ３３Ｃ




120588119894 = 120574119890minus1198640119864119877 (1)

where


















N(A)MC e

S11 e

S22 e

S33 eSn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn












Δ 119894

=


(3)





119875119899119860119872119862119890(1198781)

1 119890(1198782)

2 119890(119878119899)119899

= (119873119872119862119862 ) 119875119862119874119873 (1 minus 119875119874119873)119873119872119862minus119862

sdot [ 119899prod119894=1

119878119894119875119894 + 1198680] [ 119899prod119894=1

119896119894](4)






1198680 =

0 if119899prod119894=1

119878119894119875119894 gt 01 if

119899prod119894=1

119878119894119875119894 = 0 (6)







C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

N(A)MC e

S11 e

S22 e

S33 eSn

[(NMC



[(NMC



[(NMC



[(NMC



[(NMC



01


C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

k1 =

k2 =

ki =

1 minus

1 minus

1 minus

S = 1S = 0

k3 = 1 minus

S = 1S = 0

S = 1S = 0

S = 1S = 0

i = 234 n

ki = 1 minus S = 1

S = 0 i = 134 n

ki = 1 minus S = 1

S = 0 i = 124 n


sum4i=1 S

i gt M minus C

N(A)MC e

S11 e

S22 e

S33 e

S44


C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

S44 minus Δ 4

ki = 1 minus

Si = 0


(NMC







11986211989011987811 11989011987822 119890119878119899119899


V11986211989011987811 11989011987822 119890119878119899119899


sumforall11989011987811

sumforall11989011987822


11987511986211989011987811 11989011987822 119890119878119899119899V11986211989011987811 11989011987822 119890119878119899119899

(8)



11987111986211989011987811 11989011987822 119890119878119899119899

=

0 if119899sum119894=1

119878119894 le (119872 minus 119862)119899sum119894=1


119878119894 gt (119872 minus 119862)(9)


11987111986211989011987811 11989011987822 119890119878119899119899

= max0 119899sum119894=1

119878119894 minus (119872 minus 119862) (10)


119871= sumforall119862

sumforall11989011987811

sumforall11989011987822


(119871 (119862 11989011987811 11989011987822 119890119878119899119899 )) V11986211989011987811 11989011987822 119890119878119899119899

(11)


11987911987511986211989011987811 11989011987822 119890119878119899119899

=

119862 + 119899sum119894=1

119878119894120588119894 if119899sum119894=1

119878119894120588119894 le (119872 minus 119862)119872 if

119899sum119894=1

119878119894120588119894 gt (119872 minus 119862) (12)


11987911987511986211989011987811 11989011987822 119890119878119899119899

= max119872 119862 + 119899sum119894=1

119878119894120588119894 (13)


119879119875= sumforall119862

sumforall11989011987811


(119879119875 (119862 11989011987811 11989011987822 119890119878119899119899 )) V11986211989011987811 11989011987822 119890119878119899119899

(14)


119864119862 = sumforall119862

sumforall11989011987811


[(119879119875 (119862 11989011987811 11989011987822 119890119878119899119899 ) 119864119905119909)

+ ( 119899sum119894=1

119878119894 (1 minus 120588119894) 119864119903119909)

+ ((119872 minus 119862) + 119899sum119894=1

(1 minus 119878119894) 119864119904)] lowast V11986211989011987811 11989011987822 119890119878119899119899

(15)

6 Numerical Results
























Start




YesYes

No

i lt M

Node[i] is on

i++Node[i] is off

No

No


Yes

No

lt ϱ

Yes

No

Node [j] transmits

End

j ++ Yes j lt Ne

Yes

No i ++

j = 0



15

10

5

0

times107

Ener

gy co

nsum

ptio

n (

ＮＲ)

02

04

06

08

0304

0506

07

０ＩＨ

Markov chain

Network simulation



00204060811080604020

123

5

0

4


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107


1

05

0010203040506070809

0

3

1

2


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107















０ＩＨ

times106

1080604020108060402

10

0

15

5

0Pack

et lo

ss (P

acke

ts)


1

05

00908070605040302010

2

1


０ＩＨ

times106

Ener

gy co

nsum

ptio

n (

ＮＲ)


00204060811080604020

2

15

0

05

1


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105


1080604020108060402

005

015

01

00Pa

cket

loss

pro

babi

lity


０ＩＨ



0

05

1010203040506070809

10

32


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105







119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 360119898119860ℎ1800000ℎ = 02 120583119860 (16)




119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 40119898119860ℎ1800000ℎ = 22 119899119860 (17)













8 Conclusion



005

008

0706

0504

03

Ener

gy co

nsum

ptio

n(A

mpe

re)

08

06

04

02






０ＩＨ


005

10020406081Ener

gy co

nsum

ptio

n(A

mpe

re)

０ＩＨ


10minus1

10minus2

10minus3

10minus4


1080604020108060402

005

0

01

0Pack

et lo

ss p

roba

bilit

y

０ＩＨ







1080604020108060402

001002003004

00Pa

cket

loss

pro

babi

lity

０ＩＨ



1080604020108060402

03

02

01

00

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ


1080604020108060402

004

002

0

006

0

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ






002040608102468100

002

006008

004

Pack

et lo

ss p

roba

bilit


０ＩＨ


002040608102468

008

0

002

004

006

10Pack

et lo

ss p

roba

bilit

y


０ＩＨ


time [min]0 50 100 150

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20



time [min]0 200 400 600 800 1000 1200

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20






Acknowledgments




















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




3 System Design



























4 Priority Schemes




Slot

PS Sensor

SS Sensor

Slot

PS Sensor

SS Sensor


Slot

PS Sensor

SS Sensor


PS Frame (０ = 1)

PS Frame (０ = 1)

PS Frame (０ = 1)





hellip hellip



SS



d bits

０３1 ０３2 ０３－３３1 ３３2 ３３Ｃ




120588119894 = 120574119890minus1198640119864119877 (1)

where


















N(A)MC e

S11 e

S22 e

S33 eSn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn












Δ 119894

=


(3)





119875119899119860119872119862119890(1198781)

1 119890(1198782)

2 119890(119878119899)119899

= (119873119872119862119862 ) 119875119862119874119873 (1 minus 119875119874119873)119873119872119862minus119862

sdot [ 119899prod119894=1

119878119894119875119894 + 1198680] [ 119899prod119894=1

119896119894](4)






1198680 =

0 if119899prod119894=1

119878119894119875119894 gt 01 if

119899prod119894=1

119878119894119875119894 = 0 (6)







C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

N(A)MC e

S11 e

S22 e

S33 eSn

[(NMC



[(NMC



[(NMC



[(NMC



[(NMC



01


C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

k1 =

k2 =

ki =

1 minus

1 minus

1 minus

S = 1S = 0

k3 = 1 minus

S = 1S = 0

S = 1S = 0

S = 1S = 0

i = 234 n

ki = 1 minus S = 1

S = 0 i = 134 n

ki = 1 minus S = 1

S = 0 i = 124 n


sum4i=1 S

i gt M minus C

N(A)MC e

S11 e

S22 e

S33 e

S44


C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

S44 minus Δ 4

ki = 1 minus

Si = 0


(NMC







11986211989011987811 11989011987822 119890119878119899119899


V11986211989011987811 11989011987822 119890119878119899119899


sumforall11989011987811

sumforall11989011987822


11987511986211989011987811 11989011987822 119890119878119899119899V11986211989011987811 11989011987822 119890119878119899119899

