Optimized traffic flow assignment in multi-homed, multi ... · PDF fileOptimized trafﬁc ﬂow assignment in multi-homed, multi-radio mobile ... and radio access bearer ... is multi-homed

Computer Networks xxx (2010) xxx–xxx

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Computer Networks

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Optimized traffic flow assignment in multi-homed, multi-radiomobile hosts

Vassilis E. Zafeiris ⇑, E.A. GiakoumakisDepartment of Informatics, Athens University of Economics and Business, Patission 76, Athens 104 34, Greece

a r t i c l e i n f o

Article history:Received 30 September 2009Received in revised form 6 September 2010Accepted 3 November 2010Available online xxxxResponsible Editor: R. Sivakumar

Keywords:Traffic flow assignmentPower managementLocal searchHeuristic algorithmMulti-homingMulti-radio terminalsMulti-mode terminalsAlways Best Connected

1389-1286/$ - see front matter � 2010 Elsevier B.Vdoi:10.1016/j.comnet.2010.11.003

⇑ Corresponding author. Tel.: +30 6978005428; faE-mail addresses: [email protected] (V.E. Zafe

(E.A. Giakoumakis).

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a b s t r a c t

Multi-radio mobile communication devices are increasingly gaining market share due tothe diversity of currently deployed and continuously emerging radio access technologies.Multi-homing support in multi-radio terminals, i.e., simultaneous use of two or more radiointerfaces, provides improved user experience through increase in available bandwidthcapacity and reliability of wireless access. Furthermore, optimized assignment of applica-tion traffic flows to available interfaces and radio access bearer services contributes to eco-nomic and power consumption efficiency. We study the problem of traffic flow assignmentin a mobile node, multi-homed through a set of different technology radio interfaces. Weprovide an analytical formulation for the problem and prove its hardness through transfor-mation from the Multiple Knapsack Problem with Assignment Restrictions. Problem solu-tions are approximated with a heuristic algorithm that is based on local search and ischaracterized by efficient execution times for a wide set of realistic problem sizes. Thequality of approximation is rather satisfactory and is evaluated through comparison of heu-ristic and exact solutions for a large set of randomly generated problem instances. More-over, an evaluation of the approach through simulation supports these findings andprovides an estimation of the associated mobility management overhead that is limitedand allows real deployment of the decision mechanism.

� 2010 Elsevier B.V. All rights reserved.

1. Introduction

Wireless internet access is continuously expanding itsgeographical reach through a variety of radio access tech-nologies (RATs). However, no single RAT may completelysatisfy the bandwidth and QoS requirements set by currentand emerging multimedia applications. Moreover, eachRAT focuses on different degrees of user mobility in termsof speed and range. In order to benefit from radio accessdiversity, many modern mobile communication devicesare multi-mode, i.e., they are equipped with multiple radiointerfaces (3GPP, 802.11a/b/g/n, etc.). Moreover, specialpurpose mobile devices are emerging that provide

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, E.A. Giakoumakis, Optimmnet.2010.11.003

aggregated bandwidth capacity to mobile business orvehicular users, through multiple wireless broadbandsubscriptions [1].

A multi-mode terminal (MMT) that is multi-homed hasat least two global IP addresses, associated with respectiveradio interfaces. The IETF MONAMI6 WG has identified thebenefits that mobile host multi-homing offers to both endusers and network operators [2] and its successor, IETFMEXT WG, is working towards enhancing MIPv6 with mul-ti-homing support. This capability will be enabled byallowing the registration of multiple Care-of Addresses(CoAs) with a certain Home Address [3]. Moreover, thisspecification is being complemented with support forbinding flows to specific CoAs [4], allowing, thus, the exe-cution of handoffs at a traffic flow level.

Given these enhancements to a basic mobility manage-ment protocol such as MIPv6, a mobile MMT extends its

ized traffic flow assignment in multi-homed, multi-radio mobile

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degrees of freedom for adapting its connectivity status tothe changing traffic requirements and wireless networkingcontext. For instance, the range of options for respondingto the arrival of a traffic flow, when spare capacity in activeradio interfaces is not available, may include: (a) activationof an inactive radio interface and its attachment to anappropriate radio bearer service, (b) horizontal handoffon an active radio interface towards a higher capacitybearer service, (c) redirection of one or more traffic flows,already served by one interface, to another interface forbest utilization of available bandwidth capacity, etc. Theset of available options on each occasion depends on thewireless context and the MMT’s traffic load and hardwareconfiguration. Moreover, each alternative may have differ-ent impact on the fulfillment of user preferences and espe-cially on economic efficiency and energy autonomy. Thus,evaluation and determination of the optimal operationalstate requires advanced and fast executing decision algo-rithms. Execution efficiency is required due to the fre-quently occurring triggers for decision making thatinclude changes in served traffic, network conditions anddevice status (e.g. battery lifetime).

This work focuses on joint management of traffic, wire-less connectivity and power consumption in the context ofa multi-homed MMT operating in a dynamic environment.The MMT may have the role of an end-host serving its owntraffic or the role of a mobile router that acts as an internetgateway to a personal area or vehicular network. We studythe problem of assignment of application traffic flows(either inbound or outbound) to appropriate radio inter-faces and radio bearer services in a way that: (a) satisfiesthe traffic flows’ QoS requirements and the bearer services’capacity constraints, and (b) establishes the best tradeoffbetween economic cost and power consumption. For brev-ity reasons, the problem will be referred to as Traffic FlowAssignment Problem (TFAP). The economic cost factor ofTFAP corresponds to network usage cost, while power con-sumption is due to the operation of active radio interfaces.Due to the dynamic nature of problem parameters theMMT iteratively faces TFAP instances of variable size dur-ing its operation lifetime.

We provide an analytical formulation for the TFAP thatmaps the problem to a bi-objective combinatorial optimi-zation problem. The formulation takes into account addi-tional constraints, as compared to prior work, thatcontribute to a more realistic representation of the prob-lem domain. The bi-objective problem is solved by settingone of the objectives as a target for minimization (eco-nomic cost) and the other objective (power consumption)as an additional problem constraint by appropriatelychoosing an upper limit for its allowed values. We studythe complexity of the TFAP and prove its hardness throughtransformation from the Multiple Knapsack Problem withAssignment Restrictions that is NP-Hard [5]. Given thecomplexity of TFAP and requirements for frequent and fastexecution, we introduce a heuristic approximation algo-rithm that is based on local search and establishes a goodbalance between solution quality and execution time. Abasic feature of the proposed algorithm is the combineduse of two objective functions that guide the search to-wards minimum cost solutions with an upper limit on

Please cite this article in press as: V.E. Zafeiris, E.A. Giakoumakis, Optimhosts, Comput. Netw. (2010), doi:10.1016/j.comnet.2010.11.003

power consumption. Solution quality is evaluated by com-paring heuristic and exact solutions for a large number ofrandomly generated problem instances. Moreover, the ap-proach is evaluated with a discrete event simulator in or-der to study its merits over the time domain and theincurred mobility management overhead.

The rest of the paper is organized as follows: Section 2presents relevant literature and makes a qualitative com-parison of this work against it. Section 3 introduces an ana-lytical formulation for the TFAP along with a study of itscomplexity. Moreover, it specifies the method that we haveapplied for its solution. A heuristic algorithm for the TFAPis presented in Section 4, while an extensive evaluation ofits results and runtime performance is given in Section 5.Finally, the paper is concluded in Section 6 with open is-sues and possible extensions for future research.

2. Related work

Multi-homing is often employed by stub networks(enterprizes or Internet Service Providers – ISPs) in orderto enhance the reliability, performance or independence(avoiding lock-in to a single provider) of their internetconnectivity. Techniques and challenges related to therealization of multi-homing in IPv4 networks are summa-rized in [6]. Effective usage of a stub network’s links withits ISPs is a complementary issue to multi-homing deploy-ment and involves distributing incoming and outgoingtraffic to appropriate links for cost and performanceoptimization. Such active control of traffic routing, oftenreferred to as smart routing, is performed by the network’sedge routers. Goldenberg et al. [7] study the assignment oftraffic flows of a user, multi-homed through various ISPs,under a percentile-based charging model. Our workfocuses on link management and traffic assignment fromthe perspective of a mobile node that is multi-homedthrough two or more radio access networks. This perspec-tive differentiates the aforementioned problem in terms ofrequirements and constraints. In contrast to a multi-homed access router, available access links for a mobilenode may change over time, due to user movement to dif-ferent locations. Moreover, a MMT may not be able to uti-lize more than one links of the same RAT (if it is equippedwith a single radio interface that is compatible with thatRAT), thus, an access link selection process is involved intraffic assignment optimization. As link QoS may varyacross different RATs and operators, both QoS and capacityrequirements of traffic flows need to be taken into accountduring flow assignment. Our work incorporates powerconsumption into the set of objectives under optimization,due to the importance of user autonomy in a mobile net-working setting.

End-host multi-homing is emerging as an effectivesolution for enhancing the performance and reliability ofwireless access in a multi-access/multi-RAT network set-ting. The PERM framework is proposed towards this direc-tion [8], that enables collaborative internet access throughresidential WLANs. PERM deals with non real-time trafficflows and assigns them upon their establishment toappropriate wireless links. Flow assignment is based on:



V.E. Zafeiris, E.A. Giakoumakis / Computer Networks xxx (2010) xxx–xxx 3

(1) prediction of flows’ expected traffic volume and (2)monitoring and capacity estimation of available links.Flows are classified to light-volume and heavy-volumeones and are scheduled, on the basis of their category, toappropriate links. Specifically, the former are scheduledto links providing low RTT (Round Trip Time), while thelatter to links with high capacity. Our work focuses onscheduling of both real-time and non-real time flows foreconomic cost and power consumption optimization. Ourproposed problem formulation takes into account flowperformance in the form of guarantees on minimum QoSrequirements, rather than as objective for optimizationthat is the case in PERM.

