An access protocol for efficiency optimization in WDM networks: A propagation delay and collisions avoidance analysis

Computer Networks 57 (2013) 1234–1252

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Computer Networks

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An access protocol for efficiency optimization in WDMnetworks: A propagation delay and collisions avoidanceanalysis

1389-1286/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.comnet.2012.12.015

⇑ Corresponding author. Tel.: +30 210 7722145; fax: +30 210 7722534.E-mail address: [email protected] (P.A. Baziana).

P.A. Baziana ⇑, I.E. PountourakisSchool of Electrical and Computer Engineering, Department of Communications Electronic & Information Engineering, National Technical University of Athens,157 73 Zografou, Athens, Greece

a r t i c l e i n f o

Article history:Received 17 May 2012Received in revised form 4 October 2012Accepted 27 December 2012Available online 4 January 2013

Keywords:Wavelength Division Multiplexing (WDM)Multi-channel Control Architecture (MCA)Performance optimizationPropagation delay latency

a b s t r a c t

The main investigation of this study is the performance optimization of a WDMA protocolsuitable for a network architecture of passive star topology that uses the Multi-channelControl Architecture (MCA) and adopts asymmetric access rights over it. The access asym-metry defines that the MCA uses a separate control channel properly assigned for the freestations transmission, while the remaining control channels are used by the backloggedstations. The proposed asymmetric access protocol prevents from the data channels colli-sions, while it takes under consideration the loss due to the receiver conflicts. This isachieved by considering the propagation delay latency parameter as appropriate timeinterval in order to coordinate collisions-free data packets transmission. The performanceparameters are derived through exhaustive analytical study based on a Markovian modelof finite population, while the throughput optimization conditions are analytically investi-gated. Comparative results prove that the proposed asymmetric access protocol providesalmost 11% throughput enhancement and significant delay deterioration as compared toa relative protocol with symmetric access rights over the MCA. The proposed protocolstudy is accomplished by examining its performance for various number of control chan-nels and stations population.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

Nowadays, modern telecommunication networks poseto the network engineers the requirement for continuouslyincreasing bandwidth available to the end users to satisfythe data rates demands of today’s Internet traffic. Recentevolutions in optical networks technology have proventhat optical fibre is able to accommodate high bit rates thatreach to tens of Tbits/s [1], while each separate wavelengthis able to handle bit rates even more than 100 Gbits/s [2,3]due to the photonic components rate limitations. Althoughrecently up-coming technologies as the Nyquist-WDM

Terabit Superchannels [4,5] have arisen as the promisingtechniques for next generation optical networksimplementations, the Wavelength Division Multiplexing(WDM) technique is commonly used for dividing the enor-mous fibre bandwidth into several wavelengths (evenmore than 1000 [6]), each operating in lower data ratescompatible to the access node components.

Recent studies in literature propose the passive startopology as the most preferable one for WDM networksespecially at local area scale, while they introduce effectiveWavelength Division Multiple Access (WDMA) protocols toimprove the performance measures. Thus, an access strat-egy that optimizes the performance by eliminating themessage delay in a WDM network of passive star topologyis studied in [7]. Also, modern scheduling algorithms based

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P.A. Baziana, I.E. Pountourakis / Computer Networks 57 (2013) 1234–1252 1235

on the use of clustering techniques that aim to provide per-formance enhancement in passive star WDM networks arepresented in [8]. Moreover, a quality of service (QoS) pre-diction framework to accommodate different applicationswith various QoS requirements in WDM networks of pas-sive star topology is proposed in [9]. Particularly, diverseWDMA protocols have been studied to exploit the fibrebandwidth and to coordinate the access over it. The keyidea of most of them is to effectively face the main causesof packet loss that are: (1) the packets collisions over thecontrol and the data channels, and (2) the packets abortionat destination due to the receiver conflicts. Dominant rolein the WDMA strategies adoption plays the propagationdelay latency parameter since, as its value is getting higher,the overall performance decreases.

Especially, in literature some WDMA protocols intro-duce a specific control channel in order to exchange con-trol information prior to the data packet transmission[10]. In such WDMA protocols, the access over the datachannels is arranged according to the exchanged controlinformation in order to avoid data channels and receivercollisions. Another class of WDMA protocols proposessome pre-transmission coordination access schemes toreduce the collisions. Thus in [11], a collision-free pre-transmission coordination protocol is given to predict thetransmission requests and to eliminate the schedulingdelay time. Also, in [12] priority provision is taken in orderto support differentiated services, and some priority sched-uling algorithms are studied considering the data packetscollisions. On the other hand, the idea of the Multi-channelControl Architecture (MCA) that employs a number of con-trol channels, instead of a single control channel, for thecontrol information exchange in order to overcome theelectronic processing bottleneck [13] and to coordinatecollisions-free data packets transmission is proposed in[14–16]. Finally, although the effect of the propagation de-lay latency parameter on the system performance is criticalenough, very few studies take it under consideration whenscheduling the access algorithm. Thus, the studies of [14–16] properly exploit the propagation delay in order to im-prove performance as it is described below, while studieslike [17–20] assume the propagation delay influence onthe system efficiency.

Particularly, the studies of [14–16] consider the propaga-tion delay latency of the control packets transmission overthe MCA and properly exploit this time interval as theappropriate acknowledgment time in order to avoid thedata channels and receiver collisions and to improve perfor-mance. In more details, in the studies of [14–16] if a stationattempts transmission, it randomly selects one of the datachannels to transmit. Prior to the data packet transmission,it informs the other stations about its intention by transmit-ting a control packet over the MCA and waits the appropri-ate propagation delay time interval in order to be sure thatno other station has selected the same data channel fortransmission in order to avoid the collision. It can be under-stood that although the performance is enhanced grace tothe MCA exploitation, the system suffers from low datachannels utilization. This is due to the random way of thedata channel selection for transmission. Thus, there alwaysexist data channels collisions that reduce performance. In

order to avoid the forthcoming data channels collisions,the access algorithm of [14–16] allows the transmission ofonly one data packet per data channel and totally prohibitsthe transmission of the remaining data packets that have se-lected the same data channel, although there may existother available data channels for transmission. In this way,inefficient data bandwidth utilization is managed and con-sequently low throughput is achieved. A protocol proposalfor performance improvement is introduced in [21] thateliminates the data channel collisions stage of the above-mentioned transmission strategy by assigning a dedicateddata channel for transmission to each successful controlpacket transmission over the MCA. Thus, a limitedperformance enhancement is achieved.