(8)



11987111986211989011987811 11989011987822 119890119878119899119899

=

0 if119899sum119894=1

119878119894 le (119872 minus 119862)119899sum119894=1


119878119894 gt (119872 minus 119862)(9)


11987111986211989011987811 11989011987822 119890119878119899119899

= max0 119899sum119894=1

119878119894 minus (119872 minus 119862) (10)


119871= sumforall119862

sumforall11989011987811

sumforall11989011987822


(119871 (119862 11989011987811 11989011987822 119890119878119899119899 )) V11986211989011987811 11989011987822 119890119878119899119899

(11)


11987911987511986211989011987811 11989011987822 119890119878119899119899

=

119862 + 119899sum119894=1

119878119894120588119894 if119899sum119894=1

119878119894120588119894 le (119872 minus 119862)119872 if

119899sum119894=1

119878119894120588119894 gt (119872 minus 119862) (12)


11987911987511986211989011987811 11989011987822 119890119878119899119899

= max119872 119862 + 119899sum119894=1

119878119894120588119894 (13)


119879119875= sumforall119862

sumforall11989011987811


(119879119875 (119862 11989011987811 11989011987822 119890119878119899119899 )) V11986211989011987811 11989011987822 119890119878119899119899

(14)


119864119862 = sumforall119862

sumforall11989011987811


[(119879119875 (119862 11989011987811 11989011987822 119890119878119899119899 ) 119864119905119909)

+ ( 119899sum119894=1

119878119894 (1 minus 120588119894) 119864119903119909)

+ ((119872 minus 119862) + 119899sum119894=1

(1 minus 119878119894) 119864119904)] lowast V11986211989011987811 11989011987822 119890119878119899119899

(15)

6 Numerical Results
























Start




YesYes

No

i lt M

Node[i] is on

i++Node[i] is off

No

No


Yes

No

lt ϱ

Yes

No

Node [j] transmits

End

j ++ Yes j lt Ne

Yes

No i ++

j = 0



15

10

5

0

times107

Ener

gy co

nsum

ptio

n (

ＮＲ)

02

04

06

08

0304

0506

07

０ＩＨ

Markov chain

Network simulation



00204060811080604020

123

5

0

4


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107


1

05

0010203040506070809

0

3

1

2


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107















０ＩＨ

times106

1080604020108060402

10

0

15

5

0Pack

et lo

ss (P

acke

ts)


1

05

00908070605040302010

2

1


０ＩＨ

times106

Ener

gy co

nsum

ptio

n (

ＮＲ)


00204060811080604020

2

15

0

05

1


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105


1080604020108060402

005

015

01

00Pa

cket

loss

pro

babi

lity


０ＩＨ



0

05

1010203040506070809

10

32


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105







119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 360119898119860ℎ1800000ℎ = 02 120583119860 (16)




119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 40119898119860ℎ1800000ℎ = 22 119899119860 (17)













8 Conclusion



005

008

0706

0504

03

Ener

gy co

nsum

ptio

n(A

mpe

re)

08

06

04

02






０ＩＨ


005

10020406081Ener

gy co

nsum

ptio

n(A

mpe

re)

０ＩＨ


10minus1

10minus2

10minus3

10minus4


1080604020108060402

005

0

01

0Pack

et lo

ss p

roba

bilit

y

０ＩＨ







1080604020108060402

001002003004

00Pa

cket

loss

pro

babi

lity

０ＩＨ



1080604020108060402

03

02

01

00

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ


1080604020108060402

004

002

0

006

0

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ






002040608102468100

002

006008

004

Pack

et lo

ss p

roba

bilit


０ＩＨ


002040608102468

008

0

002

004

006

10Pack

et lo

ss p

roba

bilit

y


０ＩＨ


time [min]0 50 100 150

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20



time [min]0 200 400 600 800 1000 1200

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20






Acknowledgments




















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


















4 Priority Schemes




Slot

PS Sensor

SS Sensor

Slot

PS Sensor

SS Sensor


Slot

PS Sensor

SS Sensor


PS Frame (０ = 1)

PS Frame (０ = 1)

PS Frame (０ = 1)





hellip hellip



SS



d bits

０３1 ０３2 ０３－３３1 ３３2 ３３Ｃ




120588119894 = 120574119890minus1198640119864119877 (1)

where


















N(A)MC e

S11 e

S22 e

S33 eSn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn












Δ 119894

=


(3)





119875119899119860119872119862119890(1198781)

1 119890(1198782)

2 119890(119878119899)119899

= (119873119872119862119862 ) 119875119862119874119873 (1 minus 119875119874119873)119873119872119862minus119862

sdot [ 119899prod119894=1

119878119894119875119894 + 1198680] [ 119899prod119894=1

119896119894](4)






1198680 =

0 if119899prod119894=1

119878119894119875119894 gt 01 if

119899prod119894=1

119878119894119875119894 = 0 (6)







C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

N(A)MC e

S11 e

S22 e

S33 eSn

[(NMC



[(NMC



[(NMC



[(NMC



[(NMC



01


C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

k1 =

k2 =

ki =

1 minus

1 minus

1 minus

S = 1S = 0

k3 = 1 minus

S = 1S = 0

S = 1S = 0

S = 1S = 0

i = 234 n

ki = 1 minus S = 1

S = 0 i = 134 n

ki = 1 minus S = 1

S = 0 i = 124 n


sum4i=1 S

i gt M minus C

N(A)MC e

S11 e

S22 e

S33 e

S44


C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

S44 minus Δ 4

ki = 1 minus

Si = 0


(NMC







11986211989011987811 11989011987822 119890119878119899119899


V11986211989011987811 11989011987822 119890119878119899119899


sumforall11989011987811

sumforall11989011987822


11987511986211989011987811 11989011987822 119890119878119899119899V11986211989011987811 11989011987822 119890119878119899119899

(8)



11987111986211989011987811 11989011987822 119890119878119899119899

=

0 if119899sum119894=1

119878119894 le (119872 minus 119862)119899sum119894=1


119878119894 gt (119872 minus 119862)(9)


11987111986211989011987811 11989011987822 119890119878119899119899

= max0 119899sum119894=1

119878119894 minus (119872 minus 119862) (10)


119871= sumforall119862

sumforall11989011987811

sumforall11989011987822


(119871 (119862 11989011987811 11989011987822 119890119878119899119899 )) V11986211989011987811 11989011987822 119890119878119899119899

(11)


11987911987511986211989011987811 11989011987822 119890119878119899119899

=

119862 + 119899sum119894=1

119878119894120588119894 if119899sum119894=1

119878119894120588119894 le (119872 minus 119862)119872 if

119899sum119894=1

119878119894120588119894 gt (119872 minus 119862) (12)


11987911987511986211989011987811 11989011987822 119890119878119899119899

= max119872 119862 + 119899sum119894=1

119878119894120588119894 (13)


119879119875= sumforall119862

sumforall11989011987811


(119879119875 (119862 11989011987811 11989011987822 119890119878119899119899 )) V11986211989011987811 11989011987822 119890119878119899119899

(14)


119864119862 = sumforall119862

sumforall11989011987811


[(119879119875 (119862 11989011987811 11989011987822 119890119878119899119899 ) 119864119905119909)

+ ( 119899sum119894=1

119878119894 (1 minus 120588119894) 119864119903119909)

+ ((119872 minus 119862) + 119899sum119894=1

(1 minus 119878119894) 119864119904)] lowast V11986211989011987811 11989011987822 119890119878119899119899