Bonin et al. [9] designed and implemented a middle-ware, named Ubique, for management of a MMT’s radiointerfaces and optimal assignment of application trafficflows to them. Flow assignment is based on informationthat is modeled and stored as a set of profiles that are rel-evant to user preferences, network context, applicationrequirements etc. The middleware comprises functionalentities for the management and retrieval of profile infor-mation, as well as for decisions on flow assignment. As re-gards the latter, it is described as a multi-objectiveoptimization problem without including details on theproblem formulation and the objectives under optimiza-tion. Our work is complementary to Ubique as we specifyan approximation algorithm for the flow assignment prob-lem that can be incorporated as a decision method in thearchitecture.

Nguyen et al. [10] adopt a two phase approach for themanagement of connectivity of a multi-interface host witheach phase being triggered by different events. The firstphase involves radio interface activation, on the basis ofpolicies that take into account battery level, user prefer-ences, velocity and traffic activity. Network selection istriggered, in a second phase, by: (a) changes in radio inter-faces’ activation status, (b) user movement towards theboundaries of currently used cell(s) and (c) changes in traf-fic load. Network selection is based on a utility functionthat comprises the weighted product of various factorssuch as power consumption, cost, network load and capac-ity, and RSS. Access networks with highest utility are asso-ciated with the respective radio interfaces. A challenge forthis approach is the appropriate selection of network attri-bute weights. Moreover, the proposed network selectionprocedure is more appropriate for scenarios where a singleinterface can serve all user traffic. In case that two or moreinterfaces need to be activated, a flow-to-interface assign-ment phase must also be incorporated. The assignment oftraffic to each interface may also require the selection ofdifferent weight vectors for each interface, e.g., due tothe different QoS requirements of assigned flows. In thiswork we address the radio interface activation, networkselection and traffic assignment problems in a unifiedmanner with focus on economic efficiency and energyautonomy.

Bellavista et al. [11] provide a conceptual model forconnectivity management in a multi-access/multi-RAT set-ting. The model is based on three basic concepts: interface,connector and channel. Interfaces represent the wirelesshardware equipment of a device, while connectors corre-


spond to infrastructure or ad hoc points of access that pro-vide connectivity. A channel refers to a pair (interface,connector) properly configured for serving user traffic. Onthe basis of these concepts three levels of connectivity flex-ibility are defined: (a) 4G, where a MMT uses exactly one ofits interfaces to serve application traffic, (b) ABC (AlwaysBest Connected), where two or more interfaces may beactive at the same time, each one associated with a singleconnector and (c) ABS (Always Best Served) that extendsABC with the capability of an interface to use more thanone connectors (multiple channels per interface). Theauthors also propose a Mobility-Aware Connectivity(MAC) middleware for channel management in an ABScontext. Connector Manager (CoM) and Channel Selector(ChaS) are MAC components that are relevant to our work.CoM performs interface activation and connector selection,while ChaS assigns application traffic flows to availablechannels. The evaluation of connectors and channels ismade with appropriate metrics. Our work is based on theconceptual model of [11] and assumes an ABC level of con-nectivity flexibility. We contribute to this conceptual mod-el by providing an analytical formulation of the problemshandled by the CoM and ChaS components. These prob-lems are combined into a single optimization problemwith focus on cost and power consumption optimization.

Flow assignment in a multi-interface host is modeledas an optimization problem in [12–14]. Ref. [12] studiesthe problem from the perspective of an enterprise thatseeks to assign its outbound traffic to multiple ISPs.Two types of flows comprise outbound traffic: (1)size-fixed flows that do not usually set constraints ontransmission duration but require all their data to betransmitted and (2) time-fixed flows that have fixed dura-tion with specific QoS requirements and their transmitteddata size can be compressed. Assigning traffic flows tonetwork resources incurs economic cost due to capacityacquirement and opportunity costs when the target trans-mission rate of time-fixed tasks is not met. Flow assign-ment involves cost minimization under QoS andcapacity constraints and maps to a two dimension binpacking problem (2D-BPP).

Ref. [13] models flow assignment as a bin packing prob-lem where access networks correspond to bins and flowsto items that need to be packed. The problem is further cat-egorized as online (no knowledge is available on subse-quent items/flows that need to be packed) or offline (allitems are initially available). In [14] the problem is formu-lated as a Multiple choice Multiple dimension KnapsackProblem with Multiple Knapsacks. Specifically a set of uni-directional traffic flows is considered and each flow is asso-ciated with a QoS profile comprising various QoS levels.Available access networks are mapped to knapsacks withbounded capacity representing their bandwidth. Flowassignment is then reduced to packing flows, at appropri-ate QoS levels, to a minimal subset of knapsacks so that to-tal net utility is maximized.

The aforementioned approaches to flow assignment[12–14] are not directly applicable to the context of a mul-ti-homed mobile host. The main reason is that not all com-binations of available wireless networks, that provide thecombined capacity required by traffic flows, may be part




of a problem solution. As the MMT is equipped with a finitenumber of radio interfaces, each one supporting specificRATs and being capable of associating to a single RAN, can-didate problem solutions span only the subsets of availablenetworks that can be simultaneously bound to the MMT’sradio interfaces. This constraint maps the traffic flowassignment problem to a generalization of the MultipleKnapsack Problem with Assignment Restrictions insteadof the knapsack or bin packing problem.

A research area that is relevant to the utilization of mul-tiple radio interfaces for increasing the performance andreliability of wireless access is Bandwidth Aggregation(BAG) that is also referred to as Concurrent MultipathTransfer (CMT) [15–21]. BAG refers to the problem ofscheduling user traffic to multiple active connections in away that packet reordering in the receiver side is mini-mized. The ultimate goal is to have multiple radio accessconnections that behave as a single one with aggregatedbandwidth. Both network layer (e.g. [15]) and transportlayer (e.g. [16–21]) approaches have been proposed forBAG. Transport layer approaches focus mainly on: (a)enhancements to transport layer protocols such as TCP orSCTP [22] for the incorporation of CMT capability[16–18,21] and (b) utilization of multiple radio interfacesof a single or multiple hosts for improving TCP perfor-mance in a mobile networking setting [19,20]. BAG solu-tions schedule traffic at the packet level and not at theflow level that is the focus of our work. Scheduling of flowstrades off the fine-grained control that packet schedulingoffers, for lower processing costs and ease of deploymentwith minimal interventions in network infrastructure ordevice protocol stack. Nevertheless, the problem formula-tion proposed in the following section can be extendedfor the support of CMT-enabled SCTP flows by relaxationof the flow integrality constraint.

3. Traffic flow assignment problem – TFAP

3.1. Problem formulation

Assume a mobile multi-mode terminal (MMT) that isequipped with a set of different technology radio inter-faces, e.g., 3GPP, IEEE 802.11x, WiMAX, etc. LetR ¼ fri : 1 6 i 6 m;m 2 N�g, be the MMT’s available radiointerfaces. Moreover, the MMT has multi-homing support,i.e., it is capable of simultaneously using two or more of itsradio interfaces for serving its data traffic.

The MMT’s current location lies in the overlapping ser-vice areas of a set of radio access networks (RANs). TheRANs correspond to different radio access technologies(RATs) and are managed by one or more network opera-tors. Each RAN provides wireless access through a set ofbearer services, i.e., data transfer services characterizedby different Quality of Service guarantees. Let B ¼ fbj :

1 6 j 6 n;n 2 N�g be the set of bearer services providedby the RANs that serve the MMT’s current location. Eachbearer service bj is characterized by a set of service, costand power consumption attributes. The service and costattributes of bj are described below, while its power con-sumption attributes will be described thereafter:


� ku,j is uplink bandwidth capacity in kbps offered by theservice to the MMT,� kd,j is downlink bandwidth capacity in kbps,� Qj is a QoS class that characterizes the service’s perfor-

mance and defines upper limits for delay, jitter and biterror rate. In this work we adopt the QoS classes definedby 3GPP [23] and, thus, the domain of Qj is Background(QB), Interactive (QI), Streaming (QS), and Conversational(QC). Moreover, we assume a strict total order relationamong them, i.e., QB < QI < QS < QC denoting that QoSrequirements set by QB are lower than those of QI andso forth.� cj is cost per kbit of transferred data either in the uplink

or downlink direction.

We have adopted a volume-based charging model dueto its simplicity and fairness for both users and networkoperators that act in a competitive wireless access environ-ment where network selection is enabled at the time gran-ularity of a service session. A similar charging model isutilized today for mobile access in roaming scenarios,where a user, at any time instance between successive ser-vice sessions, is capable of selecting the services of anyoperator that has roaming agreements with its homeoperator.

The wireless access resources represented by eachbearer service bj refer to the RAN’s capacity availabilityper admitted user in the MMT’s current service area.Bearer service descriptions are retrieved by the MMT in aRAT specific manner from its current point of access orthrough a media independent mechanism as the MediaIndependent Information Service (MIIS) specified in [24].Service availability may change dynamically due to varia-tions of cell load or radio propagation conditions. TheMMT perceives these variations either directly (for cur-rently used services) or indirectly by the RANs’ informationservices.

Each radio interface ri supports a set of RATs and may beassociated with at most one bearer service of compatibleRAT. Once associated with a bearer service, a radio inter-face can serve user traffic by utilizing the service’s avail-able capacity, and contributes to the MMT’s overallpower consumption. Its power consumption depends onfactors such as: (a) RAT of the bearer service, e.g. a 3GPPradio interface has different power consumption whenassociated with a 2.5G or a 3G bearer service, (b) configu-ration of the bearer service’s network point of access, e.g.support or not of power-saving mode in 802.11 APs, (c)volume and direction of served traffic etc. We haveadopted a power consumption model proposed in [25]and used in a similar context in [13]. Since the power con-sumption coefficients of this model depend on the RAT,and a radio interface may support multiple RATs, we usethem in the TFAP problem formulation as bearer serviceattributes. Thus, the power consumption attributes of abearer service bj are:

� wrj, power consumption per kbps of received data(W/kbps),� wtj, power consumption per kbps of transmitted data

(W/kbps),



Table 1Examples of power consumption parameters.