In this paper, we explore the idea that the system effi-ciency of the studies [14–16] can be improved even more.Especially, we propose a WDMA protocol suitable for apacket based network. The proposed network architectureoccupies a number of wavelengths to interconnect a finitenumber of stations in a passive star topology. The numberof wavelengths is divided in two groups: (1) the wave-lengths that form the MCA and carry the control informa-tion, and (2) the remaining wavelengths that carry thedata packets. Unlike the studies of [14,15] that assume thatall stations may transmit their control packets over anyone of the MCA channels (and for this reason they adoptsymmetric access rights over the MCA), in this paper wefurther divide the sum of MCA channels into two groups:(1) the first group contains a specific MCA control channelthat is assigned to free stations (i.e. stations whose trans-mission buffer is empty) for control packets transmission,while (2) the second group includes the remaining MCAchannels that are used by backlogged stations (i.e. stationswhose transmission buffer is full with one data packet). Inthis way, we adopt asymmetric access rights over the MCAand we aim to essentially improve the performance, as it isproven in the Numerical Results section.

Moreover, in this study the adopted access strategyproperly faces the limited data channels utilization dueto random way that the data channels are selected in thestudies [14–16]. Thus in opposition to these studies, theproposed WDMA protocol eliminates the contention overthe data channels. This is achieved by appropriatelyexploiting the control information after the propagationdelay acknowledgement time, during a cycle period. Inother words, all stations run in a de-centralized way anappropriate algorithm for the assignment of an availabledata channel to each of the stations whose control packettransmission was successful over the MCA. In this way,there are no data channels collisions while the availablebandwidth is optimally exploited, as compared to the stud-ies of [14–16]. The adoption of the asymmetric accessrights over the MCA in conjunction with the data channelassignment algorithm that eliminates the data channelscollisions providing throughput improvement consist theinnovation of this study.

In order to explore the proposed WDMA protocol perfor-mance, a detailed Markovian model for finite population isdeveloped and the performance measures are analyticallyderived without approximations. The mathematical deriva-tion of the performance parameters values that optimize the

1236 P.A. Baziana, I.E. Pountourakis / Computer Networks 57 (2013) 1234–1252

system performance is given and the system performanceunder optimization conditions is explored. In this way, theproposed WDMA protocol extends the investigation of[22] that ignores the optimization conditions. The analysisconsiders the receiver collisions effect [14–16].

Our investigation is carried out as follows: The networkmodel and the assumptions are described in Section 2. InSection 3, the Markovian analysis is studied taking into ac-count the receiver collisions phenomenon, while the per-formance measures are analytically derived. The protocolperformance measures optimization is analytically ex-plored in Section 4. In Section 5, the numerical resultsare extensively studied for various numbers of controlchannels and stations, investigating the effect of the threeperformance parameters: (1) the receiver collisions, (2) thepropagation delay latency and (3) the asymmetric accessrights over the MCA. Finally, the concluding remarks areoutlined in Section 6.

2. Network model

We assume a passive star network, as Fig. 1 shows. Thesystem uses v + N (v = N) wavelengths kc1, . . . , kcv, kd1, -. . . , kdN to serve a finite number M of stations. The multi-channel system at wavelengths kc1, . . . , kcv forms theMCA, while the remaining N channels at wavelengths kd1, -. . . , kdN are used as data channels. The v control channels inthe MCA are numbered as control channel-1, control chan-nel-2, . . . control channel-v.

The proposed MCA network model is described as[CC]v-TT-[FR]v-[TR]. Each station has a tunable transmitterthat can be tuned to a wavelength in the set kc1,, . . . , kcv,-kd1,, . . . , kdN. The outcoming traffic of a station is connectedto an input of the passive star coupler. Each station uses vfixed receivers one for each control channel and one tun-able receiver to any of data channels kd1, . . . , kdN. Theincoming traffic to a station is splitted into v + 1 portionsby an 1 � (v + 1) WDMA splitter, as Fig. 1 illustrates. Espe-cially, the WDMA splitter operation at each station is to

Fig. 1. Passive star multi-wa

split the multiplexed optical signal that it is out-comingfrom the passive star coupler into v + 1 wavelengths: thev wavelengths constitute the MCA and they carry the con-trol packets that are received by the fixed receivers, whilethe remaining wavelength carries the possible data packetand it is received by the tunable receiver. Based on the re-cent technology evolutions, we assume that the networklosses that are inserted by the use of the WDMA splitterare negligible.

The transmission time of a control packet is used astime unit (control slot). The data packet transmission timenormalized in time units is L (data slot). The control packetincludes the source and the destination address of the rel-ative data packet. The normalized round trip propagationdelay time between any station to the star coupler huband to any other station is equal to R data slots (R � L timeunits). In other words, it is assumed that all stations areequally spaced far from the hub. Although this assumptionlacks from generality, it provides a simple fixed time framein order to obtain the proposed protocol performance mea-sure evaluation through exhaustive and accurate Markov-ian analysis.

Both control and data channels use the same time refer-ence which we call cycle. We define as cycle the time inter-val C that includes one time unit for control packetstransmission plus the normalized round trip propagationtime R � L plus the data packet transmission time L. Thus,as Fig. 2 presents, the cycle time duration is:

C ¼ 1þ ðRþ 1Þ � L time units ð1Þ

Time axis is divided into contiguous cycles of equal length.At any point in time each station is able to transmit at a gi-ven wavelength kT and simultaneously to receive from awavelength kR. Finally, for the tunable transceivers, we as-sume negligible tuning times and very large tunableranges. Although in real networks the tuning time of lasersis countable, it is not taken under consideration in ourprotocol analysis. This is because our study aims to analyt-ically study the asymmetric as compared to the symmetric

velength architecture.

Fig. 2. Cycle structure.


access rights over the MCA and to provide an estimation ofthe performance measures improvement based on theaccurate Markovian modelling.