(15)

6 Numerical Results
























Start




YesYes

No

i lt M

Node[i] is on

i++Node[i] is off

No

No


Yes

No

lt ϱ

Yes

No

Node [j] transmits

End

j ++ Yes j lt Ne

Yes

No i ++

j = 0



15

10

5

0

times107

Ener

gy co

nsum

ptio

n (

ＮＲ)

02

04

06

08

0304

0506

07

０ＩＨ

Markov chain

Network simulation



00204060811080604020

123

5

0

4


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107


1

05

0010203040506070809

0

3

1

2


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107















０ＩＨ

times106

1080604020108060402

10

0

15

5

0Pack

et lo

ss (P

acke

ts)


1

05

00908070605040302010

2

1


０ＩＨ

times106

Ener

gy co

nsum

ptio

n (

ＮＲ)


00204060811080604020

2

15

0

05

1


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105


1080604020108060402

005

015

01

00Pa

cket

loss

pro

babi

lity


０ＩＨ



0

05

1010203040506070809

10

32


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105







119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 360119898119860ℎ1800000ℎ = 02 120583119860 (16)




119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 40119898119860ℎ1800000ℎ = 22 119899119860 (17)













8 Conclusion



005

008

0706

0504

03

Ener

gy co

nsum

ptio

n(A

mpe

re)

08

06

04

02






０ＩＨ


005

10020406081Ener

gy co

nsum

ptio

n(A

mpe

re)

０ＩＨ


10minus1

10minus2

10minus3

10minus4


1080604020108060402

005

0

01

0Pack

et lo

ss p

roba

bilit

y

０ＩＨ







1080604020108060402

001002003004

00Pa

cket

loss

pro

babi

lity

０ＩＨ



1080604020108060402

03

02

01

00

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ


1080604020108060402

004

002

0

006

0

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ






002040608102468100

002

006008

004

Pack

et lo

ss p

roba

bilit


０ＩＨ


002040608102468

008

0

002

004

006

10Pack

et lo

ss p

roba

bilit

y


０ＩＨ


time [min]0 50 100 150

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20



time [min]0 200 400 600 800 1000 1200

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20






Acknowledgments




















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Slot

PS Sensor

SS Sensor

Slot

PS Sensor

SS Sensor


Slot

PS Sensor

SS Sensor


PS Frame (０ = 1)

PS Frame (０ = 1)

PS Frame (０ = 1)





hellip hellip



SS



d bits

０３1 ０３2 ０３－３３1 ３３2 ３３Ｃ




120588119894 = 120574119890minus1198640119864119877 (1)

where


















N(A)MC e

S11 e

S22 e

S33 eSn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn












Δ 119894

=


(3)





119875119899119860119872119862119890(1198781)

1 119890(1198782)

2 119890(119878119899)119899

= (119873119872119862119862 ) 119875119862119874119873 (1 minus 119875119874119873)119873119872119862minus119862

sdot [ 119899prod119894=1

119878119894119875119894 + 1198680] [ 119899prod119894=1

119896119894](4)






1198680 =

0 if119899prod119894=1

119878119894119875119894 gt 01 if

119899prod119894=1

119878119894119875119894 = 0 (6)







C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

N(A)MC e

S11 e

S22 e

S33 eSn

[(NMC



[(NMC



[(NMC



[(NMC



[(NMC



01


C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

k1 =

k2 =

ki =

1 minus

1 minus

1 minus

S = 1S = 0

k3 = 1 minus

S = 1S = 0

S = 1S = 0

S = 1S = 0

i = 234 n

ki = 1 minus S = 1

S = 0 i = 134 n

ki = 1 minus S = 1

S = 0 i = 124 n


sum4i=1 S

i gt M minus C

N(A)MC e

S11 e

S22 e

S33 e

S44


C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

S44 minus Δ 4

ki = 1 minus

Si = 0


(NMC







11986211989011987811 11989011987822 119890119878119899119899


V11986211989011987811 11989011987822 119890119878119899119899


sumforall11989011987811

sumforall11989011987822


11987511986211989011987811 11989011987822 119890119878119899119899V11986211989011987811 11989011987822 119890119878119899119899

(8)



11987111986211989011987811 11989011987822 119890119878119899119899

=

0 if119899sum119894=1

119878119894 le (119872 minus 119862)119899sum119894=1


119878119894 gt (119872 minus 119862)(9)


11987111986211989011987811 11989011987822 119890119878119899119899

= max0 119899sum119894=1

119878119894 minus (119872 minus 119862) (10)


119871= sumforall119862

sumforall11989011987811

sumforall11989011987822


(119871 (119862 11989011987811 11989011987822 119890119878119899119899 )) V11986211989011987811 11989011987822 119890119878119899119899

(11)


11987911987511986211989011987811 11989011987822 119890119878119899119899

=

119862 + 119899sum119894=1

119878119894120588119894 if119899sum119894=1

119878119894120588119894 le (119872 minus 119862)119872 if

119899sum119894=1

119878119894120588119894 gt (119872 minus 119862) (12)


11987911987511986211989011987811 11989011987822 119890119878119899119899

= max119872 119862 + 119899sum119894=1

119878119894120588119894 (13)


119879119875= sumforall119862

sumforall11989011987811


(119879119875 (119862 11989011987811 11989011987822 119890119878119899119899 )) V11986211989011987811 11989011987822 119890119878119899119899

(14)


119864119862 = sumforall119862

sumforall11989011987811


[(119879119875 (119862 11989011987811 11989011987822 119890119878119899119899 ) 119864119905119909)

+ ( 119899sum119894=1

119878119894 (1 minus 120588119894) 119864119903119909)

+ ((119872 minus 119862) + 119899sum119894=1

(1 minus 119878119894) 119864119904)] lowast V11986211989011987811 11989011987822 119890119878119899119899

(15)

6 Numerical Results
























Start




YesYes

No

i lt M

Node[i] is on

i++Node[i] is off

No

No


Yes

No

lt ϱ

Yes

No

Node [j] transmits

End

j ++ Yes j lt Ne

Yes

No i ++

j = 0



15

10

5

0

times107

Ener

gy co

nsum

ptio

n (

ＮＲ)

02

04

06

08

0304

0506

07

０ＩＨ

Markov chain

Network simulation



00204060811080604020

123

5

0

4


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107


1

05

0010203040506070809

0

3

1

2


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107















０ＩＨ

times106

1080604020108060402

10

0

15

5

0Pack

et lo

ss (P

acke

ts)


1

05

00908070605040302010

2

1


０ＩＨ

times106

Ener

gy co

nsum

ptio

n (

ＮＲ)


00204060811080604020

2

15

0

05

1


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105


1080604020108060402

005

015

01

00Pa

cket

loss

pro

babi

lity


０ＩＨ



0

05

1010203040506070809

10

32


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105







119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 360119898119860ℎ1800000ℎ = 02 120583119860 (16)




119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 40119898119860ℎ1800000ℎ = 22 119899119860 (17)













8 Conclusion



005

008

0706

0504

03

Ener

gy co

nsum

ptio

n(A

mpe

re)

08

06

04

02






０ＩＨ


005

10020406081Ener

gy co

nsum

ptio

n(A

mpe

re)