RAT Parameter type

Base (lW) Transmission(lW/kbps)

Reception(lW/kbps)

UMTS 107.2 8.3 4.9GPRS 313.47 0.76 0.36IEEE 802.11a 368 0.32 0.14IEEE 802.11b 262.7 1.22 1.22


� wbj, power consumption (W) due to base operation ofthe radio interface without transferring data.

The power consumption in Watts of a radio interfacethat sends and receives data with rates bwt and bwr kbpsrespectively through bearer service bj is P = wbj + bwtwtj +bwrwrj. Table 1 includes example values of power con-sumption parameters for four RATs as estimated and usedin [13,25].

The set B of available bearer services can be partitionedinto m = jRj disjoint subsets, i.e., B = B1 [ B2 � � �[ Bm, whereeach subset Bi comprises services that are compatible withradio interface ri.

Definition 1. A radio interface activation B0 represents theassociation of one or more radio interfaces of the MMTwith compatible bearer services in order to serve usertraffic. B0 is a subset of B with at most one element from B1,B2, . . .,Bm, i.e., B0 # B,jB0j 6m. The inequality correspondsto the case where one or more radio interfaces of the MHare deactivated.

The presence of an element from Bi in a radio interfaceactivation B0 denotes that radio interface ri is activated1 andassociated with that bearer service. On the other hand, theabsence of an element from Bi denotes that ri is deactivated.Given the set of available bearer services B = B1 [ B2

� � � [ Bm, the number of possible radio interface activationsis (jB1j + 1)(jB2j + 1)� � �(jBmj + 1)�1. This accrues from thejBij + 1 possibilities for each radio interface (i.e., jBij alterna-tive bearer services plus the possibility of being deactivated)with the exclusion of the case of all interfaces beingdeactivated.

The data traffic served by the MMT is modeled in termsof uplink and downlink traffic flows that are generated byuser applications. Let F ¼ ffz : 1 6 z 6 v; v 2 N�g be the setof traffic flows that are served by the MMT at a given timeinstance. A flow fz, that may be uplink or downlink, is char-acterized by a set of attributes, i.e., fz = (bwu,z,bwd,z,qz). Spe-cifically, bwu,z represents the flow’s required bandwidthcapacity in kbps in the uplink, while bwd,z states therespective requirements in the downlink. For an uplinkflow fz it holds that bwd,z = 0, while for a downlink onebwu,z = 0. As regards qz, its value represents a QoS classand has the same domain with the respective attribute ofa bearer service.

1 We will henceforth use the term activated radio interface to refer toboth a bearer service bj 2 B0 and its corresponding radio interface.


Each flow fz must be assigned to exactly one activatedradio interface in order to be served. The current problemformulation does not assume flows that use a CMT proto-col (like SCTP) for their transport and, thus, their trafficmay be split across two or more activated radio interfaces.A possible extension for the incorporation of this feature isthe association of each flow fz with a set of coefficients aiz,where i ranges over the set of available radio interfaces.Each coefficient aiz represents the fraction of flow trafficthat is assigned to a radio interface ri. Given an interfaceactivation B0, it holds that aiz 2 (0,1] for activated radiointerfaces and aiz = 0 for deactivated ones. The assignmentof a CMT-based flow fz, given a radio interface activation B0,involves fixing the values of aiz in a way that

Piaiz ¼ 1. The

bandwidth capacity occupied by fz on ri is aizbz. As regardsnon CMT-based flows, their respective coefficients are al-lowed to take only integer values, thus aiz 2 {0,1}. A moredetailed study of this feature and its implications on prob-lem complexity will be part of future extensions of thiswork.

Definition 2. A traffic flow assignment S with respect tothe sets R, B and F, comprises a radio interface activationB0 = {b1,b2, . . .,bk},k 6m and a partition of F into k foreignsubsets F = F1 [ F2 [� � �[ Fk, such that the flows of each Fj

are served by a corresponding bj 2 B0 without violating thebearer’s capacity constraints and the flows’ bandwidth andQoS requirements.

Given a radio interface activation B0, the partition of Finto subsets must be appropriately selected in a way thatfor each Fj served by a bj 2 B0:

� uplink capacity of bj is not exceeded

ized tr

Xfz2Fj

bwu;z 6 ku;j; ð1Þ

� downlink capacity of bj is not exceeded
Xfz2Fj
bwd;z 6 kd;j; ð2Þ

� QoS requirements of flows are satisfied

qz 6 Q j;8fz 2 Fj: ð3Þ

The economic cost of a traffic flow assignment S is equalto the sum of the costs incurred due to the operation ofeach one of the MMT’s activated radio interfaces. LetCM(S) be the function that returns the economic cost of aflow assignment S and B0 the radio interface activation thatcorresponds to S. Furthermore, let Fj be the set of flowsserved by each bj 2 B0. The economic cost of each activatedinterface is equal to the cost cj of its associated bearer ser-vice bj multiplied by the total bandwidth capacity reservedby its served flows Fj. Note that CM(S) is measured in mon-etary units per second and represents the incurred eco-nomic cost for each second of MMT operation under flowassignment S. The function CM(S) is defined as:

CMðSÞ ¼Xbj2B0

cj

Xfz2Fj

ðbwu;z þ bwd;zÞ: ð4Þ

affic flow assignment in multi-homed, multi-radio mobile



The power consumption of a traffic flow assignment S isdefined in a similar manner and is given by Eq. (5):

CPðSÞ ¼Xbj2B0ðwbj þwrj

Xfz2Fj

bwd;z þwtj

Xfz2Fj

bwu;zÞ: ð5Þ

According to Eq. (5), the power consumption of eachactivated radio interface bj 2 B0 is equal to the sum ofthree addends: (a) power consumption due to base oper-ation of the radio interface, (b) power consumption due todata reception of its inbound flows, and (c) power con-sumption due to data transmission of its outbound flowsrespectively.

Definition 3. Given three sets R, B and F that correspondto available radio interfaces of a MMT, available bearerservices and traffic flows that need to be served, the trafficflow assignment problem (TFAP) involves finding a flowassignment S that minimizes both economic cost CM(S) andpower consumption CP(S).

The TFAP is, therefore, an optimization problem withtwo objectives: economic cost CM and power consumptionCP. These objectives are independent and usually conflict-ing, especially in cases that the MMT serves high trafficload. Assume that the MMT’s radio interfaces have accessto bearer services of comparable cost and there exists a po-sitive correlation between cost and provided capacity. Ifthe MMT’s traffic load cannot be served by a single inter-face (due to capacity or QoS restrictions) then optimizationof CM involves distributing traffic flows to radio interfaceswith access to the cheapest bearer services. On the otherhand, optimization of CP requires the activation of the leastpossible number of radio interfaces by associating themwith high capacity and usually higher cost bearers. Thus,TFAP is a multi-objective optimization problem (MOOP)and, depending on the problem instance, may have morethan one Pareto optimal solutions (traffic flow assign-ments) Sp.

3.2. TFAP solution method

Various methods have been proposed for solvingMOOPs [26]. A widely used method that transforms theMOOP to a single objective problem is the weighted-summethod. The method involves prioritization of problemobjectives by associating them with appropriate weightvalues. Then, a single objective function is defined by theweighted sum of the individual objective functions. De-spite the method’s simplicity, the selection of objectiveweights may prove a challenging issue especially in caseswhere: (a) objective values are not expressed in the samemeasurement unit and (b) measurements units do not di-rectly reflect user utility. In TFAP, economic cost CM is theprimary user objective and is expressed in monetary units,a common measure of user utility. On the other hand, CP isexpressed in Watts and is related to energy autonomy ofthe MMT. Assessing the economic value of energy auton-omy of specific duration is a difficult task.

These characteristics of TFAP objectives lead us to ap-ply the e-constraint method for solving the TFAP [26].


This method also transforms a MOOP to a single-objectiveproblem and its application involves selection of oneobjective (the most preferred) for optimization and intro-duction of one problem constraint for each one of theremaining objectives. The resulting single-objective prob-lem is then solved for various bounds on problem con-straints in order to generate the set of Pareto optimalsolutions. In the case of the TFAP, the primary objectiveis the economic cost CM, while power consumption canact as problem constraint. Although MOOP solving meth-ods focus on the generation of a set of Pareto optimalsolutions, the TFAP solution procedure targets a singlesolution, that is the economically most efficient flowassignment that does not violate a power consumptionlimit Pmax. This is due to the fact that users are mainlyconcerned on economic cost, as soon as their autonomy,till next battery recharge, is ensured.

As regards the range of values for Pmax, it depends eachtime on the user context which can be classified into threebasic categories:

1. ‘‘Infinite’’ energy resources (Pmax ?1), where the MMTis either plugged into an energy source or an energysource is easily accessible, e.g., when the user is athome. In this case the power consumption cost can beignored by the user and the TFAP becomes a singleobjective, economic cost minimization problem, thatwill be referred to as TFAPM.

2. Depleting energy reserves (Pmax ? 0), where the MMT’sbattery level is low and immediate access to an energysource is not possible (e.g. user not at home or office). Inthis case the TFAP concerns power consumption opti-mization and economic cost is ignored. This problemwill be referred to as TFAPP.

3. Any other situation, where the value of Pmax may rangein an interval [Pa,Pb], where Pa, Pb represent the mini-mum and maximum power consumption for servinguser traffic at a given networking context and userdevice configuration.

The execution of the TFAP solution procedure is trig-gered whenever the MMT perceives events related tochanges in the problem parameters R, B, F or Pmax. Typicalevents are: (a) availability of new bearer services or immi-nent unavailability of already used services, (b) degrada-tion of the QoS of one or more currently used bearerservices, (c) arrival or termination of application trafficflows, (d) changes in the value of Pmax.