Each station is equipped with a transmitter buffer withcapacity of one data packet. As it is defined in the Introduc-tion Section, if the buffer is empty the station is said to befree, otherwise it is backlogged. If a station is backloggedand generates a new packet, the packet is lost. Packetsare generated independently at each station following ageometric distribution, i.e. a packet is generated at each cy-cle with probability p. A backlogged station retransmits theunsuccessfully transmitted packet following a geometricdistribution with probability p1. Free stations that unsuc-cessfully transmit on the control channels or their datapackets are rejected at destination due to receiver colli-sions during a cycle are getting backlogged on the next cy-cle. A backlogged station is getting free at the next cycle ifit manages to retransmit without collision over a controlchannel and if its data packet retransmission is not aborteddue to receiver collisions.

2.1. Access strategy

At the beginning of each cycle if a station has to send adata packet, it informs the other stations by sending a

control packet over the MCA. Especially, free stationstransmit the control packets with probability p over con-trol channel-1, while backlogged stations retransmit thecontrol packets with retransmission probability p1 onone of the remaining v-1 retransmission channels, i.e. con-trol channel-2, control channel-3, etc. Each of the remain-ing v-1 retransmission channels is selected with equal andconstant probability Pi = 1/(v � 1). The control packetscompete according to the Slotted Aloha scheme to gain ac-cess over the (v-1) channels. The station continuouslymonitors the MCA with its fixed receivers. The outcomeof its control packet is known R � L time units later(acknowledgement time) because of the broadcast natureof the control channels.

After the end of this period, the station is informedabout the transmission claims of the stations whose con-trol packets have been successfully transmitted and whichhave won the receiver collision competition. At that timeinstant, a data channel assignment algorithm (DCAA) is ap-plied to all stations. This means that each station runs in ade-centralized way an appropriate algorithm for theassignment of an available data channel to each stationwhose control packet has been successfully transmittedand which have won the receiver collision competition(we can imagine several assignment rules, as the corre-

Fig. 3. Simulation diagram for a station actions for transmission during a cycle.


spondence of the control channel id to the data channel id,etc). Since, the control channels are equal than the datachannels (v = N), it is evident that all stations whose con-trol packets have been successfully transmitted gain accessto the data channels and an available data channel is as-signed to them.

The flow of the proposed access protocol is given in Fig. 3which illustrates the simulation diagram of the actions per-formed by a station for transmission during a cycle.

2.2. Reception strategy

After the data packet transmission, the destinationwaits R � L time units while the data packet is transmitted.Then it adjusts its tunable receiver to the data channelspecified by the DCAA for reception.

3. Protocol Markovian analysis

The system performance can be described by a discretetime Markov chain. We denote the state of the examinedsystem by Xt, t = 0, 1, 2, . . . ,where Xt = 0, 1, . . . ,M is thenumber of backlogged stations at the beginning of each cy-cle. Let:

Ht = The number of new packets arrivals at the begin-ning of a cycle, t = 0, 1, 2, . . .

At = The number of correctly received data packets atthe end of a cycle, t = 0, 1, 2, . . .

S(k) = The number of success over the (v-1) retransmis-sion channels, given that k backlogged stations attemptto transmit during a cycle, 0 6 S(k) 6min(v � 1,k).F(m) = The number of success over the control channel-1, given that m free stations attempt to transmit duringa cycle, where: m = 0, 1, . . . , M and

FðmÞ ¼ 1; if m ¼ 10; otherwise

�.

A(n) = The number of correctly received data packets atdestination, conditional that n successful (re)transmis-sions occurred during a cycle, 1 6 A(n) 6 S(k) for everyS(k) > 0.

The probability Pr[S(k) = n], of n successes over the (v-1)retransmission channels from k retransmissions during acycle is given by [23]:

Pr½SðkÞ ¼ n� ¼ ð�1Þnðv �1Þ!k!

ðv �1Þkn!

Xminðv�1;kÞ

j¼n

ð�1Þjðv �1� jÞk�j

ðj�nÞ!ðv �1� jÞ!ðk� jÞ!

ð2Þ

where 0 6 n 6min (v-1,k) and k � n – 1.The probability Pr[A(n) = s], of s correctly received

packets at destination from n successfully (re)transmittedstations during a cycle is given [24] by:


Pr½AðnÞ ¼ s� ¼M

s

� �Xs

i¼0

ð�1Þis

i

� �s� iM

� �n

ð3Þ

where 1 6 s 6min(v � 1,n) for every n P 1.We define the function U(x,y,z) as the product of the

probability of y successes from x transmissions over the

Pij ¼

Q 0;i

Xminði;v�1Þ

n¼i�j

qn;i

Xn

s¼i�j

Uðn; s; i� jÞ þXi

n¼vqn;i

Xv�2

s¼i�j

Uðn; s; i� jÞ !

þQ 1;i

Xminði;v�1Þ

n¼i�j

qn;i

Xn

s¼i�j

Uðn; sþ 1; i� jþ 1Þ þXi

n¼vqn;i

Xv�2

s¼i�j

Uðn; sþ 1; i� jþ 1Þ !

þXminðM�i;v�1þj�iÞ

m¼2

Qm;i

Xminði;v�1Þ

n¼i�jþm

qn;i

Xn

s¼i�jþm

Uðn; s; i� jþmÞ

þXminðM�i;vþj�i�2Þ

m¼2

Qm;i

Xi

n¼vqn;i

Xv�2

s¼i�jþm

Uðn; s; i� jþmÞ

8>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>:

ð11Þ

v � 1 retransmission control channels, times the probabil-ity of z correctly received packets at destination during acycle. It is:

Uðx; y; zÞ ¼ Pr½SðxÞ ¼ y�Pr½Aðyþ kÞ ¼ z� ð4Þ

where

k ¼1; if there is a success over channel-10; otherwise

�ð5Þ

We define the conditional probability qin that i out of nbacklogged stations attempt to retransmit with probabilityp1 during the cycle. qin is given by:

qin ¼ binðn; i;p1Þ ð6Þ

where

binði; j;pÞ ¼i

j

� �pjð1� pÞi�j

; i P j ð7Þ

Similar, the conditional probability Qin that i out of (M � n)free stations attempt to transmit with probability p duringthe cycle, is defined as:

Q in ¼ binðM � n; i; pÞ ð8Þ

The Markov chain Xt t = 1, 2. . . is homogeneous, aperi-odic and irreducible. The one step transition probabilitiesare given by Pij = (Xt+1 = j—Xt = i), where:

Case A: if j < i � (v � 1) i.e. if the number of backloggedstations decreases more than v � 1 then:

Pij ¼ 0 ð9Þ

Case B: if j = i � (v � 1) i.e. if the number of backloggedstations decreases equal to v � 1 then:

Pij ¼ qv�1;iðQ 0;iUðv � 1;v � 1;v � 1Þþ Q 1;iUðv � 1; v; vÞÞ ð10Þ

Case C: if i � (v � 1) < j < i + 1 i.e. if the number of back-logged stations decreases less than v � 1 then:

Case D: if j = i + 1 i.e. if the number of backlogged sta-tions increases about 1 then:

Pij ¼

XminðM�i;v�1Þ

m¼1

Q mþ1;i

Xminði;v�1Þ

n¼m

qn;i

Xn�m

s¼0

Uðn;mþ s;mÞ

þXminðM�i;v�2Þ

m¼1

Q mþ1;i

Xi

n¼vqn;i

Xv�m�2

s¼0

Uðn;mþ s;mÞ

8>>>>><>>>>>:

ð12Þ

Case E: if j > i + 1 i.e. if the number of backlogged sta-tions increases more than 1 then:

Pij ¼

XminðM�i;v�1Þ

m¼0

Q mþj�i;i

Xminði;v�1Þ

n¼m

qn;i

Xn�m

s¼0

Uðn;mþ s;mÞ

þXminðM�i;v�2Þ

m¼0

Q mþj�i;i

Xi

n¼vqn;i

Xv�m�2

s¼0

Uðn;mþ s;mÞ

8>>>>><>>>>>:

ð13Þ

3.1. Performance measures

Since the Markov chain {Xt, t = 0, 1, 2, . . .} is ergodic, thesteady state probabilities can be obtained by solving thesystem of the following linear equations:

p ¼ pP ð14Þ

and:

XM

i¼0

pi ¼ 1 ð15Þ

where P is the transition matrix with elements the proba-bilities Pij and p is a row vector with elements the steadystate probabilities pi.

The conditional throughput S(i) is the expected value ofsuccessful receptions at destination during a cycle, giventhat the number of the backlogged stations at the begin-ning of the cycle is i, i.e:

SðiÞ ¼ E½AtjXt ¼ i� ð16Þ


SðiÞ ¼

Xminði;v�1Þ

k¼1

kð1� Q 1;iÞXminði;v�1Þ

n¼k

qn;i

Xv�1�k

s¼0

Uðn; kþ s; kÞ

þXminði;v�1Þ

k¼1

kQ1;i

Xi

n¼vqn;i

Xv�1�k

s¼0

Uðn; kþ s; kÞ

þXminði;v�2Þ

k¼1

k ð1� Q1;iÞXi

n¼vqn;i

Xv�k�2

s¼0

Uðn; kþ s; kÞ !

þXminðiþ1;vÞ

k¼1

kQ1;i

Xminði;v�1Þ

n¼0

qn;i

Xv�k

s¼0

Uðn; kþ s; kÞ !

8>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>:

ð17Þ

The steady state average throughput S is given by:

S ¼ LC

E½SðiÞ� ¼ LC

XM

i¼0

SðiÞpi ð18Þ

The steady state average number B of backlogged stationsis given by:

B ¼ E½i� ¼XM

i¼0

ipi ð19Þ

The conditional input rate Sin(i) is the expected number ofnew packet arrivals during a cycle given that the back-logged stations at the beginning of the cycle are i:

SinðiÞ ¼ E½HtjXt ¼ i� ¼ ðM � iÞp ð20Þ

The average input rate Sin is:

Sin ¼XM

i¼0

ðM � iÞppi ð21Þ

Under steady state conditions the average input rate Sin

should equal to the average throughput S, i.e. it is:

S ¼ ðM � BÞp ð22Þ

The delay D is defined as the average number of time slotsthat a packet has to wait until its successful transmission.Delay is calculated by Little’s formula:

D ¼ C þ CBS

ð23Þ

We define the throughput per data channel Src in steadystate as the number of the successfully transmitted datapackets per data channel during a cycle. It is given by:

Src ¼SN

ð24Þ

3.2. Probability of packet rejection Prej

The probability of packet rejection at destination Prej isevaluated as the ratio of the expected number of packetsrejections per cycle due to buffer overflow, to the expectednumber of successfully transmitted packets over the multi-channel system per cycle in steady state. So, we get:

PrejðpÞ ¼SccðpÞ � SðpÞ

SccðpÞð25Þ

where Scc(p) is the system throughput if we ignore the re-ceiver collisions effect and we assume only the channelcollisions. Scc(p) can be extracted by [25].

4. Performance optimization

In order to achieve the optimum system performance,we consider the followings:

The conditional throughput Sb(i) from the (v � 1)retransmission control channels that are used by back-logged stations is given by [25]:

SbðiÞ ¼ ip1 1� p1

v � 1

� �i�1ð26Þ

Similar, we define the conditional throughput Sf(i) from thecontrol channel-1 that is used by free stations as:

Sf ðiÞ ¼ ðM � iÞpð1� pÞM�i�1 ð27Þ

We define the conditional throughput Sv(i) from the v con-trol packets as the sum of Sb(i) and Sf(i), that is:

SvðiÞ ¼ ip1 1� p1

v � 1

� �i�1þ ðM � iÞpð1� pÞM�i�1 ð28Þ

4.1. An approximate analysis

We consider that S(k) + F(m) = n control packets are suc-cessfully transmitted over the v control channels during acycle, given that the state of the system is i. Since v = N,it is obvious that the corresponding n data packets are suc-cessfully transmitted over the N data channels during a cy-cle. We assume that the n data packets are uniformlydistributed among the M stations (for sake of simplicityof the analysis, we consider that a station may send pack-ets to itself). Thus, the random distribution in M stationsgives Mn arrangements each with probability M�n.