０ＩＨ


10minus1

10minus2

10minus3

10minus4


1080604020108060402

005

0

01

0Pack

et lo

ss p

roba

bilit

y

０ＩＨ







1080604020108060402

001002003004

00Pa

cket

loss

pro

babi

lity

０ＩＨ



1080604020108060402

03

02

01

00

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ


1080604020108060402

004

002

0

006

0

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ






002040608102468100

002

006008

004

Pack

et lo

ss p

roba

bilit


０ＩＨ


002040608102468

008

0

002

004

006

10Pack

et lo

ss p

roba

bilit

y


０ＩＨ


time [min]0 50 100 150

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20



time [min]0 200 400 600 800 1000 1200

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20






Acknowledgments




















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



hellip hellip



SS



d bits

０３1 ０３2 ０３－３３1 ３３2 ３３Ｃ




120588119894 = 120574119890minus1198640119864119877 (1)

where


















N(A)MC e

S11 e

S22 e

S33 eSn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn












Δ 119894

=


(3)





119875119899119860119872119862119890(1198781)

1 119890(1198782)

2 119890(119878119899)119899

= (119873119872119862119862 ) 119875119862119874119873 (1 minus 119875119874119873)119873119872119862minus119862

sdot [ 119899prod119894=1

119878119894119875119894 + 1198680] [ 119899prod119894=1

119896119894](4)






1198680 =

0 if119899prod119894=1

119878119894119875119894 gt 01 if

119899prod119894=1

119878119894119875119894 = 0 (6)







C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

N(A)MC e

S11 e

S22 e

S33 eSn

[(NMC



[(NMC



[(NMC



[(NMC



[(NMC



01


C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

k1 =

k2 =

ki =

1 minus

1 minus

1 minus

S = 1S = 0

k3 = 1 minus

S = 1S = 0

S = 1S = 0

S = 1S = 0

i = 234 n

ki = 1 minus S = 1

S = 0 i = 134 n

ki = 1 minus S = 1

S = 0 i = 124 n


sum4i=1 S

i gt M minus C

N(A)MC e

S11 e

S22 e

S33 e

S44


C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

S44 minus Δ 4

ki = 1 minus

Si = 0


(NMC







11986211989011987811 11989011987822 119890119878119899119899


V11986211989011987811 11989011987822 119890119878119899119899


sumforall11989011987811

sumforall11989011987822


11987511986211989011987811 11989011987822 119890119878119899119899V11986211989011987811 11989011987822 119890119878119899119899

(8)



11987111986211989011987811 11989011987822 119890119878119899119899

=

0 if119899sum119894=1

119878119894 le (119872 minus 119862)119899sum119894=1


119878119894 gt (119872 minus 119862)(9)


11987111986211989011987811 11989011987822 119890119878119899119899

= max0 119899sum119894=1

119878119894 minus (119872 minus 119862) (10)


119871= sumforall119862

sumforall11989011987811

sumforall11989011987822


(119871 (119862 11989011987811 11989011987822 119890119878119899119899 )) V11986211989011987811 11989011987822 119890119878119899119899

(11)


11987911987511986211989011987811 11989011987822 119890119878119899119899

=

119862 + 119899sum119894=1

119878119894120588119894 if119899sum119894=1

119878119894120588119894 le (119872 minus 119862)119872 if

119899sum119894=1

119878119894120588119894 gt (119872 minus 119862) (12)


11987911987511986211989011987811 11989011987822 119890119878119899119899

= max119872 119862 + 119899sum119894=1

119878119894120588119894 (13)


119879119875= sumforall119862

sumforall11989011987811


(119879119875 (119862 11989011987811 11989011987822 119890119878119899119899 )) V11986211989011987811 11989011987822 119890119878119899119899

(14)


119864119862 = sumforall119862

sumforall11989011987811


[(119879119875 (119862 11989011987811 11989011987822 119890119878119899119899 ) 119864119905119909)

+ ( 119899sum119894=1

119878119894 (1 minus 120588119894) 119864119903119909)

+ ((119872 minus 119862) + 119899sum119894=1

(1 minus 119878119894) 119864119904)] lowast V11986211989011987811 11989011987822 119890119878119899119899

(15)

6 Numerical Results
























Start




YesYes

No

i lt M

Node[i] is on

i++Node[i] is off

No

No


Yes

No

lt ϱ

Yes

No

Node [j] transmits

End

j ++ Yes j lt Ne

Yes

No i ++

j = 0



15

10

5

0

times107

Ener

gy co

nsum

ptio

n (

ＮＲ)

02

04

06

08

0304

0506

07

０ＩＨ

Markov chain

Network simulation



00204060811080604020

123

5

0

4


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107


1

05

0010203040506070809

0

3

1

2


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107















０ＩＨ

times106

1080604020108060402

10

0

15

5

0Pack

et lo

ss (P

acke

ts)


1

05

00908070605040302010

2

1


０ＩＨ

times106

Ener

gy co

nsum

ptio

n (

ＮＲ)


00204060811080604020

2

15

0

05

1


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105


1080604020108060402

005

015

01

00Pa

cket

loss

pro

babi

lity


０ＩＨ



0

05

1010203040506070809

10

32


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105







119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 360119898119860ℎ1800000ℎ = 02 120583119860 (16)




119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 40119898119860ℎ1800000ℎ = 22 119899119860 (17)













8 Conclusion



005

008

0706

0504

03

Ener

gy co

nsum

ptio

n(A

mpe

re)

08

06

04

02






０ＩＨ


005

10020406081Ener

gy co

nsum

ptio

n(A

mpe

re)

０ＩＨ


10minus1

10minus2

10minus3

10minus4


1080604020108060402

005

0

01

0Pack

et lo

ss p

roba

bilit

y

０ＩＨ







1080604020108060402

001002003004

00Pa

cket

loss

pro

babi

lity

０ＩＨ



1080604020108060402

03

02

01

00

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ


1080604020108060402

004

002

0

006

0

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ






002040608102468100

002

006008

004

Pack

et lo

ss p

roba

bilit


０ＩＨ


002040608102468

008

0

002

004

006

10Pack

et lo

ss p

roba

bilit

y


０ＩＨ


time [min]0 50 100 150

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20



time [min]0 200 400 600 800 1000 1200

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20






Acknowledgments




















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





N(A)MC e

S11 e

S22 e

S33 eSn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn












Δ 119894

=


(3)





119875119899119860119872119862119890(1198781)

1 119890(1198782)

2 119890(119878119899)119899

= (119873119872119862119862 ) 119875119862119874119873 (1 minus 119875119874119873)119873119872119862minus119862

sdot [ 119899prod119894=1

119878119894119875119894 + 1198680] [ 119899prod119894=1

119896119894](4)






1198680 =

0 if119899prod119894=1

119878119894119875119894 gt 01 if

119899prod119894=1

119878119894119875119894 = 0 (6)







C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

N(A)MC e

S11 e

S22 e

S33 eSn

[(NMC



[(NMC



[(NMC



[(NMC



[(NMC



01


C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

k1 =

k2 =

ki =

1 minus

1 minus

1 minus

S = 1S = 0

k3 = 1 minus

S = 1S = 0

S = 1S = 0

S = 1S = 0

i = 234 n

ki = 1 minus S = 1

S = 0 i = 134 n

ki = 1 minus S = 1

S = 0 i = 124 n


sum4i=1 S

i gt M minus C

N(A)MC e

S11 e

S22 e

S33 e

S44


C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

S44 minus Δ 4

ki = 1 minus

Si = 0


(NMC







11986211989011987811 11989011987822 119890119878119899119899


V11986211989011987811 11989011987822 119890119878119899119899


sumforall11989011987811

sumforall11989011987822


11987511986211989011987811 11989011987822 119890119878119899119899V11986211989011987811 11989011987822 119890119878119899119899