The determination of the current value of Pmax is asubproblem that will be delegated to the MMT’s PowerManagement Subsystem (PMS). Specifically, PMS will peri-odically evaluate and update the value of Pmax with theobjective of providing energy sufficiency to the MMT fora specified time duration D. The minimum duration ofMMT energy autonomy D is a user input that representsan estimation of the time until next battery recharge. Inaddition to D, other factors that determine the value ofPmax are: (a) current battery energy availability E, (b) lasttime instance tD of user update of D, (c) amount of servedtraffic since tD, (d) expected traffic load until the expirationof D, etc. The specification of power management policies




or decision mechanisms for fixing Pmax is out of scope ofthis work.

Given the value of Pmax, TFAP is a combinatorial optimi-zation problem and methods relevant to this problem cat-egory may be applied for its solution. An Integer LinearProgramming formulation of the TFAP is presented in[27]. On the basis of this formulation exact solutions ofthe TFAP can be produced with the help of proprietary oropen source software. Such software is used for the gener-ation of exact solutions in the experiments described inSection 5. However, finding exact solutions even for prob-lems of moderate size, requires often several seconds ofexecution in a standard workstation PC. As a result, theexecution of an exact algorithm in processing power lim-ited mobile devices will be certainly inefficient in termsof responsiveness and utilization of device resources. Onthe other hand, its deployment to the network side andexecution for large numbers of MMT’s may raise scalabilityissues. For these reasons, an algorithm that establishes agood trade off between solutions’ quality and responsive-ness is required for the TFAP. Towards this direction weintroduce a heuristic algorithm for solving the TFAP thatis based on local search [28]. The algorithm performs aguided search in the problem state space (valid flowassignments) in search of efficient solutions and is charac-terized by low execution times as it enumerates a rela-tively small subset of the actual problem state space.

3.3. Problem complexity

The maximization version of TFAP is a generalizationof the Multiple Knapsack Problem with AssignmentRestrictions (MKAR). MKAR is a variant of the MultipleKnapsack Problem (MKP) [29] and is NP-Hard [5]. MKARis defined as the problem of finding a maximum profitassignment of n items uj 2 U to m knapsacks vi 2 V of fi-nite capacity. Each item uj has a weight wj, independentof the knapsack that is assigned to, and its assignmentto any knapsack brings in profit pj. Moreover, each knap-sack vi has a finite capacity ki and sets restrictions on theitems that it can admit. Let Ni # U be the set of itemsthat are allowed to be assigned to a knapsack vi. TheMKAR problem involves finding a partition of U into mdisjoint subsets U = U1 [ U2 � � � [ Um, Ui # Ni, "i 2{1, . . .,m}, for assignment of their items to correspondingknapsacks vi, in a way that maximizes profit without vio-lating knapsack capacity constraints:

maximize M ¼Xv i2V

Xuj2Ui

pj;

subject toXuj2Ui

wj 6 ki; 8v i 2 V :

MKAR is NP-Hard in the strong sense even in the case ofequal knapsack capacities [5]. TFAP is at least as difficult asMKAR which can be proved by restriction [30], i.e., byshowing that TFAP contains the MKAR as a special case.However, MKAR is a maximization problem and, thus,our proof will be based on the maximization version ofTFAP, MAX-TFAP. MAX-TFAP is equivalent to TFAP, i.e., a


MAX-TFAP solution is also a solution to TFAP and viceversa, and derives from TFAP through a simpletransformation.

Assume a TFAP problem instance (R,B,F,Pmax) and let tbe a positive real number with t > maxbj2Bcj. The profitassociated with the use of a bearer service bj is pj = t�cj

and has the same measurement unit with cj. Moreover,let W be the total traffic requirements in kbps of the TFAPinstance, i.e., W ¼

Pfz2Fðbwu;z þ bwd;zÞ. The assignment of a

flow fz to a service bj yields profit pjz = pj(bwu,z + bwd,z),while the total profit of a traffic flow assignment S, thathas a corresponding radio interface activation B0, is givenby function PM(S):

PMðSÞ ¼Xbj2B0

pj

Xfz2Fj

ðbwu;z þ bwd;zÞ

¼Xbj2B0ðt � cjÞ

Xfz2Fj

ðbwu;z þ bwd;zÞ

¼ tXbj2B0

Xfz2Fj

ðbwu;z þ bwd;zÞ �Xbj2B0

cj

Xfz2Fj

ðbwu;z þ bwd;zÞ

¼ tW � CMðSÞ:

Note thatP

bj2B0P

fz2Fjðbwu;z þ bwd;zÞ ¼W , since by the

definition of a traffic flow assignment the union of all sub-sets Fj is equal to F. The first term of PM(S) is constant for agiven TFAP instance and independent of S, thus, a flowassignment that minimizes CM(S) maximizes PM(S) and viceversa. MAX-TFAP involves maximization of PM(S) subject tothe same constraints with TFAP. Therefore, a solution of aMAX-TFAP problem instance is also a solution of its corre-sponding TFAP instance.

Our proof on the hardness of MAX-TFAP involves thespecification of restrictions on its instances so that theresulting problem instances are identical to MKAR [30].Let (R,B,F) be a MAX-TFAP instance with Pmax limit onpower consumption. Recall that B = B1 [ B2 [� � �[ Bm,where each subset Bi includes services compatible with aspecific radio interface ri. The following restrictions are ap-plied to the elements of each Bi ¼ fb1; b2; . . . bti

g:

� ku;1 ¼ ku;2 � � � ¼ ku;ti, i.e., uplink capacities of bearer ser-

vices are equal to each other,� kd;1 ¼ kd;2 � � � ¼ kd;ti

, i.e., downlink capacities of bearerservices are equal to each other,� Q1 ¼ Q 2 ¼ � � � ¼ Qti

, i.e., provided QoS is equal for allbearer services in Bi,� wb1 ¼ wb2 ¼ � � � ¼ wbti

;wr1 ¼ wr2 ¼ � � � ¼ wrti;wt1 ¼

wt2 ¼ � � � ¼ wtti, i.e., power consumption coefficients

are equal to each other.

Moreover, assume that all bearer services have thesame cost, i.e., cj = c, "bj 2 B, and t = c + 1. Then, the profitpj corresponding to each service bj is pj = t�c = 1. As regardstraffic flows, we assume that they are all downlink, i.e.,bwu,z = 0, "fz 2 F.

Since bearer services that are included in each subset Bi

are identical in terms of their service, cost and power con-sumption attributes, the restricted problem does not in-volve bearer selection at a radio interface level. Thus,




each restricted problem instance is based on a setB00 # B,jB00j = m, that includes one randomly selectedelement from each subset Bi, 1 6 i 6m. The restrictedproblem involves finding an assignment of flows to bearerservices in B00 (i.e., a partition of F into m disjoint sets) thatmaximizes profit subject to bearer services’ capacity con-straints and traffic flows’ QoS requirements. The existenceof bearer services without any assigned flows in a problemsolution implies that the respective radio interfaces aredeactivated.

The restriction that we apply to the values of Pmax en-ables the simultaneous use of all m radio interfaces forserving application traffic without exceeding the maxi-mum allowed power consumption:

Pmax ¼Xbj2B00ðwbj þwrjkd;jÞ: ð6Þ

Thus, the constraint on power consumption can be elimi-nated from the restricted version of MAX-TFAP.

With reference to the MKAR problem definition, theprofit from assigning a flow fz to any bearer service bj ispz = pjbwd,z = bwd,z, while the ‘‘weight’’ of each flow iswz = bwd,z that is also independent of the service that is as-signed to. Let Nj be the subset of flows that are allowed tobe assigned to a service bj on the basis of their QoS require-ments, i.e., Nj = {fz 2 F: qz 6 Qj}. The constraint representedby Eq. (3) in the formulation of TFAP can, then, be rewrittenas Fj # Nj.

On the basis of the aforementioned assumptions andrestrictions the restricted MAX-TFAP problem can be sta-ted as: Find a partition of F into m = jB00j disjoint subsetsFj, j 2 {1, . . .,m}, each one corresponding to a bearer servicebj 2 B00, that maximizes profit without violating problemconstraints:

maximize M ¼Xbj2B00

Xfz2Fj

pz

subject toXfz2Fj

wz 6 kd;j; 8bj 2 B00;

Fj # Nj; 8bj 2 B00:

This problem formulation corresponds to the MKARoptimization problem and, thus, MAX-TFAP and its equiv-alent TFAP are NP-hard.

4. A heuristic algorithm for the TFAP

In this section we introduce a heuristic algorithm forapproximating the solution of a TFAP instance. Thealgorithm, that is based on local search, starts from initialproblem solutions and gradually modifies them towardsa better approximation of the actual solution. Initial prob-lem solutions are obtained through heuristic constructionalgorithms. These algorithms ‘‘construct’’ a valid trafficflow assignment S by assigning flows one-by-one to appro-priate radio interfaces with a first-fit assignment scheme.Assuming an ordered set of radio interfaces, first-fitassignment places each flow to the first activated interfacethat satisfies its bandwidth and QoS requirements.