Let PM0(n, i) be the conditional probability that no onefrom the n successfully transmitted data packets has asdestination the station X. Thus, the n data packets shouldbe destined to the remaining (M � 1) stations in (M � 1)n

different ways. Then, PM0(n, i) can be written as [24]:

PM0ðn; iÞ ¼1

Mn ðM � 1Þn ¼ 1� 1M

� �n

ð29Þ

In steady state it is:

E½SðkÞ þ FðmÞ ¼ n� ¼ SvðiÞ ð30Þ

Consequently, in steady state (29) is written as:

PM0ðiÞ ¼ 1� 1M

� �Sv ðiÞ

ð31Þ

We define the conditional probability PM(i) that one datapacket with destination X is received correctly without col-lisions during a cycle in steady state. It is:

PMðiÞ ¼ 1� PM0ðiÞ ¼ 1� 1� 1M

� �Sv ðiÞ

ð32Þ

Let HM{Sv(i)} be the random variable representing thenumber of different stations selected as destination, giventhat Sv(i) is the conditional output rate of successful(re)transmitted control packets over the v control chan-nels, during a cycle in steady state. Also, we define thePr[HM{Sv(i)} = y] as the conditional probability that y differ-


ent stations have been selected as destination during a cy-cle in steady state. It is:

Pr½HMfSvðiÞg ¼ y� ¼M

y

� �ðPMðiÞÞyð1� PMðiÞÞM�y ð33Þ

We define the conditional throughput S(i) at the destina-tions as:

SðiÞ ¼ E½Pr½HMfSvðiÞg ¼ y�� ¼ MPMðiÞ ð34Þ

Substituting (32)–(34), we get:

SðiÞ ¼ M 1� 1� 1M

� �Sv ðiÞ !

ð35Þ

4.2. Optimum retransmission probability p1�opt

For each cycle, the system state is denoted by i. Theoptimum retransmission probability p1�opt is obtained bysetting the first derivative of (35) with respect to p1 equalto zero. It is:

@SðiÞ@p1

¼ 0) @SvðiÞ@p1

¼ 0 ð36Þ

Since 0 6 p1�opt 6 1, we get:

p1�opt ¼

v�1i ; i > v � 1

1; 0 < i 6 v � 10; i ¼ 0

8><>: ð37Þ

5. Performance evaluation

In this section, the numerical solution of the proposedprotocol is presented, while the throughput optimization

Fig. 4. Throughput per data channel Src vs birth probability p f

conditions of (37) are followed. Our goal is to explore theeffect on the proposed protocol performance of three mainprotocol characteristics: (1) the receiver collisions consid-eration, (2) the propagation delay latency exploitation,and (3) the asymmetric access rights assumption overthe MCA, for diverse number of control channels in theMCA and system population. In this way, a complete studyof the proposed protocol is given, while its advantages toenhance performance as compared with other protocolsare investigated.

5.1. Receiver collisions effect

In order to study the influence of the receiver collisionson the proposed protocol, we chose to compare its perfor-mance measures with those of the protocol that ignoresthe destination conflicts and its performance measuresare extracted by [25].

Fig. 4 illustrates the throughput per data channel Src

curves versus the birth probability p for M = 30 stations,R = 5 time units, and various number v of control channelsin the MCA, v = 5, 10,15,20, for the cases that we considerthe receiver collisions and we ignore them. As it is ob-served for the proposed protocol that takes under consid-eration the receiver collisions phenomenon, the Src is adecreasing function of v, for all p. This is because as v in-creases, the number of successfully transmitted controlpackets either by free stations over the control channel-1or by backlogged stations over the remaining control chan-nels of the MCA, is getting higher. This fact gives rise to theoutput from the MCA and consequently increases the ac-tual throughput from all the data channels. For this reason,the Src is getting lower. This behaviour can be observed forexample for p = 0.9, the Src is: 0.058 control packets/cycle

or M = 30 stations, R = 5 time units, and v = 5, 10, 15, 20.


for v = 5, 0.054 control packets/cycle for v = 10, 0.053 con-trol packets/cycle for v = 15, and 0.052 control packets/cy-cle for v = 20. Also, it can be noticed that for these highoffered load conditions (for high p values), the Src achievedhas almost identical values for high values of v, v = 10, 15,20. This is grace to the fact that the numerical results arecomputed assuming the performance optimization condi-tions, i.e. the p1�opt. For this reason, the throughputachieved reaches high values for all v. The effect of thenumber v variation on the Src can be better explored forlower offered load conditions, for example for p = 0.25where: Src is: 0.058 control packets/cycle for v = 5, 0.054control packets/cycle for v = 10, 0.05 control packets/cyclefor v = 15, and 0.041 control packets/cycle for v = 20.

Also, in Fig. 4 the influence of the receiver collisionsphenomenon on the Src is studied. It is observed that forall values of v, the proposed protocol which assumes thereceiver collisions is less efficient as compared with thatwhich ignores them. This means that the analysis of thelatest protocol over-estimates the throughput since it doesnot consider a realistic parameter that plays a significantrole to the system performance: the receiver collisions.On the contrary, the proposed protocol analysis that takesunder consideration the receiver collisions effect derives alower Src value, giving a more realistic protocol study. Spe-cifically, in Fig. 4 it is noticed that for fixed M and for a gi-ven value of p, the difference between the curves thatconsider the receiver collisions and those that ignore them,is getting wider as v increases. The explanation comes fromthe fact that as v increases, the control channels collisions(either by free or by backlogged stations) over the MCA arereduced. This fact causes the increase of the output from

Fig. 5. Backlogged stations B of vs birth probability p for

the MCA and gives rise to the receiver collision phenome-non. This behaviour is observed for example for p = 0.9,where the Src value if we assume the receiver collisionsas compared with the relative value if we ignore them isreduced about: 1.7% for v = 5, 3.7% for v = 10, 7.5% forv = 15, and 11.5% for v = 20.

The above discussion about the effect on the proposedprotocol performance of the receiver collisions can be val-idated in Fig. 5 that presents the number of backlogged sta-tions B curves versus the birth probability p for M = 30,R = 5, and v = 10, 15, 20, for the cases that we considerthe receiver collisions and we ignore them. As it is noticed,for the proposed protocol the number B is a decreasingfunction of v. This is because as v increases, the numberof control packets that are successfully transmitted overthe MCA is getting higher, as previously discussed. In thiscase, although the number of data packets that are des-tined to the same destinations is getting higher giving riseto the rejections due to receiver collisions, the overallnumber of backlogged stations is getting lower, as Fig. 5presents. For example, for p = 0.9 the B reaches: 27 stationsfor v = 10, 24.5 stations for v = 15, and 23.2 stations forv = 20. Also, it is observed that for fixed M and for a givenvalue of p, the difference between the curves that considerthe receiver collisions and those that ignore them, is get-ting wider as v increases. This fact is an immediate resultof the above discuss and proves that as v increases thenumber of successfully transmitted control packets overthe MCA is higher, giving rise to the receiver collisionseffect.