(8)



11987111986211989011987811 11989011987822 119890119878119899119899

=

0 if119899sum119894=1

119878119894 le (119872 minus 119862)119899sum119894=1


119878119894 gt (119872 minus 119862)(9)


11987111986211989011987811 11989011987822 119890119878119899119899

= max0 119899sum119894=1

119878119894 minus (119872 minus 119862) (10)


119871= sumforall119862

sumforall11989011987811

sumforall11989011987822


(119871 (119862 11989011987811 11989011987822 119890119878119899119899 )) V11986211989011987811 11989011987822 119890119878119899119899

(11)


11987911987511986211989011987811 11989011987822 119890119878119899119899

=

119862 + 119899sum119894=1

119878119894120588119894 if119899sum119894=1

119878119894120588119894 le (119872 minus 119862)119872 if

119899sum119894=1

119878119894120588119894 gt (119872 minus 119862) (12)


11987911987511986211989011987811 11989011987822 119890119878119899119899

= max119872 119862 + 119899sum119894=1

119878119894120588119894 (13)


119879119875= sumforall119862

sumforall11989011987811


(119879119875 (119862 11989011987811 11989011987822 119890119878119899119899 )) V11986211989011987811 11989011987822 119890119878119899119899

(14)


119864119862 = sumforall119862

sumforall11989011987811


[(119879119875 (119862 11989011987811 11989011987822 119890119878119899119899 ) 119864119905119909)

+ ( 119899sum119894=1

119878119894 (1 minus 120588119894) 119864119903119909)

+ ((119872 minus 119862) + 119899sum119894=1

(1 minus 119878119894) 119864119904)] lowast V11986211989011987811 11989011987822 119890119878119899119899

(15)

6 Numerical Results
























Start




YesYes

No

i lt M

Node[i] is on

i++Node[i] is off

No

No


Yes

No

lt ϱ

Yes

No

Node [j] transmits

End

j ++ Yes j lt Ne

Yes

No i ++

j = 0



15

10

5

0

times107

Ener

gy co

nsum

ptio

n (

ＮＲ)

02

04

06

08

0304

0506

07

０ＩＨ

Markov chain

Network simulation



00204060811080604020

123

5

0

4


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107


1

05

0010203040506070809

0

3

1

2


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107















０ＩＨ

times106

1080604020108060402

10

0

15

5

0Pack

et lo

ss (P

acke

ts)


1

05

00908070605040302010

2

1


０ＩＨ

times106

Ener

gy co

nsum

ptio

n (

ＮＲ)


00204060811080604020

2

15

0

05

1


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105


1080604020108060402

005

015

01

00Pa

cket

loss

pro

babi

lity


０ＩＨ



0

05

1010203040506070809

10

32


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105







119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 360119898119860ℎ1800000ℎ = 02 120583119860 (16)




119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 40119898119860ℎ1800000ℎ = 22 119899119860 (17)













8 Conclusion



005

008

0706

0504

03

Ener

gy co

nsum

ptio

n(A

mpe

re)

08

06

04

02






０ＩＨ


005

10020406081Ener

gy co

nsum

ptio

n(A

mpe

re)

０ＩＨ


10minus1

10minus2

10minus3

10minus4


1080604020108060402

005

0

01

0Pack

et lo

ss p

roba

bilit

y

０ＩＨ







1080604020108060402

001002003004

00Pa

cket

loss

pro

babi

lity

０ＩＨ



1080604020108060402

03

02

01

00

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ


1080604020108060402

004

002

0

006

0

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ






002040608102468100

002

006008

004

Pack

et lo

ss p

roba

bilit


０ＩＨ


002040608102468

008

0

002

004

006

10Pack

et lo

ss p

roba

bilit

y


０ＩＨ


time [min]0 50 100 150

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20



time [min]0 200 400 600 800 1000 1200

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20






Acknowledgments




















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












Δ 119894

=


(3)





119875119899119860119872119862119890(1198781)

1 119890(1198782)

2 119890(119878119899)119899

= (119873119872119862119862 ) 119875119862119874119873 (1 minus 119875119874119873)119873119872119862minus119862

sdot [ 119899prod119894=1

119878119894119875119894 + 1198680] [ 119899prod119894=1

119896119894](4)






1198680 =

0 if119899prod119894=1

119878119894119875119894 gt 01 if

119899prod119894=1

119878119894119875119894 = 0 (6)







C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

N(A)MC e

S11 e

S22 e

S33 eSn

[(NMC



[(NMC



[(NMC



[(NMC



[(NMC



01


C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

k1 =

k2 =

ki =

1 minus

1 minus

1 minus

S = 1S = 0

k3 = 1 minus

S = 1S = 0

S = 1S = 0

S = 1S = 0

i = 234 n

ki = 1 minus S = 1

S = 0 i = 134 n

ki = 1 minus S = 1

S = 0 i = 124 n


sum4i=1 S

i gt M minus C

N(A)MC e

S11 e

S22 e

S33 e

S44


C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

S44 minus Δ 4

ki = 1 minus

Si = 0


(NMC







11986211989011987811 11989011987822 119890119878119899119899


V11986211989011987811 11989011987822 119890119878119899119899


sumforall11989011987811

sumforall11989011987822


11987511986211989011987811 11989011987822 119890119878119899119899V11986211989011987811 11989011987822 119890119878119899119899

(8)



11987111986211989011987811 11989011987822 119890119878119899119899

=

0 if119899sum119894=1

119878119894 le (119872 minus 119862)119899sum119894=1


119878119894 gt (119872 minus 119862)(9)


11987111986211989011987811 11989011987822 119890119878119899119899

= max0 119899sum119894=1

119878119894 minus (119872 minus 119862) (10)


119871= sumforall119862

sumforall11989011987811

sumforall11989011987822


(119871 (119862 11989011987811 11989011987822 119890119878119899119899 )) V11986211989011987811 11989011987822 119890119878119899119899

(11)


11987911987511986211989011987811 11989011987822 119890119878119899119899

=

119862 + 119899sum119894=1

119878119894120588119894 if119899sum119894=1

119878119894120588119894 le (119872 minus 119862)119872 if

119899sum119894=1

119878119894120588119894 gt (119872 minus 119862) (12)


11987911987511986211989011987811 11989011987822 119890119878119899119899

= max119872 119862 + 119899sum119894=1

119878119894120588119894 (13)


119879119875= sumforall119862

sumforall11989011987811


(119879119875 (119862 11989011987811 11989011987822 119890119878119899119899 )) V11986211989011987811 11989011987822 119890119878119899119899

(14)


119864119862 = sumforall119862

sumforall11989011987811


[(119879119875 (119862 11989011987811 11989011987822 119890119878119899119899 ) 119864119905119909)

+ ( 119899sum119894=1

119878119894 (1 minus 120588119894) 119864119903119909)

+ ((119872 minus 119862) + 119899sum119894=1

(1 minus 119878119894) 119864119904)] lowast V11986211989011987811 11989011987822 119890119878119899119899

(15)

6 Numerical Results
























Start




YesYes

No

i lt M

Node[i] is on

i++Node[i] is off

No

No


Yes

No

lt ϱ

Yes

No

Node [j] transmits

End

j ++ Yes j lt Ne

Yes

No i ++

j = 0



15

10

5

0

times107

Ener

gy co

nsum

ptio

n (

ＮＲ)