Algorithm 1. Heuristic traffic flow assignmentalgorithm

input: Power consumption limit Pmax, Radiointerfaces R, Bearer services B, Flows FOutput: A valid traffic flow assignment S

1 SM findMinimumCostSolution (R, B, F);2 SP findMinimumPwrConsSolution (R, B, F);3 S1 localSearch(SM,Pmax);4 S2 localSearch(SP,Pmax);

/* If S1 has lower economic cost and respects

the limit Pmax*/

5 if CM(S1) < CM(S2) and CP(S1) 6 Pmax thenreturn S1;/* If S2 has lower economic cost and respects

the limit Pmax*/

6 if CM(S2) <CM(S1) and CP(S2) 6 Pmax then return S2;/* If neither of the above was true then it

holds that either

CM(S1) = CM(S2) or the limit Pmax cannot be

met. Select the

lowest power consumption solution. */7 if CP(S1) < CP(S2) then return S1;8 else return S2;

Algorithm 1 gives an overview of the TFAP solution pro-
cedure and presents the synergy between constructionheuristics and local search. The notation Sx represents a va-lid traffic flow assignment. In the rest of this paper theterms problem state and problem solution will also beused, denoting a valid traffic flow assignment, as it is spec-ified in Definition 2 of Section 3.1. Procedures findMini-mumCostSolution and findMinimumPwrConsSolution
implement the First Fit construction heuristics that gener-ate the initial problem states (SM, SP) for local search. Initialproblem states are constructed with focus on the optimiza-tion of a single objective. Thus, SM approximates theminimum economic cost problem solution, while SP

approximates the minimum power consumption one. Thefunctions CM(S) and CP(S) return the economic and powerconsumption cost of a given problem state S.

The notation that will be used in the description of thealgorithms corresponds to that introduced in Sections 3.1and 3.3. As regards the bearer service concept, we willintroduce additional notation for a more concise descrip-tion of the algorithms. Recall from Section 3.3 that Nj # Frepresents the set of ‘‘admissible’’ traffic flows for a bearerservice bj, i.e., the set of flows that bj satisfies their QoSrequirements and, thus, can be assigned to it (when associ-ated with an appropriate radio interface). The ‘‘effective’’uplink and downlink bandwidth capacity of a bearer ser-vice bj are defined, respectively, as:

k0u;j ¼ min ku;j;Xfz2Nj

bwu;j

0@

1A;

k0d;j ¼min kd;j;Xfz2Nj

bwd;j

0@

1A:

Based on the notion of effective capacity, we introduce thepower consumption coefficient wj for a bearer service bj that




represents the power consumption per unit of effectivecapacity of the bearer service:

wj ¼wbj þwrjk

0d;j þwtjk

0u;j

k0d;j þ k0u;j:

In the rest of this section a distinction will be made amongthe power consumption of a radio interface ri due to itscurrently assigned flows, total power consumption, andthe coefficient wj that refers to its currently associatedbearer service bj. Accordingly, the total economic cost of aradio interface refers to the cost due to its currently as-signed flows in a given problem state S, while the cost cj

corresponds to the cost of its associated bearer service bj.The localSearch procedure implements the local

search algorithm that, given an initial problem state,performs successive transitions to other problem stateswith aim to converge to one that has the minimum possibleeconomic cost and a power consumption that does not vio-late the upper limit Pmax. A series of state transitions thatdecrease CM are usually followed by an increase in CP. Thisis due to the gradual activation of available radio interfaces,as traffic flows are distributed to the cheapest possible ser-vices that are accessible through each radio interface. Theassumption here is that traffic requirements exceed thecapacity of the cheapest bearer service and bearer servicecost is positively correlated with its QoS and capacity. Onthe other hand, state transitions that gradually decreaseCP probably increase CM, given that higher capacity, higherQoS bearers usually have higher usage cost. This potentialtrade-off between economic cost and power consumption

, ,


is taken into account in the design of the local search strat-egy. Thus, local search is guided towards either: (a) optimi-zation of CM with minimum increase in CP, if CP(Si) 6 Pmax

holds for the initial state Si or (b) optimization of CP withminimum increase in CM, if CP(Si) > Pmax.

The core part of the localSearch procedure is de-scribed in Algorithm 2. It represents a local search iterationthat targets economic cost optimization. Thus, the condi-tion CP(S) 6 Pmax must be true for the algorithm parameterS (initial problem state). If CP(S) > Pmax then algorithm exe-cution will not lead to a state transition. However, in thiscase the control logic of the localSearch procedure willinvoke a variation of Algorithm 2 that performs power con-sumption optimization until reaching the limit Pmax. Its dif-ferences from Algorithm 2 are localized in statements 1, 8and 11. Specifically, a) in statement 1 radio interfaces aresorted by descending wj of their associated bearers servicesfirst and then by total economic cost, b) in statement 8 thelast parameter of searchStep is set to false and c) in state-ment 11 a different objective function is used (function g).The role of the boolean parameter in searchStep will beexplained thereafter. The control flow of localSearch in-volves the iterative execution of Algorithm 2 and its varia-tion. The value of CP(S0), where S0 is the problem state aftera local search iteration, determines which of the two algo-

( )

{ }f

F




rithms will be executed in the next iteration. Their execu-tion is, thus, interleaved until a maximum number of iter-ations is reached or until two successive iterations result inidentical problem states.

The main idea behind the algorithm for the local searchiteration is the permutation of flows across pairs of radiointerfaces in a way that the objective function is mini-mized. Specifically, starting from the most expensive orenergy demanding radio interface (depending on the algo-rithm variation), a permutation procedure is executed foreach served flow against the other radio interfaces. Thispermutation procedure, called searchStep, is describedby Algorithm 3 and results to: (a) no state transition or(b) transition to a new valid problem state. Thus, search-Step constitutes the neighborhood operation of the localsearch algorithm. The possible state transitions concerninga certain flow fz are evaluated by an objective function andthe algorithm continues from the state that minimizes itsvalue.

The neighborhood operation searchStep requires fourparameters: (a) a source radio interface rs, (b) a traffic flowf, served by rs (c) a target radio interface rt and (d) a bool-ean optimizeCM that is set to true when searchStep isinvoked during an economic cost optimization iterationor false when invoked during power consumption minimi-zation. Its purpose is to assign f to rt by associating rt withan appropriate bearer and possibly replacing one or moreof its served flows. The function candidateBearers (r)

returns the bearer services of the same RAT with radiointerface r, while the function associatedBearer (r) re-turns the bearer service that is associated with r in the cur-rent problem state. Procedure searchStep tries to assign fto rt by checking each candidate bearer service, startingfrom bta and continuing with ascending cost cj or ascendingwj, depending on the value of optimizeCM. Flow assign-ment is performed by procedure append that a) assigns fto bj, if it has spare bandwidth (note that bj is consideredto be serving the flows already assigned to its correspond-ing radio interface rt), or b) replaces one or more servedflows of rt so as to save the required bandwidth. Flowreplacement applies to flows that have QoS requirementsequal or lower than f and their aggregate bandwidthrequirements are lower than those of f. Thus, append re-turns a set of flows Ft that contains: (a) ; if f was assignedto bj without replacing any flows, (b) {f} if assignment of fwas not possible, (c) one or more served flows of rt. Re-placed flows Ft are assigned to rs that has the requiredcapacity, as replaced flows have an aggregate bandwidththat is less than the required bandwidth of f.

Eqs. (7) and (8) describe the objective functions f and g,that are used respectively in Algorithm 2 and its variationfor power consumption minimization. Each objective func-tion evaluates a state transition from state Sa to state Sb gi-ven a power consumption limit P. Function f favours statetransitions that reduce economic cost and also cause theleast increase in power consumption per unit of cost de-crease. State transitions that either violate the power con-sumption limit or increase the economic cost are mappedto a very large constant K. Finally, no state transition(Sa � Sb) results to a function value of 0. Objective function


g has a similar role that favours power consumptionminimization.

f ðSa; Sb; PÞ ¼

CP ðSbÞ�CP ðSaÞCM ðSbÞ�CMðSaÞj j ; CPðSbÞ 6 P ^ CMðSbÞ < CMðSaÞ0; Sa � Sb

K !1; in any other case;

8><>:

ð7Þ

gðSa; Sb; PÞ ¼

CMðSbÞ�CMðSaÞCP ðSbÞ�CP ðSaÞj j ; CPðSbÞ 6 P ^ CPðSbÞ < CPðSaÞ0; Sa � Sb

K !1; in any other case:

8><>:

ð8Þ

Finally, Algorithm 4 describes the construction of prob-lem solutions that will be used as initial states in localsearch. The algorithm describes the procedure findMini-mumCostSolution of Algorithm 1, that approximates theminimum cost solution SM of a TFAP instance. The algo-rithm performs a first fit assignment of flows to bearer ser-vices with priority to low cost services. Assignment takesplace with the use of append that was also used insearchStep. The construction of SM is based on the prin-ciple of reserving capacity (through assignment of flows)from the most cost efficient bearers. Thus, bearer servicesare sorted in ascending cost order prior to flow assignment.In case that two or more bearers with the same cost have




different capacity, priority is given to the highest capacitybearer. The idea is to utilize as much as possible capacityat a given cost and leave less traffic to be assigned to sub-sequent and, thus, more expensive bearers.

The minimum power consumption solution SP of aproblem instance is approximated by a variation of Algo-rithm 4 that differs from it in statement 1, where bearerservices are sorted by ascending wj and then by descendingbandwidth. In this algorithm version the power consump-tion represents the cost factor and, thus, priority is given tocapacity reservation on the most power efficient bearers.

5. Evaluation of algorithm results and runtimeperformance

5.1. Solution accuracy and runtime performance

5.1.1. Experimental settingThe evaluation of the local search algorithm for the

TFAP is based on the comparison of heuristic and exactsolutions for a large number of randomly generated prob-lem instances. Heuristic solutions are produced from a Javaimplementation of the proposed algorithm for the TFAP,while exact solutions result from a tool capable of solvingInteger Linear Programming problems [31] that will behenceforth referred to as ILP solver. The random generationof problem instances is based on three problem templates,corresponding to typical use case scenarios that motivateour approach. Each problem template specifies the prob-lem dimensions, i.e., the number of flows, radio interfacesand available bearers per radio interface. The other prob-lem parameters are randomly generated resulting in prob-lem instances that are characterized by different capacityavailability and bandwidth requirements.

The three use case scenarios are characterized by differ-ent types of terminal devices where the algorithm logic isdeployed, and different numbers of simultaneous users.These scenarios are described below:

Table 2Flows that constitute user traffic in the use case scenarios.