Moreover, this behaviour can be observed in Fig. 6 thatdepicts the rejection probability Prej curves versus the birth

M = 30 stations, R = 5 time units, and v = 10, 15, 20.

Fig. 6. Packet rejection probability Prej vs birth probability p for M = 30 stations, R = 5 time units, and v = 10, 15, 20.

Fig. 7. Delay D vs throughput per data channel Src for M = 30 stations, R = 5 time units, and v = 10, 15, 20.


probability p for M = 30, R = 5, and v = 10,15,20. For exam-ple, for p = 0.9 the Prej reaches 0.05 for v = 10, while it in-creases to: 0.079 for v = 15, and 0.108 for v = 20.

The overall performance is studied in Fig. 7 that showsthe delay D curves versus Src for M = 30, R = 5, and v = 10,15, 20. As it is shown for the same Src value, as v increases

Fig. 8. Throughput per data channel Src vs birth probability p for v = 10 control channels, R = 5 time units, and M = 20, 30, 40.

Fig. 9. Packet rejection probability Prej vs birth probability p for v = 10 control channels, R = 5 time units, and M = 20, 30, 40.


the system delay decreases. This is due to the fact that as vincreases the number of backlogged stations is gettinglower, as Fig. 5 depicts. This means that the time that thesystem needs to serve the backlogged stations is gettinglower causing the total delay D reduction. On the other

hand, Fig. 7 verifies the results of Fig. 4: as v increasesthe maximum Src achieved is getting lower. Finally, inFig. 7 the results of the previous figures study about the ef-fect of the receiver collisions are validated. In other words,for the same offered load conditions the proposed protocol

Fig. 10. Delay D vs throughput per data channel Src for v = 10 control channels, R = 5 time units, and M = 15, 30, 45.

Fig. 11. Backlogged stations B vs birth probability p for v = 10 control channels, R = 5 time units, and M = 20, 30, 40.


that considers the receiver conflicts provides lowerthroughput and higher delay as compared with that whichignores them, for all values of v. Finally, it is worth-mentioning that both the system that considers and the

system that ignores the receiver collisions are unstablebecause there are two different values of D associated witha given Src value, as Fig. 7 shows. This behaviour consti-tutes an identical attribute of the random multiple access


protocols. On the other hand, the slope of the curves athigh values of Src decreases as the number of control chan-nels v increases, which gives robustness in the stability andmanoeuvrability to load demands.

On the contrary, the reverse behaviour is observed incase that the population M varies. Fig. 8 illustrates the Src

curves versus the birth probability p for v = 10 controlchannels, R = 5 time units, and various number M of sta-tions, M = 20,30,40, for the cases that we consider the re-ceiver collisions and we ignore them. As Fig. 8 shows, forthe proposed protocol as M increases the Src value in-creases too, for fixed v and p. This result is explained bythe fact that as M increases the offered load to the MCA in-creases too, which causes increase of the number of controlpackets collisions either by free stations over the controlchannel-1 or by backlogged stations over the remainingcontrol channels. For this reason the throughput from allthe MCA is getting lower. On the other hand, as M increasesthe successfully transmitted data packets are distributed tomore destination stations, giving rise to the throughput aswell as to the Src achieved. This behaviour can be noticedfor example for low p values, for p = 0.1 where Src reaches0.025 data packets/cycle for M = 20, while it increases to:0.038 data packets/cycle for M = 30 and 0.053 data pack-ets/cycle for M = 40. As we discussed in Fig. 4, for high pvalues the Src value achieved is almost similar for all M.The explanation is based on the fact that we use the opti-mum retransmission probability p1�opt and it is similar tothe Fig. 4 comments.

Also, in Fig. 8 we notice the effect of the receiver colli-sions phenomenon. Thus, it is presented that as M in-creases the difference between the curves that considerthe receiver collisions and those that ignore them, is

Fig. 12. Delay D vs throughput per data channel Src for M = 30 st

getting narrower. This is because, as M increases the con-trol channels collisions over the MCA increases too. In thiscase, the number of data packets that are transmitted overthe data channels decreases, while they are destined tomore destinations as M increases. This fact has as immedi-ate result the reduction of the number of rejections at des-tination. In other words, the influence of the receivercollisions phenomenon is less significant with the increaseof M. This can be observed for example for p = 0.9 wherethe Src reduces due to the receiver conflicts about: 5.8%for M = 20, 3.8% for M = 30 and 1.2% for M = 40.

The above discuss explains the variation of the packetrejection probability Prej curves versus the birth probabilityp for v = 10, R = 5, and M = 20,30,40 which is depicted inFig. 9. Especially, for p = 0.9 the Prej reaches 0.072 forM = 20, while it is reduced to 0.05 for M = 30 and 0.037for M = 40.

Finally, the overall performance variation can be stud-ied in Fig. 10 that depicts the delay D curves versus theSrc for v = 10, R = 5, and M = 15,30,45, for the cases thatwe consider the receiver collisions and we ignore them.It is observed that for fixed v and the same offered loadconditions, the system delay D increases with the increaseof M. This is because, as M increases the control channelscollisions are getting higher, since the offered load is high-er. This fact has as result the increase of the number of B inthe system, as M increases. This behaviour can be studiedin Fig. 11 that shows the B curves versus the birth probabil-ity p for v = 10, R = 5, and M = 20,30,40. This means that asM increases the time that a packet has to wait until its suc-cessful transmission is getting higher, giving rise to thesystem delay D value. Concluding as Fig. 10 presents, boththe system that considers and the system that ignores the

ations, v = 10 control channels, and R = 0, 5, 10 time units.