02

04

06

08

0304

0506

07

０ＩＨ

Markov chain

Network simulation



00204060811080604020

123

5

0

4


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107


1

05

0010203040506070809

0

3

1

2


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107















０ＩＨ

times106

1080604020108060402

10

0

15

5

0Pack

et lo

ss (P

acke

ts)


1

05

00908070605040302010

2

1


０ＩＨ

times106

Ener

gy co

nsum

ptio

n (

ＮＲ)


00204060811080604020

2

15

0

05

1


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105


1080604020108060402

005

015

01

00Pa

cket

loss

pro

babi

lity


０ＩＨ



0

05

1010203040506070809

10

32


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105







119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 360119898119860ℎ1800000ℎ = 02 120583119860 (16)




119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 40119898119860ℎ1800000ℎ = 22 119899119860 (17)













8 Conclusion



005

008

0706

0504

03

Ener

gy co

nsum

ptio

n(A

mpe

re)

08

06

04

02






０ＩＨ


005

10020406081Ener

gy co

nsum

ptio

n(A

mpe

re)

０ＩＨ


10minus1

10minus2

10minus3

10minus4


1080604020108060402

005

0

01

0Pack

et lo

ss p

roba

bilit

y

０ＩＨ







1080604020108060402

001002003004

00Pa

cket

loss

pro

babi

lity

０ＩＨ



1080604020108060402

03

02

01

00

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ


1080604020108060402

004

002

0

006

0

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ






002040608102468100

002

006008

004

Pack

et lo

ss p

roba

bilit


０ＩＨ


002040608102468

008

0

002

004

006

10Pack

et lo

ss p

roba

bilit

y


０ＩＨ


time [min]0 50 100 150

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20



time [min]0 200 400 600 800 1000 1200

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20






Acknowledgments




















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

N(A)MC e

S11 e

S22 e

S33 eSn

[(NMC



[(NMC



[(NMC



[(NMC



[(NMC



01


C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

Sn minus Δn

k1 =

k2 =

ki =

1 minus

1 minus

1 minus

S = 1S = 0

k3 = 1 minus

S = 1S = 0

S = 1S = 0

S = 1S = 0

i = 234 n

ki = 1 minus S = 1

S = 0 i = 134 n

ki = 1 minus S = 1

S = 0 i = 124 n


sum4i=1 S

i gt M minus C

N(A)MC e

S11 e

S22 e

S33 e

S44


C eS11 minus Δ 1 e

S22 minus Δ 2 e

S33 minus Δ 3 e

S44 minus Δ 4

ki = 1 minus

Si = 0


(NMC







11986211989011987811 11989011987822 119890119878119899119899


V11986211989011987811 11989011987822 119890119878119899119899


sumforall11989011987811

sumforall11989011987822


11987511986211989011987811 11989011987822 119890119878119899119899V11986211989011987811 11989011987822 119890119878119899119899

(8)



11987111986211989011987811 11989011987822 119890119878119899119899

=

0 if119899sum119894=1

119878119894 le (119872 minus 119862)119899sum119894=1


119878119894 gt (119872 minus 119862)(9)


11987111986211989011987811 11989011987822 119890119878119899119899

= max0 119899sum119894=1

119878119894 minus (119872 minus 119862) (10)


119871= sumforall119862

sumforall11989011987811

sumforall11989011987822


(119871 (119862 11989011987811 11989011987822 119890119878119899119899 )) V11986211989011987811 11989011987822 119890119878119899119899

(11)


11987911987511986211989011987811 11989011987822 119890119878119899119899

=

119862 + 119899sum119894=1

119878119894120588119894 if119899sum119894=1

119878119894120588119894 le (119872 minus 119862)119872 if

119899sum119894=1

119878119894120588119894 gt (119872 minus 119862) (12)


11987911987511986211989011987811 11989011987822 119890119878119899119899

= max119872 119862 + 119899sum119894=1

119878119894120588119894 (13)


119879119875= sumforall119862

sumforall11989011987811


(119879119875 (119862 11989011987811 11989011987822 119890119878119899119899 )) V11986211989011987811 11989011987822 119890119878119899119899

(14)


119864119862 = sumforall119862

sumforall11989011987811


[(119879119875 (119862 11989011987811 11989011987822 119890119878119899119899 ) 119864119905119909)

+ ( 119899sum119894=1

119878119894 (1 minus 120588119894) 119864119903119909)

+ ((119872 minus 119862) + 119899sum119894=1

(1 minus 119878119894) 119864119904)] lowast V11986211989011987811 11989011987822 119890119878119899119899

(15)

6 Numerical Results
























Start




YesYes

No

i lt M

Node[i] is on

i++Node[i] is off

No

No


Yes

No

lt ϱ

Yes

No

Node [j] transmits

End

j ++ Yes j lt Ne

Yes

No i ++

j = 0



15

10

5

0

times107

Ener

gy co

nsum

ptio

n (

ＮＲ)

02

04

06

08

0304

0506

07

０ＩＨ

Markov chain

Network simulation



00204060811080604020

123

5

0

4


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107


1

05

0010203040506070809

0

3

1

2


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107















０ＩＨ

times106

1080604020108060402

10

0

15

5

0Pack

et lo

ss (P

acke

ts)


1

05

00908070605040302010

2

1


０ＩＨ

times106

Ener

gy co

nsum

ptio

n (

ＮＲ)


00204060811080604020

2

15

0

05

1


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105


1080604020108060402

005

015

01

00Pa

cket

loss

pro

babi

lity


０ＩＨ



0

05

1010203040506070809

10

32


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105







119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 360119898119860ℎ1800000ℎ = 02 120583119860 (16)




119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 40119898119860ℎ1800000ℎ = 22 119899119860 (17)













8 Conclusion



005

008

0706

0504

03

Ener

gy co

nsum

ptio

n(A

mpe

re)

08

06

04

02






０ＩＨ


005

10020406081Ener

gy co

nsum

ptio

n(A

mpe

re)

０ＩＨ


10minus1

10minus2

10minus3

10minus4


1080604020108060402

005

0

01

0Pack

et lo

ss p

roba

bilit

y

０ＩＨ







1080604020108060402

001002003004

00Pa

cket

loss

pro

babi

lity

０ＩＨ



1080604020108060402

03

02

01

00

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ


1080604020108060402

004

002

0

006

0

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ






002040608102468100

002

006008

004

Pack

et lo

ss p

roba

bilit


０ＩＨ


002040608102468

008

0

002

004

006

10Pack

et lo

ss p

roba

bilit

y


０ＩＨ


time [min]0 50 100 150

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20



time [min]0 200 400 600 800 1000 1200

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20






Acknowledgments




















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





11986211989011987811 11989011987822 119890119878119899119899


V11986211989011987811 11989011987822 119890119878119899119899


sumforall11989011987811

sumforall11989011987822


11987511986211989011987811 11989011987822 119890119878119899119899V11986211989011987811 11989011987822 119890119878119899119899

(8)



11987111986211989011987811 11989011987822 119890119878119899119899

=

0 if119899sum119894=1

119878119894 le (119872 minus 119862)119899sum119894=1


119878119894 gt (119872 minus 119862)(9)


11987111986211989011987811 11989011987822 119890119878119899119899

= max0 119899sum119894=1

119878119894 minus (119872 minus 119862) (10)


119871= sumforall119862

sumforall11989011987811

sumforall11989011987822


(119871 (119862 11989011987811 11989011987822 119890119878119899119899 )) V11986211989011987811 11989011987822 119890119878119899119899