FlowId

Sessiontype

FlowType

Direction QoS Bandwidthrequirements(kbps)

F1 Videoconference

Audio In C 16,32,64

F2 Audio Out C 16,32,64F3 Video In C 64, 128, 192, 384F4 Video Out C 64, 128, 192, 384F5 Voice Call Audio In C 16,32,64F6 Audio Out C 16,32,64F7 Video

streamingVideo In S 64, 128, 192, 384

F8 Audiostreaming

Audio In S 16, 32, 64

F9 Emaildownload

Data In I 64, 128, 256

F10 Email upload Data Out I 64, 128, 256F11 Ftp upload Data In B 64, 128, 256, 384,

512F12 Ftp download Data Out B 64, 128, 256, 384,

512


� UC0, UC1: A single mobile user is equipped with asmart-phone or netbook (MT1) that integrates twoand three radio interfaces (e.g. 3GPP, 802.11a/b,WiMax) respectively. The user is engaged to variousapplication sessions resulting in a total number of 7flows in UC0 and 11 traffic flows in UC1, either inboundor outbound with different QoS and bandwidthrequirements.� UC2: The terminal device is a notebook (MT2) that inte-

grates four radio interfaces (3GPP, WiMax, 2 x IEEE802.11a/b). The notebook serves its user’s traffic, as wellas traffic generated by other users working in the sameteam and using MT2 as an internet gateway. We assumethat the connectivity between MT2 and other user ter-minals is established through Bluetooth, forming thusa personal area network. The traffic comprises 19 flows,either inbound or outbound, with different QoS andbandwidth requirements.� UC3: A vehicular network setting is assumed in this use

case scenario, where the access device is a mobile rou-ter (MT3) with six radio interfaces. The mobile router isincorporated in a vehicle (e.g. car or bus) and serves thetraffic generated by passengers on board. The trafficcomprises 32 inbound or outbound flows at variousQoS levels.

The different traffic flows that are served by the termi-nal devices in the various use case scenarios are describedin Table 2. The Flow Id column assigns an identifier to eachflow for referencing purposes. Column Session type de-scribes the user session that each flow is part of, while Flowtype refers to the type of content that a flow transfers.Direction refers to the flow direction, either inbound or out-bound, and the QoS column states the QoS requirements ofeach flow. These requirements are specified by means of aQoS class value that best matches the delay and jitterrequirements of the user session. The QoS classes that areconsidered are documented by 3GPP and range over: (i)Conversational – C, (ii) Streaming – S, (iii) Interactive – Iand (iv) Background – B. Finally, Bandwidth requirementscolumn refers to alternative bandwidth requirements of aflow depending on user preferences, mobile terminal capa-bilities, available codecs etc. During random problem in-stance generation the bandwidth requirements of flowsare randomly selected among the values contained in theaforementioned column.

Table 3 presents the served traffic in each use case sce-nario in terms of traffic flows that are defined in Table 2.The multiplication of a set of flows by a number denotesthe number of active instances of the respective flows in

Table 3Traffic load served in use case scenarios.

Use casescenario

Active flows Number offlows

UC0 F1, F2, F3, F4, F9, F11, F12 7UC1 F1, F2, F3, F4, F7, F9, F10, 2 � (F11,F12) 11UC2 2 � (F1,F2,F3,F4), F7, 2 � (F9,F10),

3 � (F11,F12)19

UC3 3 � (F1,F2,F3,F4), F5, F6, F7, F8,3 � (F9, F10), 4 � (F11,F12)

32



Table 5Algorithm performance results per experiment.

Exp. Id Description �em% �ep% Th (ms) Te (ms)

1 UC0, L 4.32 �1.49 4.68 174.902 UC0, M 3.99 �1.52 5.12 181.263 UC0, H 4.94 �2.51 5.88 194.894 UC1, L 6.30 �2.39 14.35 972.075 UC1, M 5.74 �2.03 16.74 1263.356 UC1, H 5.32 �2.03 22.46 1040.077 UC2, L 7.39 �2.17 58.74 4702.568 UC2, M 8.11 �2.36 68.50 5160.619 UC2, H 5.40 �2.40 91.82 4868.9410 UC3, L 11.89 �3.45 400.31 9459.9711 UC3, M 13.07 �3.51 536.60 11157.3012 UC3, H 7.44 �2.95 600.06 16442.40

Table 4Bearer capacity availability scenarios.

Capacity availability Bandwidth capacity values (kbps)

L 64, 128, 192, 256, 320, 384M 256, 320, 384, 448, 512H 384, 448, 512, 576, 640, 704, 768, 832


the use case scenario. Thus, 2x (F11,F12) means that themobile terminal serves two flows of type F11 and two oftype F12. As regards the radio access availability, we assumethe accessibility of 6 providers per radio interface, each oneproviding internet access at four QoS level (C, S, I, B). Thus,the total number of available bearer services per radio inter-face is 24 (6 Conversational, 6 Streaming, 6 Interactive and 6Background). The RAT for each one of the 24 bearer servicesaccessible through a specific radio interface is selected in arandom manner among the radio interface’s supportedRATs. The supported RATs for a 3GPP radio interface areUMTS and GPRS, while for a WLAN radio interface the sup-ported RATs are IEEE 802.11a and IEEE 802.11b. The costof each bearer service is randomly generated while itscapacity is randomly selected from a number of predefinedcapacity values. We consider 3 scenarios of capacity avail-ability for all bearer services: Low (L), Medium (M) and High(H). For each capacity availability scenario, bearer capacities(equal for both uplink and downlink) are randomly selectedfrom the value sets included in Table 4.

For each combination of use case and capacity availabil-ity scenario, we conduct an experiment for the evaluationof the TFAP heuristic algorithm. Thus, our algorithm evalu-ation process involves 12 experiments, each one corre-sponding to a different combination of problem size andcapacity availability. The tasks that are performed duringeach experiment are:

1. Generation of a large number of problem instances byrandomly fixing the values of: (a) flow bandwidth, (b)bearer service uplink and downlink capacity, (c) bearerservice cost, (d) bearer RAT. Each problem instance ischaracterized by different bandwidth requirementsand capacity availability.

2. Finding of the exact solution Se and the heuristic solu-tion Sh of each problem instance for 10 different limitson power consumption (Pi, i 2 {1, . . .,10}). Therefore,each problem instance produces 10 pairs of exact andheuristic solutions (Se, Sh). The set P =[ {Pi} for eachproblem instance is generated after finding its mini-mum cost solution Sm and minimum power consump-tion solution Sp with the help of the ILP solver. Let Pm

be the power consumption of Sm and Pp the respectivevalue for Sp. As Sp corresponds to a global minimumon power consumption, it holds that Pm P Pp. Theequality denotes a single global solution Sm for themulti-objective optimization problem and, thus, theset of limits contains just the value Pp. If Pm > Pp thenthe set of limits comprises 10 equidistant values inthe interval [Pp,Pm], including Pp, Pm.

3. Calculation for each pair of solutions (Se, Sh) of theapproximation error em ¼ CMðShÞ�CM ðSeÞ

CM ðSeÞ of the heuristicsolution against the optimal one in terms of economic


cost. In the following section a product of em by 100 willbe used and referred to as percent approximation error.An equivalent metric ep is also calculated for the powerconsumption.

5.1.2. Computational resultsTable 5 summarizes the algorithm performance results

for 12 experiments that correspond to the use case scenar-ios UC0-UC3. The results that are presented and analyzedcorrespond to 900 different problems per experiment, eachon being solved for 10 different limits on power consump-tion. Thus, each experiment is evaluated on the basis ofabout 9000 exact and heuristic problem solutions.

The first column (Exp. Id) of Table 5 assigns an identifierto each experiment, while column Description refers to thecombination of use case and capacity availability scenariothat characterize each experiment. The third column in-cludes the average percent approximation error in eco-nomic cost per experiment, while the fourth presents therespective average percent approximation error in powerconsumption. The negative values denote that the powerconsumption of heuristic solutions is generally lower thanthat of exact solutions. Given the tradeoff that exists be-tween economic cost and power consumption in the TFAPthese values are expected. Thus, the loss in economic costis to a certain extent compensated by the improvement inpower consumption. Columns five and six present theaverage execution time of the heuristic algorithm and theILP solver for solving the various problem instances on astandard workstation with a 2.2 GHz dual core processorand 2 GB of RAM. Our algorithm has an order of magnitudelower execution time that ensures fast response and allowsits deployment to mobile devices with limited processingpower capabilities.

Fig. 1 presents the cumulative distribution of percentapproximation error values for the entire set of probleminstances generated by the various experiments. The graphshows that 77% of problem instances are solved with a per-cent approximation error in economic cost lower than 10%,while 84% of them (65% of total) have percent approxima-tion error lower than 5%. On the other hand, the probabilityof having a percent approximation error higher than 40% is2.5%.

A detailed presentation of the distribution of approxi-mation error values em per experiment is included inFig. 2. Specifically, the diagram includes a different curvefor each value {1, . . .,9} of the Experiment Id axis (x-axis),



1 2

3 4

5 6

7 8

9

Experiment id

1015 0

20 40

60 80

100

Approx. error in economic cost

0

0.2

0.4

0.6

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1

Distribution of approx. error in econ. cost0.950.80.60.4

Fig. 2. Distribution of percent approximation error in economic cost for experiments 1–9.

0.7

0.95

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5 1015 30 0 20 40 60 80 100 120 140Approximation error in economic cost

Distribution of approximation error in economic cost

Fig. 1. Distribution of percent approximation error in economic cost over all problem instances.

2 Based on the problem formulation described in [27] each problem


that correspond to the distribution of approximation errorvalues em of the experiments included in Table 5. Theprojections of the distribution curves in the xy plane pres-ent the approximation error values em that correspond tothe points 40%, 60%, 80% and 95% of the cumulative distri-bution. The graph shows that 80% of problem instanceswith low to medium size are solved with relatively highaccuracy (15%), while about 75% of them (curve at 60% of


cumulative distribution) are solved with worst caseapproximation error lower equal to 6%.