Fig. 13. Study [7]: Simulation diagram for a station actions for transmission during a cycle.


receiver collisions are unstable. This is understood since fora given Src value there are two different D values. As it ismentioned above, this behaviour is met in protocols withrandom multiple access. As it is shown, the slope of thecurves at high values of Src decreases as the number of sta-tions M increases, which supports the system stability.

5.2. Propagation delay latency effect

It is obvious that the proposed protocol performancedepends on the network dimensions which determinethe propagation delay R value. This means that as the aver-age distance among the stations increases the R is gettinghigher and its influence to the system performance is morecritical. This is because in the proposed protocol theacknowledgement time interval R � L in order to coordi-nate collisions-free transmission is a linear proportionalof the R value. In other words, as R increases the cycleduration C increases too, as (1) proves. This has as animmediate result that as R increases the cycle percentagethat the system is involved into successful transmissionsis getting lower, causing Src reduction. This conclusion

can be also validated by (18). Moreover, it is understoodthat as R increases the time that the system has to wait un-til the data packets successful transmission is getting high-er, since the cycle duration C increases. This fact causessignificant delay D increase. These comments are verifiedin Fig. 12 that illustrates the D curves versus the Src forM = 30, v = 10, and various values R of propagation delay,R = 0, 5, 10, for the case that we consider the receivercollisions.

5.3. Asymmetric access rights effect

In the following figures, we explore the effect of theadoption of the asymmetric access rights over the MCA.In order to quantify its benefits and study the performanceimprovement that it provides, we choose to compare theproposed asymmetric access rights protocol with a relativeone studied in [7]. This latest protocol adopts the MCA too,but in opposition to the proposed protocol that assumesasymmetric access over the MCA, it assumes symmetric ac-cess over it, i.e. each station selects with equal probabilityPi = 1/v one of the MCA channels for transmission. Also, in

Fig. 14. Proposed asymmetric vs symmetric access protocol: Throughput per data channel Src vs birth probability p for M = 30 stations, R = 5 time units, andv = 10, 15, 20.

Fig. 15. Proposed asymmetric vs symmetric access protocol: Delay D vs throughput per data channel Src for M = 30 stations, R = 5 time units, and v = 10, 15,20.


opposition to the proposed protocol that properly assignsthe data channels among the stations to avoid data channelcollisions, it considers the probability of data channel col-

lisions and the consequent packet loss. For a meaningfulcomparison, the flow of the access protocol of [7] is givenin Fig. 13 which illustrates the simulation diagram of the


actions performed by a station for transmission during acycle.

Fig. 14 shows the Src versus p for M = 30, R = 5, v = 10,15, 20 for the case that we consider the receiver collisions,for the proposed asymmetric access rights protocol and therelative one of [7]. The comparison clearly presents thebenefits provided by the asymmetric access and the DCAA,as a function of the number v. As it is noticed, the proposedprotocol provides significant performance improvementfor all values of v. For example, for p = 0.9, the Src improve-ment is almost similar for all values of v and reaches 10.5%.For lower offered load conditions (smaller p values) the Src

improvement seems to be a decreasing function of v. Inother words, for example for p = 0.3, the Src improvementreaches 10.5% for v = 10, 6.2% for v = 15 and 1.1% forv = 20. This is because as v increases for high offered load,the packet rejection probability is getting higher, as Fig. 6presents. This means that there are more backlogged sta-tions competed for the (v � 1) MCA channels. In this case,the existence of a single control channel explicitly accessedby the free stations, as in the proposed protocol, provideshigher probability for successful control packet transmis-sion by free stations over it providing throughput improve-ment, which is proven to be almost equal for all v values.On the contrary for low offered load, as v increases the sys-tem provides less backlogged stations as Fig. 5 shows, sincethe control channels collisions probability over the (v � 1)MCA channels is lower. This fact provides increase of thefree stations number, which results to more free stationscontrol channel collisions over the control channel-1 andconsequent lower throughput improvement, as comparedto the symmetric access protocol.

Fig. 16. Proposed asymmetric vs symmetric access protocol: Throughput per daunits, and M = 20, 30, 40.

Also, these results can be extracted by Fig. 15 that pre-sents the D curves versus the Src for M = 30, R = 5 andv = 10, 15, 20 for the case that we consider the receiver col-lisions, for the proposed asymmetric access rights protocoland the relative one of [7]. Indeed, as it is shown the pro-posed asymmetric access rights protocol provides highermaximum throughput values as compared with the proto-col of [7], while the throughput improvement seems to beidentical (almost 10.5%) for all v values, as in Fig. 14. More-over, the delay D variation is conformed to the previous re-marks. In other words, Fig. 15 depicts that for low offeredload, the proposed protocol provides higher delay than thisof the protocol of [7]. This is due to the fact that in this casethe number of free stations attempting transmission is lowenough, which leads to under-utilization of the controlchannel-1 that is explicitly assigned to them. This meansthat, in opposition to the symmetric access protocol of[7] that gives the opportunity to all stations to select oneof the v control channels for transmission, the proposedasymmetric access protocol prohibits the exploitation ofthe control channel-1 by backlogged stations although thischannel may be unutilized by free stations during some cy-cles. This fact gives rise to the backlogged stations numberand consequently to the system delay, as compared withthe symmetric access protocol. On the other hand, for highoffered load, the proposed asymmetric access protocol pro-vides significant decrease of the delay D, as Fig. 15 depicts.This is grace to the fact that for high load the number ofbacklogged stations is high enough, while the number offree stations competing for access over the control chan-nel-1 is lower. This fact has as an immediate result thatthe transmission probability over the control channel-1

ta channel Src vs birth probability p for v = 10 control channels, R = 5 time

Fig. 17. Proposed asymmetric vs symmetric access protocol: Delay D vs throughput per data channel Src for v = 10 control channels, R = 5 time units, andM = 20, 30, 40.

Fig. 18. Study of receiver collisions and asymmetric access rights effect: Src(max) for v = 10, 15, 20 and M = 20, 30, 40, R = 5.


that is explicitly assigned to free stations is getting higher,giving rise to system throughput and reducing the timethat the system has to serve the incoming traffic, i.e. reduc-ing the total delay D experienced, as compared with thesymmetric access protocol of [7]. In other words, the ben-efits of the proposed asymmetric access protocol as com-pared with the symmetric access one are more noticeableunder high offered load, while it is an engineer decisionto determine the operation conditions in order to obtainthe desired throughput improvement level.