(11)


11987911987511986211989011987811 11989011987822 119890119878119899119899

=

119862 + 119899sum119894=1

119878119894120588119894 if119899sum119894=1

119878119894120588119894 le (119872 minus 119862)119872 if

119899sum119894=1

119878119894120588119894 gt (119872 minus 119862) (12)


11987911987511986211989011987811 11989011987822 119890119878119899119899

= max119872 119862 + 119899sum119894=1

119878119894120588119894 (13)


119879119875= sumforall119862

sumforall11989011987811


(119879119875 (119862 11989011987811 11989011987822 119890119878119899119899 )) V11986211989011987811 11989011987822 119890119878119899119899

(14)


119864119862 = sumforall119862

sumforall11989011987811


[(119879119875 (119862 11989011987811 11989011987822 119890119878119899119899 ) 119864119905119909)

+ ( 119899sum119894=1

119878119894 (1 minus 120588119894) 119864119903119909)

+ ((119872 minus 119862) + 119899sum119894=1

(1 minus 119878119894) 119864119904)] lowast V11986211989011987811 11989011987822 119890119878119899119899

(15)

6 Numerical Results
























Start




YesYes

No

i lt M

Node[i] is on

i++Node[i] is off

No

No


Yes

No

lt ϱ

Yes

No

Node [j] transmits

End

j ++ Yes j lt Ne

Yes

No i ++

j = 0



15

10

5

0

times107

Ener

gy co

nsum

ptio

n (

ＮＲ)

02

04

06

08

0304

0506

07

０ＩＨ

Markov chain

Network simulation



00204060811080604020

123

5

0

4


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107


1

05

0010203040506070809

0

3

1

2


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107















０ＩＨ

times106

1080604020108060402

10

0

15

5

0Pack

et lo

ss (P

acke

ts)


1

05

00908070605040302010

2

1


０ＩＨ

times106

Ener

gy co

nsum

ptio

n (

ＮＲ)


00204060811080604020

2

15

0

05

1


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105


1080604020108060402

005

015

01

00Pa

cket

loss

pro

babi

lity


０ＩＨ



0

05

1010203040506070809

10

32


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105







119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 360119898119860ℎ1800000ℎ = 02 120583119860 (16)




119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 40119898119860ℎ1800000ℎ = 22 119899119860 (17)













8 Conclusion



005

008

0706

0504

03

Ener

gy co

nsum

ptio

n(A

mpe

re)

08

06

04

02






０ＩＨ


005

10020406081Ener

gy co

nsum

ptio

n(A

mpe

re)

０ＩＨ


10minus1

10minus2

10minus3

10minus4


1080604020108060402

005

0

01

0Pack

et lo

ss p

roba

bilit

y

０ＩＨ







1080604020108060402

001002003004

00Pa

cket

loss

pro

babi

lity

０ＩＨ



1080604020108060402

03

02

01

00

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ


1080604020108060402

004

002

0

006

0

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ






002040608102468100

002

006008

004

Pack

et lo

ss p

roba

bilit


０ＩＨ


002040608102468

008

0

002

004

006

10Pack

et lo

ss p

roba

bilit

y


０ＩＨ


time [min]0 50 100 150

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20



time [min]0 200 400 600 800 1000 1200

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20






Acknowledgments




















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia
























Start




YesYes

No

i lt M

Node[i] is on

i++Node[i] is off

No

No


Yes

No

lt ϱ

Yes

No

Node [j] transmits

End

j ++ Yes j lt Ne

Yes

No i ++

j = 0



15

10

5

0

times107

Ener

gy co

nsum

ptio

n (

ＮＲ)

02

04

06

08

0304

0506

07

０ＩＨ

Markov chain

Network simulation



00204060811080604020

123

5

0

4


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107


1

05

0010203040506070809

0

3

1

2


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107















０ＩＨ

times106

1080604020108060402

10

0

15

5

0Pack

et lo

ss (P

acke

ts)


1

05

00908070605040302010

2

1


０ＩＨ

times106

Ener

gy co

nsum

ptio

n (

ＮＲ)


00204060811080604020

2

15

0

05

1


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105


1080604020108060402

005

015

01

00Pa

cket

loss

pro

babi

lity


０ＩＨ



0

05

1010203040506070809

10

32


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105







119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 360119898119860ℎ1800000ℎ = 02 120583119860 (16)




119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 40119898119860ℎ1800000ℎ = 22 119899119860 (17)













8 Conclusion



005

008

0706

0504

03

Ener

gy co

nsum

ptio

n(A

mpe

re)

08

06

04

02






０ＩＨ


005

10020406081Ener

gy co

nsum

ptio

n(A

mpe

re)

０ＩＨ


10minus1

10minus2

10minus3

10minus4


1080604020108060402

005

0

01

0Pack

et lo

ss p

roba

bilit

y

０ＩＨ







1080604020108060402

001002003004

00Pa

cket

loss

pro

babi

lity

０ＩＨ



1080604020108060402

03

02

01

00

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ


1080604020108060402

004

002

0

006

0

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ






002040608102468100

002

006008

004

Pack

et lo

ss p

roba

bilit


０ＩＨ


002040608102468

008

0

002

004

006

10Pack

et lo

ss p

roba

bilit

y


０ＩＨ


time [min]0 50 100 150

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20



time [min]0 200 400 600 800 1000 1200

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20






Acknowledgments




















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Start




YesYes

No

i lt M

Node[i] is on

i++Node[i] is off

No

No


Yes

No

lt ϱ

Yes

No

Node [j] transmits

End

j ++ Yes j lt Ne

Yes

No i ++

j = 0



15

10

5

0

times107

Ener

gy co

nsum

ptio

n (

ＮＲ)

02

04

06

08

0304

0506

07

０ＩＨ

Markov chain

Network simulation



00204060811080604020

123

5

0

4


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107


1

05

0010203040506070809

0

3

1

2


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107















０ＩＨ

times106

1080604020108060402

10

0

15

5

0Pack

et lo

ss (P

acke

ts)


1

05

00908070605040302010

2

1


０ＩＨ

times106

Ener

gy co

nsum

ptio

n (

ＮＲ)


00204060811080604020

2

15

0

05

1


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105


1080604020108060402

005

015

01

00Pa

cket

loss

pro

babi

lity


０ＩＨ



0

05

1010203040506070809

10

32


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105







119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 360119898119860ℎ1800000ℎ = 02 120583119860 (16)




119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 40119898119860ℎ1800000ℎ = 22 119899119860 (17)













8 Conclusion



005

008

0706

0504

03

Ener

gy co

nsum

ptio

n(A

mpe

re)

08

06

04

02






０ＩＨ


005

10020406081Ener

gy co

nsum

ptio

n(A

mpe

re)

０ＩＨ


10minus1

10minus2

10minus3

10minus4


1080604020108060402

005

0

01

0Pack

et lo

ss p

roba

bilit

y

０ＩＨ







1080604020108060402

001002003004

00Pa

cket

loss

pro

babi

lity

０ＩＨ



1080604020108060402

03

02

01

00

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ


1080604020108060402

004

002

0

006

0

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ






002040608102468100

002

006008

004

Pack

et lo

ss p

roba

bilit


０ＩＨ


002040608102468

008

0

002

004

006

10Pack

et lo

ss p

roba

bilit

y


０ＩＨ


time [min]0 50 100 150

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20



time [min]0 200 400 600 800 1000 1200

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20






Acknowledgments




















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



00204060811080604020

123

5

0

4


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107


1

05

0010203040506070809

0

3

1

2


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times107















０ＩＨ

times106

1080604020108060402

10

0

15

5

0Pack

et lo

ss (P

acke

ts)