As regards the problems that are generated on the basisof use case scenario UC3, their exact solution can be ob-tained by solving relatively large ILP problems2, with ILP

instance comprises 4752 variables and 359 constraints.



0.8

0.95

0

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0.4

0.6

0.8

1

5 1015 30 0 20 40 60 80 100 120 140Approximation error in economic cost

Distribution of approx. error in economic cost - Exp. 10- Exp. 11- Exp. 12

Fig. 3. Distribution of percent approximation error in economic cost for experiments 10–12.


solver execution times that range from several seconds tohours. As the process of generating a sufficient number ofproblem solutions was rather time consuming, we havedecided to use as benchmark the solutions of a relaxationof the TFAP. This relaxation is obtained by removing the flowintegrality constraints and, thus, allowing the distribution ofeach flow to more than one interfaces. The resulting prob-lem is a Mixed Integer Programming problem that is gener-ally easier to solve than the pure ILP. A mixed integersolution of a problem instance is better or equal to therespective integer solution. Thus, the approximation errorem of heuristic solutions for the experiments 10, 11 and12, as presented in Table 5 and Fig. 3, is overestimated. Nev-ertheless, given the problem size, the results are rather sat-isfactory as 90% of problem instances for each experimenthave approximation error less than 29%.

5.2. Performance evaluation in a dynamic simulationenvironment

The scope of this work lies in the specification and eval-uation of a decision mechanism for optimized utilization ofconnectivity and energy resources of a multi-homed MMT.The MMT serves application traffic flows of one or moreusers and operates in a dynamic environment. Thus, thedecision context is not static but instead depends onchanging application requirements and available radio ac-cess resources. In this section we evaluate through simula-tion the merits and performance implications of thedecision mechanism when applied to the MMT over a spe-cific time horizon. Issues related to the actual enforcementof flow assignment decisions, that involve execution ofhandoffs and flow redirections, are complementary to this


work and out of scope of this paper. For this reason, as wellas for reasons of simplicity and execution efficiency, theevaluation is based on a discrete event simulation systemthat is driven by events at flow, rather than packet granu-larity. The focus of the evaluation is threefold: (a) estima-tion of the approximation error of the proposed heuristicalgorithm ALGh when taking into account the domain oftime, (b) comparison of ALGh with an extended version ofan algorithm ALGu that employs utility functions for net-work selection in a multi-mode device [10], and (c) estima-tion of the mobility management overhead associated witheach algorithm.

The discrete event simulator is implemented in Java andmodels the random arrival of events that correspond to: (a)arrival and termination of application traffic flows and (b)changes in the available capacity of a set of radio accessnetworks. The traffic flows are generated by a number ofusers, that engage in video-conference, ftp upload/down-load and http sessions. Session arrival for each user followsa Poisson arrival process with a rate that depends on theapplication type. The duration of video-conference ses-sions is exponentially distributed with mean value 5 minand their arrival rate is 2 sessions/h. Each non real-time(NRT) session comprises a number of packet calls that isgeometrically distributed with mean 5. The arrival ratefor NRT sessions (FTP, HTTP) is 6 sessions/h for eachsession type. The data volume and inter-arrival times ofpacket calls within a NRT session are randomly generatedaccording to [32].

Each video-conference session corresponds to a pair of(incoming/outgoing) audio flows, each one requiring12 kbps of bandwidth capacity, and a pair of 128 kbps vi-deo flows. As regards NRT sessions, each packet call pz with



0.04

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Economic cost Consumed energyApproximation error

Heuristic AlgorithmUtility Algorithm

Fig. 4. Average approximation error in economic cost and consumed energy over the entire set of simulation executions.


data volume vz is mapped to a traffic flow fz. The band-width bz of fz is set to the minimum required bandwidthfor meeting a maximum tolerated file download time dz.Thus, bz = vz/dz, where dz depends on the application typeand the data volume vz. In our simulations we set dz = 3 sfor HTTP flows, while for FTP flows dz is set to: (a) 45 s,vz 6 2.5 MB, (b) 120 s, 2.5 MB < vz 6 5 MB and (c) 240 s,vz > 5 MB. Note that in a real setting dz will probably bepart of user preferences.

The time variation of each RAN’s available capacity ismodeled according to the methodology used in [33] forthe evaluation of network selection algorithms. Specifi-cally, each RAN is modeled as a Markov chain with 7states and each state corresponds to a level of capacityavailability, characterized by available bandwidth and ac-cess delay. State transitions occur according to the statetransition matrix used in [33]. The intervals betweenstate transitions are randomly generated and follow anexponential distribution. Each state transition corre-sponds to a simulation event that, along with flow arrivaland flow termination events, trigger flow assignmentdecisions.

The simulation system models the operation of a mul-ti-homed mobile router, deployed in a vehicle (e.g. a sight-seeing bus) that moves with relatively low speed in anurban area. The mobile router is equipped with 2 UMTSand 2 WLAN (IEEE802.11a/b) radio interfaces. We assumethat throughout the simulation duration the mobile rou-ter’s location is constantly served by 4 UMTS, 5 IEEE802.11a and 5 IEEE 802.11b access networks. The chargingrates of UMTS networks are higher than those of the IEEE802.11a/b networks. Specifically, the rate for each UMTSnetwork is fixed throughout the simulation duration and


ranges from 6 to 9 monetary units per kbit, while forWLANs the charging rates range from 1 to 5 units per kbit.The router’s served traffic comprises of traffic flows that ar-rive randomly from 5 users that engage in web browsing,FTP and video-conference sessions.

Each simulation execution corresponds to 3 h of simu-lated time and focuses on the minimization of the totallyincurred economic cost. The randomly arriving flow andnetwork events are processed by the ILP Solver, ALGh andALGu. Each algorithm maintains its own, probably differ-ent, flow assignment state that is updated after each exe-cution. The ILP Solver decisions result to the minimumpossible cost for a given event sequence. The proposedheuristic algorithm ALGh is also compared with a networkselection algorithm ALGu that takes into account multiplecriteria of different priority evaluated by utility functions[10]. The criteria considered in this evaluation are: (a) costCc, (b) power consumption gain Cge [10], (c) available band-width Cb, (d) required QoS class Cq. The priorities of Cc, Cge

are set to 3 (high), 0 (ignored) respectively for all simula-tion executions. Other priority levels used in [10] are 2(medium) and 1 (low). The priorities of Cb, Cq depend onthe served traffic and their configuration is explainedbelow.

Note that ALGu, as specified in [10], focuses on theselection of a single RAN, while for capacity or economicefficiency reasons more than one radio interfaces mayneed to be activated. In our evaluation ALGu is used forthe selection of more than one RANs by applying it itera-tively for the assignment of flows of QoS class C (Conversa-tional) and then for S, I and B classes respectively. Theiteration for each QoS class Qi involves the followingsimple steps:



0

1

2

3

4

5

Redirections/min Horizontal Handoffs/min

Heuristic AlgorithmUtility Algorithm

Fig. 5. Average number of flow redirections and horizontal handoffs per minute.


1. Set the priority of Cq to 3, 2, 1 or 0 according to the cur-rent value of Qi (C, S, I or B respectively).

2. Set the priority of Cb on the basis of the ratio of totalrequired bandwidth of Qi class flows to the availablecapacity through all radio interfaces for traffic of classQi. This ratio is normalized and mapped to the allowablepriority values {0, . . .,3}.

3. Evaluate available bearers with QoS class better orequal to Qi according to ALGu.

4. Assign flows of class Qi to the first possible bearer(s).

Fig. 4 presents the percent approximation error in eco-nomic cost and energy consumption of ALGh and ALGu, as itis averaged on 100 simulations. The performance of eachalgorithm is compared against the economic cost and en-ergy consumption incurred by executing the ILP solverand enforcing its decisions upon all simulation events. Asregards the execution frequency of ALGh and ALGu, we haveadopted a different policy that is more appropriate for areal-world deployment, where optimality needs to be bal-anced with system stability. Specifically, each execution ofALGh or ALGu is followed by a phase where new events arehandled with the least possible modifications to the cur-rent state. For instance, on a flow arrival event the newflow is assigned to the cheapest radio interface with sparecapacity, on a flow termination event no action is taken,etc. This phase ends with the arrival of any event thatinvalidates the current flow assignment, e.g. the QoS of aused bearer service violates its flows’ requirements orassignment of a new flow is not possible. A new valid flowassignment is derived through algorithm execution andthe process continues. As illustrated in Fig. 4, ALGh providesa good approximation to the optimal cost, despite the


aforementioned conservative execution policy. Due to thelarge decline from optimal economic cost, ALGu outper-forms ALGh in terms of power consumption.

The average mobility management overhead caused bythe application of the algorithms’ (ALGh,ALGu) decisions ineach simulated scenario is depicted in Fig. 5. The figurepresents the average number of flow redirections and hor-izontal handoffs per minute triggered by each algorithm. Aflow redirection refers to the change of the serving radiointerface of an active flow, while a horizontal handoff oc-curs when an active radio interface changes its point ofattachment to a different RAN. The graph shows that theoverhead of ALGh is very close to the respective overheadof algorithm ALGu, that represents a simpler and morestraightforward flow assignment scheme. In any case, theincurred mobility management actions are limited, giventhe gain in economic cost and the number of concurrentlyserved users.