Finally as it is discussed in Fig. 7, both the systems withsymmetric and asymmetric access rights over the MCA are

unstable since there are two different values of D associ-ated with a given Src value. This fact can be representa-tively studied in Fig. 15. The explanation is based on therandom multiple access nature of the proposed protocoland it is similar to the comments on Fig. 7.

The above remarks are validated in the following figuresthat study the asymmetric access rights effect on thesystem performance as a function of M. Thus, Fig. 16illustrates the Src versus p for v = 10, R = 5, M = 20, 30, 40for the case that we consider the receiver collisions, forthe proposed asymmetric access rights protocol and therelative one of [7]. As Fig. 16 shows, for a wide offered load


range (from p = 0.3 to p � 1) the proposed asymmetric ac-cess protocol provides almost 10.5% Src improvement forall M values as compared with the symmetric access proto-col of [7]. The explanation is similar to the comments inFig. 14. For low offered load (for example p = 0.1) the rela-tive Src improvement reaches almost 0.5% for all M values.

On the other hand, the delay D variation is studied inFig. 17 which shows the D curves versus the Src forv = 10, R = 5, M = 20, 30, 40 for the case that we considerthe receiver collisions, for the proposed asymmetric accessrights protocol and the relative one of [7]. The commentsare similar to these of Fig. 15. In other words, the inferior-ity of the proposed asymmetric access rights protocol isproven to be under high offered loads, where the assign-ment of a specific control channel to free stations for trans-mission gives higher transmission probability to them ascompared with the symmetric access protocol of [7]. Thisis the reason why, under high load the proposed asymmet-ric access right protocol provides essentially reduced D val-ues as compared with the symmetric access protocol of [7].Finally as Fig. 17 presents, both the systems with symmet-ric and asymmetric access rights over the MCA are unsta-ble. The explanation is similar to the comments on Fig. 10.

Finally, the above results that are extracted from thesub-sections 5.1 and 5.3 are validated in the followingFig. 18 that presents the maximum throughput valueSrc(max) for various numbers of M and v and R = 5, for threeWDMA protocols: (1) the proposed asymmetric accessrights protocol that ignores the receiver collisions, (2) theproposed asymmetric access rights protocol that takes un-der consideration the receiver collisions, and (3) the sym-metric access rights protocol of [7] that takes underconsideration the receiver collisions. It is obvious that thecomparison between the above protocol cases 1 and 2gives the impact of the receiver collisions phenomenonon the proposed asymmetric access rights protocol, whilethe comparison between the protocol cases 2 and 3 givesthe impact of the asymmetric access rights considerationover the MCA in conjunction with the DCAA, for variousnumbers of M and v.

6. Conclusions

In this paper, we investigate the conditions for thethroughput optimization and the performance improve-ment of a WDM passive star network. The proposed net-work architecture exploits the propagation delay latencyas acknowledgement time to adopt a synchronous trans-mission WDMA protocol that uses the MCA and suppliesasymmetric access rights over it. The proposed asymmetricaccess rights protocol provides significant performanceimprovement as compared with the symmetric access casegrace to the adopted access strategy over the MCA. In otherwords, the asymmetric access restricts the control packetscollisions of backlogged stations over a dedicated controlchannels group, giving rise to the throughput from free sta-tions and consequently to the total system throughput,especially under high load conditions.

A Markovian model of finite population is adopted toderive the performance measures through exhaustive anal-

ysis, while the performance optimization conditions aremathematically defined. The detailed study shows thatthe proposed asymmetric access protocol performance de-pends on the following network parameters: the numberof control channels on the MCA, the system populationand the propagation delay latency value. Especially, thenumerical results prove that the proposed protocolthroughput per data channel is a decreasing function ofthe number of control channels in the MCA, while it is anincreasing function of the system population. Finally, thecomparative study demonstrates that the considerationof the receiver collisions phenomenon in the analysis givesa realistic base for performance evaluation, while its effectdepends on the number of control channels in the MCA andthe system population.

The main innovation of the proposed protocol is theadoption of the asymmetric access rights over the MCA.Comparative study proves that this adoption providesmore than 10% of throughput improvement and essentialdelay reduction under high offered load conditions for allnumber of control channels and system population, ascompared with the protocol of [7] that adopts symmetricaccess rights over the MCA. For this reason, the proposedasymmetric access rights protocol can provide the networkengineers with useful analytical tools and ideas of accessstrategies in order to improve even more the systemperformance.

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Peristera A. Baziana received the Diplomadegree of Electrical and Computer Engineerfrom the University of Patras, Greece in 1998.From 1999 to 2002, she has participated inresearch programs of the Greek PTT Organi-zation (O.T.E.) as a researcher of University ofPatras. In 2008 she received the Ph.D. degreeat the Communications, Electronic and Infor-mation Engineering Division, School of Elec-trical and Computer Engineering of NationalTechnical University of Athens (N.T.U.A),Greece at the field of architectures and pro-

tocols for optical networks. Since 2008, she has been working as a seniorpost doctoral researcher at the Optical Networks Laboratory, School ofElectrical and Computer Engineering of N.T.U.A, Greece. Her current
research interests include optical communications, OBS networks, MACprotocols and queuing analysis. She is member of IEEE and the TechnicalChamber of Greece.
Ioannis E. Pountourakis (M’90) is a Professorat the Communications, Electronic and Infor-mation Engineering Division, School of Elec-trical and Computer Engineering of NationalTechnical University of Athens (N.T.U.A). Hisresearch interests include Optical Communi-cation Networks, Network Architecture andProtocols, Performance Evaluation and Sta-bility. He has taught several undergraduateand graduate courses at NTUA, supervisedmany doctoral students working in the areasof queuing analysis of contention resolution

mechanisms in local area networks and optical networks, WDM networkdesign, optical networks architectures, analysis of data link layer proto-cols, evaluation of performance of computer systems, etc. and has been
reviewer in International Journals, Conferences, and research projectproposals. He has participated and organized many International Con-ferences. He has also participated in several RACE projects and in severalnational research programs dealing with communication networks. He ismember of IEEE and the Greek society of Computer Science.

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An access protocol for efficiency optimization in WDM networks: A propagation delay and collisions avoidance analysis