1

05

00908070605040302010

2

1


０ＩＨ

times106

Ener

gy co

nsum

ptio

n (

ＮＲ)


00204060811080604020

2

15

0

05

1


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105


1080604020108060402

005

015

01

00Pa

cket

loss

pro

babi

lity


０ＩＨ



0

05

1010203040506070809

10

32


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105







119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 360119898119860ℎ1800000ℎ = 02 120583119860 (16)




119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 40119898119860ℎ1800000ℎ = 22 119899119860 (17)













8 Conclusion



005

008

0706

0504

03

Ener

gy co

nsum

ptio

n(A

mpe

re)

08

06

04

02






０ＩＨ


005

10020406081Ener

gy co

nsum

ptio

n(A

mpe

re)

０ＩＨ


10minus1

10minus2

10minus3

10minus4


1080604020108060402

005

0

01

0Pack

et lo

ss p

roba

bilit

y

０ＩＨ







1080604020108060402

001002003004

00Pa

cket

loss

pro

babi

lity

０ＩＨ



1080604020108060402

03

02

01

00

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ


1080604020108060402

004

002

0

006

0

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ






002040608102468100

002

006008

004

Pack

et lo

ss p

roba

bilit


０ＩＨ


002040608102468

008

0

002

004

006

10Pack

et lo

ss p

roba

bilit

y


０ＩＨ


time [min]0 50 100 150

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20



time [min]0 200 400 600 800 1000 1200

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20






Acknowledgments




















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




０ＩＨ

times106

1080604020108060402

10

0

15

5

0Pack

et lo

ss (P

acke

ts)


1

05

00908070605040302010

2

1


０ＩＨ

times106

Ener

gy co

nsum

ptio

n (

ＮＲ)


00204060811080604020

2

15

0

05

1


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105


1080604020108060402

005

015

01

00Pa

cket

loss

pro

babi

lity


０ＩＨ



0

05

1010203040506070809

10

32


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105







119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 360119898119860ℎ1800000ℎ = 02 120583119860 (16)




119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 40119898119860ℎ1800000ℎ = 22 119899119860 (17)













8 Conclusion



005

008

0706

0504

03

Ener

gy co

nsum

ptio

n(A

mpe

re)

08

06

04

02






０ＩＨ


005

10020406081Ener

gy co

nsum

ptio

n(A

mpe

re)

０ＩＨ


10minus1

10minus2

10minus3

10minus4


1080604020108060402

005

0

01

0Pack

et lo

ss p

roba

bilit

y

０ＩＨ







1080604020108060402

001002003004

00Pa

cket

loss

pro

babi

lity

０ＩＨ



1080604020108060402

03

02

01

00

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ


1080604020108060402

004

002

0

006

0

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ






002040608102468100

002

006008

004

Pack

et lo

ss p

roba

bilit


０ＩＨ


002040608102468

008

0

002

004

006

10Pack

et lo

ss p

roba

bilit

y


０ＩＨ


time [min]0 50 100 150

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20



time [min]0 200 400 600 800 1000 1200

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20






Acknowledgments




















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



0

05

1010203040506070809

10

32


Ener

gy co

nsum

ptio

n (

ＮＲ)

０ＩＨ

times105







119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 360119898119860ℎ1800000ℎ = 02 120583119860 (16)




119868119904119897119900119905 = 119868119905119879119904119897119900119905 = 40119898119860ℎ1800000ℎ = 22 119899119860 (17)













8 Conclusion



005

008

0706

0504

03

Ener

gy co

nsum

ptio

n(A

mpe

re)

08

06

04

02






０ＩＨ


005

10020406081Ener

gy co

nsum

ptio

n(A

mpe

re)

０ＩＨ


10minus1

10minus2

10minus3

10minus4


1080604020108060402

005

0

01

0Pack

et lo

ss p

roba

bilit

y

０ＩＨ







1080604020108060402

001002003004

00Pa

cket

loss

pro

babi

lity

０ＩＨ



1080604020108060402

03

02

01

00

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ


1080604020108060402

004

002

0

006

0

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ






002040608102468100

002

006008

004

Pack

et lo

ss p

roba

bilit


０ＩＨ


002040608102468

008

0

002

004

006

10Pack

et lo

ss p

roba

bilit

y


０ＩＨ


time [min]0 50 100 150

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20



time [min]0 200 400 600 800 1000 1200

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20






Acknowledgments




















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












8 Conclusion



005

008

0706

0504

03

Ener

gy co

nsum

ptio

n(A

mpe

re)

08

06

04

02






０ＩＨ


005

10020406081Ener

gy co

nsum

ptio

n(A

mpe

re)

０ＩＨ


10minus1

10minus2

10minus3

10minus4


1080604020108060402

005

0

01

0Pack

et lo

ss p

roba

bilit

y

０ＩＨ







1080604020108060402

001002003004

00Pa

cket

loss

pro

babi

lity

０ＩＨ



1080604020108060402

03

02

01

00

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ


1080604020108060402

004

002

0

006

0

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ






002040608102468100

002

006008

004

Pack

et lo

ss p

roba

bilit


０ＩＨ


002040608102468

008

0

002

004

006

10Pack

et lo

ss p

roba

bilit

y


０ＩＨ


time [min]0 50 100 150

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20



time [min]0 200 400 600 800 1000 1200

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20






Acknowledgments




















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



005

008

0706

0504

03

Ener

gy co

nsum

ptio

n(A

mpe

re)

08

06

04

02






０ＩＨ


005

10020406081Ener

gy co

nsum

ptio

n(A

mpe

re)

０ＩＨ


10minus1

10minus2

10minus3

10minus4


1080604020108060402

005

0

01

0Pack

et lo

ss p

roba

bilit

y

０ＩＨ







1080604020108060402

001002003004

00Pa

cket

loss

pro

babi

lity

０ＩＨ



1080604020108060402

03

02

01

00

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ


1080604020108060402

004

002

0

006

0

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ






002040608102468100

002

006008

004

Pack

et lo

ss p

roba

bilit


０ＩＨ


002040608102468

008

0

002

004

006

10Pack

et lo

ss p

roba

bilit

y


０ＩＨ


time [min]0 50 100 150

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20



time [min]0 200 400 600 800 1000 1200

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20






Acknowledgments




















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



1080604020108060402

001002003004

00Pa

cket

loss

pro

babi

lity

０ＩＨ



1080604020108060402

03

02

01

00

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ


1080604020108060402

004

002

0

006

0

(Am

pere

)En

ergy

cons

umpt

ion


０ＩＨ






002040608102468100

002

006008

004

Pack

et lo

ss p

roba

bilit


０ＩＨ


002040608102468

008

0

002

004

006

10Pack

et lo

ss p

roba

bilit

y


０ＩＨ


time [min]0 50 100 150

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20



time [min]0 200 400 600 800 1000 1200

Nod

es [N

umbe

r of n

odes

]

0

5

10

15

20






Acknowledgments




















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



002040608102468100

002

006008

004

Pack

et lo

ss p

roba

bilit


０ＩＨ


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０ＩＨ


time [min]0 50 100 150

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0

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time [min]0 200 400 600 800 1000 1200

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Acknowledgments




















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





Acknowledgments




















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia
























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

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