6. Conclusions and future work

We have studied the problem of traffic flow assignmentin a mobile node, multi-homed through a set of differenttechnology radio interfaces. The problem involves associa-tion of a subset of available radio interfaces with appropri-ate radio bearer services and assignment of applicationtraffic flows to them, in a way that economic cost is mini-mized and power consumption does not exceed a prede-fined limit. We have provided an analytical formulationfor the problem and described its relationship with theMultiple Knapsack Problem with Assignment Restrictions.Problem solutions are approximated with a heuristic




algorithm that is based on local search and is characterizedby efficient execution times for a wide set of realistic prob-lem sizes. The quality of approximation is rather satisfac-tory and is evaluated through comparison of heuristicand exact solutions for a large set of randomly generatedproblem instances. Moreover, an evaluation of the ap-proach through simulation supports these findings andprovides an estimation of the associated mobility manage-ment overhead that is limited and allows real deploymentof the decision mechanism.

In our future work we will consider extensions to theproblem formulation and the respective flow assignmentalgorithm so as to handle special requirements such as:(a) support of real-time flows with alternative levels ofbandwidth requirements, where each level may corre-spond to a different codec or codec configuration, (b) sup-port of flows that use transport protocols with ConcurrentMultipath Transfer capabilities and can be distributed totwo or more radio interfaces. Moreover, we will extendthe proposed traffic flow assignment scheme with a deci-sion mechanism for automatically fixing the limit onpower consumption in response to changes in served traf-fic, minimum energy autonomy preferences, battery charg-ing level, etc. Last but not least, our research will embraceissues related to inferring the application type or QoSrequirements of traffic flows in cases that this informationcannot be obtained from the execution environment of theflow assignment algorithm. This capability is more impor-tant for a mobile node that has the role of an internet gate-way in a personal area or vehicular network.

Acknowledgements

The authors thank the anonymous reviewers for theirconstructive comments that contributed to the improve-ment of the extent and quality of this work. Special thanksneed to be attributed to Lecturer Evangelos Markakis forthe useful discussions we had on the proof of the TrafficFlow Assignment Problem’s complexity.

References

[1] Mushroom Networks Inc., Wireless broadband bonding networkappliance, 2010, <http://www.mushroomnetworks.com>

[2] T. Ernst, N. Montavont, R. Wakikawa, K. Kuladinithi, Motivations andScenarios for Using Multiple Interfaces and Global Addresses,Internet-Draft, IETF MONAMI6 Working Group, May 2008.

[3] R. Wakikawa, V. Devarapalli, G. Tsirtsis, T. Ernst, K. Nagami, Multiplecare-of addresses registration, draft-ietf-monami6-multiplecoa-14.txt (work in progress), IETF MEXT Working Group, May 2009.

[4] H. Soliman, G. Tsirtsis, N. Montavont, G. Giaretta, K. Kuladinithi, Flowbindings in mobile ipv6 and nemo basic support, draft-ietf-mext-flow-binding-03.txt (work in progress), IETF MEXT Working Group,July 2009.

[5] M. Dawande, J. Kalagnanam, P. Keskinocak, F. Salman, R. Ravi,Approximation algorithms for the multiple knapsack problem withassignment restrictions, Journal of Combinatorial Optimization 4(2000) 171–186, doi:10.1023/A:1009894503716.

[6] X. Liu, L. Xiao, A survey of multihoming technology in stub networks:current research and open issues, IEEE Network 21 (3) (2007) 32–40.

[7] D.K. Goldenberg, L. Qiuy, H. Xie, Y.R. Yang, Y. Zhang, Optimizing costand performance for multihoming, SIGCOMM ComputerCommunications Review 34 (4) (2004) 79–92.

[8] N. Thompson, G. He, H. Luo, Flow scheduling for end-hostmultihoming, in: Proceedings of the IEEE International Conferenceon Computer Communications (INFOCOM’06), 2006, pp. 1–12.


[9] J.-M. Bonnin, I. Lassoued, Z.B. Hamouda, Automatic multi-interfacemanagement through profile handling, Springer Mobile Networksand Applications 14 (1) (2009) 4–17.

[10] Q.-T. Nguyen-Vuong, N. Agoulmine, Y. Ghamri-Doudane, A user-centric and context-aware solution to interface management andaccess network selection in heterogeneous wireless environments,Elsevier Computer Networks 52 (2008) 3358–3372.

[11] P. Bellavista, A. Corradi, C. Giannelli, Mobility-aware management ofinternet connectivity in always best served wireless scenarios,Springer Mobile Networks and Applications 14 (1) (2009) 18–34.

[12] N. Kasap, H. Aytug, S.S. Erenguc, Provider selection and taskallocation issues in networks with different QoS levels and all youcan send pricing, Elsevier Decision Support Systems 43 (2) (2007)375–389.

[13] B. Xing, N. Venkatasubramanian, Multi-constraint dynamic accessselection in always best connected networks, in: Proceedings of theInternational Conference on Mobile and Ubiquitous Systems(Mobiquitous’05), 2005, pp. 56–64.

[14] V. Gazis, Toward a Generic ‘‘Always Best Connected’’ Capability inIntegrated WLAN/UMTS Cellular Mobile Networks (and Beyond) 12(3) (2005) 20–29.

[15] K. Chebrolu, R. Rao, Bandwidth aggregation for real-timeapplications in heterogeneous wireless networks, IEEETransactions on Mobile Computing 5 (4) (2006) 388–403.

[16] J. Iyengar, P. Amer, R. Stewart, Concurrent multipath transfer usingSCTP multihoming over independent end-to-end paths, IEEE/ACMTransactions on Networking 14 (5) (2006) 951–964.

[17] J. Liao, J. Wang, X. Zhu, A multi-path mechanism for reliable VoIPtransmission over wireless networks, Elsevier Computer Networks52 (13) (2008) 2450–2460.

[18] R. Fracchia, C. Casetti, C.-F. Chiasserini, M. Meo, WiSE: best-pathselection in wireless multihoming environments, IEEE Transactionson Mobile Computing 6 (10) (2007) 1130–1141.

[19] K.-H. Kim, K.G. Shin, PRISM: improving the performance of inverse-multiplexed TCP in wireless networks, IEEE Transactions on MobileComputing 6 (2007) 1297–1312.

[20] C.-L. Tsao, R. Sivakumar, On effectively exploiting multiplewireless interfaces in mobile hosts, in: CoNEXT ’09: Proceedings ofthe 5th International Conference on Emerging NetworkingExperiments and Technologies, ACM, New York, NY, USA, 2009, pp.337–348.

[21] K.-H. Kim, Y. Zhu, R. Sivakumar, H.-Y. Hsieh, A receiver-centrictransport protocol for mobile hosts with heterogeneous wirelessinterfaces, Wireless Networks 11 (4) (2005) 363–382.

[22] R. Stewart, Q. Xie, K. Morneault, C. Sharp, H. Schwarzbauer, T. Taylor,I. Rytina, M. Kalla, L. Zhang, V. Paxson, Stream Control TransmissionProtocol, Standard RFC 2960, IETF Network Working Group (Oct.2000).

[23] 3GPP, Quality of Service (QoS) concept and architecture (Release 8),Tech. Rep. TS 23.107 V8.0.0 (12, 2008).

[24] IEEE 802.21 Working Group, Media Independent Handover Services,Draft standard, IEEE, 2007.

[25] J. Lorchat, T. Noel, Power performance comparison of heterogeneouswireless network interfaces, in: IEEE 58th Veh. TechnologyConference (VTC’03-Fall), 2003, pp. 2182–2186.

[26] C.A. Coello, An updated survey of GA-based multiobjectiveoptimization techniques, ACM Computing Surveys 32 (2) (2000)109–143.

[27] V.E. Zafeiris, E.A. Giakoumakis, Towards flow schedulingoptimization in multihomed mobile hosts, in: Proceedings of theIEEE 19th International Symposium on Personal, Indoor and MobileRadio Communications (PIMRC 2008), 2008, pp. 1–5.

[28] S. Russell, P. Norvig, Artificial Intelligence: A Modern Approach,second ed., Prentice Hall, 2003. pp. 94–136.

[29] S. Martello, P. Toth, Knapsack Problems: Algorithms and ComputerImplementations, John Wiley and Sons, 1990.

[30] M.R. Garey, D.S. Johnson, Computers and Intractability; A Guide tothe Theory of NP-Completeness, W.H. Freeman & Co., New York, NY,USA, 1990.

[31] LINDO Systems, LINGO – Optimization Modeling Software for Linear,Nonlinear, and Integer Programming, <http://www.lindo.com>,2010.

[32] 3GPP, Feasibility Study for Orthogonal Frequency DivisionMultiplexing (OFDM) for UTRAN enhancement (Release 6), Tech.Rep. TR 25.892 V6.0.0 (6 2004).

[33] E. Stevens-Navarro, V. Wong, Comparison between vertical handoffdecision algorithms for heterogeneous wireless networks, in: IEEE63rd Vehicular Technology Conference (VTC’06), vol. 2, 2006, pp.947–951.


http://www.mushroomnetworks.com

http://dx.doi.org/10.1023/A:1009894503716

http://www.lindo.com


omputer Networks xxx (2010) xxx–xxx

Vassilis E. Zafeiris is Ph.D. researcher in theInformatics Department of the Athens Uni-versity of Economics and Business. Hereceived his Dipl. in Electrical Engineeringfrom the National Technical University ofAthens (NTUA) in 2001 and a M.Sc. in Infor-mation Systems from the Athens University ofEconomics and Business in 2003. His researchinterests include mobility management innext generation networks, handover man-agement in heterogeneous radio access net-works, software agents and their application

in mobile networking.

18 V.E. Zafeiris, E.A. Giakoumakis / C


Emmanouel A. Giakoumakis is an associateprofessor of Software Engineering in theInformatics Department of the Athens Uni-versity of Economics and Business. Hereceived his Dipl. in Electrical Engineering andPh.D. in Computer Engineering from theNational Technical University of Athens(NTUA) in 1981 and 1988 respectively. He hasserved as President of the Hellenic RegulatoryAuthority for Telecommunications (2000–2005). His research interests include softwareengineering, software architectures and

interoperability, biomedical applications and regulation and competitionin electronic services.



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