IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 1

Power-Efficient Load Distribution for MultihomedServices With Sleep Mode Over Heterogeneous

Wireless Access NetworksJoohyung Lee, Nga T. Dinh, Ganguk Hwang, Member, IEEE, Jun Kyun Choi, Senior Member, IEEE, and

Chimoon Han, Member, IEEE

Abstract— The use of multi-interfaced devices has been steadilyincreasing due to the popularity of multihomed streaming ser-vices in heterogeneous wireless access networks. However, runningmultiple interfaces simultaneously in a mobile terminal (MT)may cause serious battery drain even when interfaces employsleep modes. In addition, sleep modes may result in significantdegradation of the quality of service (QoS) in terms of packet delayor jitter. This paper examines multihomed MTs and the use of datastripping load distribution across the multiple wireless interfacesof the MTs to minimize their power consumption. This paper thendevelops a theoretical framework for a power-efficient multipathload distribution that encompasses a dynamic load distributionto each interface employed with sleep mode. For this purpose,the paper first presents analytical models for power consump-tion and the delay of each interface by considering a mediumaccess control (MAC) operation. Using these models, two simplegreedy distribution algorithms are proposed to optimize the loaddistribution. Extensive simulations in an ns-2 simulator undervarious practical configurations demonstrate that the proposed al-gorithms significantly reduce power consumption while satisfyingQoS constraints.

Index Terms—Heterogeneous wireless access networks, loaddistribution, packet reordering (PR), power consumption.

Manuscript received June 23, 2012; revised June 14, 2013, August 4, 2013,and October 7, 2013; accepted October 27, 2013. This work was supportedin part by the Korea Evaluation Institute of Industrial Technology of theMinistry of Knowledge and Economy of Korea through the Information andTechnology Research and Development Program under Grant 10039160 (Re-search on Core Technologies for Self-Management of Energy Consumptionin Wired and Wireless Networks) and in part by the Seoul MetropolitanGovernment through the Research and Business Development Program underGrant WR080951. An earlier version of this paper was presented at theIEEE Global Communications Conference (Selected Areas in CommunicationsSymposium—Green Communication Systems and Network Track), Houston,TX, USA, December 2011. The review of this paper was coordinated byProf. F. R. Yu.

J. Lee and J. K. Choi are with the Department of Electrical Engineering,Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea(e-mail: joohyung08@kaist.ac.kr; jkchoi@ee.kaist.ac.kr).

N. T. Dinh is with Bell Labs Seoul, Seoul 120-270, Korea (e-mail:dinh.nga@alcatel-lucent.com).

G. Hwang is with the Department of Mathematical Sciences, Korea Ad-vanced Institute of Science and Technology, Daejeon 305-701, Korea (e-mail:guhwang@kaist.edu).

C. Han is with the Department of Electronics and Information Engineer-ing, Hankuk University of Foreign Studies, Daejeon 305-701, Korea (e-mail:cmhan@hufs.ac.kr).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2013.2289390

I. INTRODUCTION

THE DEMAND for broadband multimedia services (e.g.,Internet Protocol and Smart TVs) over wireless access

networks is dramatically increasing with the widespread adop-tion of multi-interfaced devices such as smartphones and PCtablets. Users can easily access multimedia content anytimeand anywhere through such multi-interfaced handheld devicesby securing the required bandwidth from all available wirelessaccess networks using multihoming capabilities. Multihomingis a promising solution for heterogeneous wireless access net-works due to its many benefits, including load balancing andreliability [1].

There are various approaches to realizing efficient load dis-tribution solutions that address the QoS in multi-interfaceddevices with multihoming capability by taking advantage ofheterogeneity and a high degree of network connectivity. Themajor problems with these approaches are load imbalance andpacket reordering (PR) [2], [3]. Additionally, running multipleinterfaces simultaneously can significantly reduce the batterylife of a mobile terminal (MT). To the best of our knowledge,there has been no significant research on load distributionover heterogeneous wireless access networks to simultaneouslymeet QoS requirements and improve power efficiency. Loaddistribution in multihoming thus remains an open issue, and thisis the inspiration for this paper.

To reduce the power consumption of MTs, a sleep modeis employed on the medium access control (MAC) layer inwireless access networks [4]. Existing solutions have consid-ered the optimization problem of the sleep duration with agiven load for different wireless access networks (e.g., 802.16,802.11, etc., [5]–[8]). However, these solutions consider only asingle interface. Hence, they are not applicable to multihomingsituations. In addition, there have been no studies on load distri-bution on those devices where sleep mode is employed for eachinterface.

In this paper, we propose novel load distribution algorithmsfor multihomed services. To overcome the limitations of con-ventional solutions, the proposed scenario includes a multi-interfaced device with multihoming capability, and each of theinterfaces employs a sleep-mode mechanism to reduce powerconsumption. Here, a multi-interfaced device decides how todistribute the load from all available wireless access networksto minimize its power consumption while guaranteeing the

0018-9545 © 2013 IEEE

2 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY

required QoS. The contributions of this paper are summarizedas follows:

• This paper presents analytical models for power consump-tion and delay for different kinds of interfaces of an MTand describes their performance.

• Two novel power-efficient load distribution (PELD) algo-rithms for multihomed services are proposed. In particular,the paper first formulates the optimization problem forminimizing power under the delay requirement. The algo-rithm is then extended to alleviate the reordering problemwith delay difference boundary condition.

• Basically, the proposed optimization problem is noncon-vex. Thus, effective greedy distribution algorithms to findan optimal solution are considered.

• NS-2 based simulation results are provided to demonstratethe effectiveness of the proposed greedy algorithms bypresenting how much the power consumption is reduced,whereas other important performances such as packet lossrate and delay are reasonably guaranteed.

The remainder of this paper is organized as follows.Section II summarizes previous works on load distribution formultihoming and sleep mode for an MT. Section III presentsmodels for power consumption and delay, and explains theirperformance under different scenarios. Based on these mod-els, the load distribution algorithms are then described inSection IV. A simulation evaluation is provided in Section V.Finally, Section VI concludes this paper.

II. RELATED WORK

A. Load Distribution Techniques in Multihoming

An introduction to load distribution techniques in multipathnetworks and related challenges and issues can be found in [3].Notably, because load distribution techniques can affect varioussystem performances such as throughput, load balancing, andPR, it has attracted a tremendous amount of research. Earlystudies on load distribution over multipath networks focusedon designing a stripping mechanism in different layers such astransport or network layers [9], [10]. However, these studies didnot consider QoS, cost, latency, etc., in various applications.Thus, to address these shortcomings, various approaches toload distribution over multipath networks have been suggested.The most well-known approach is the round robin (RR)-basedscheme [2], which focuses on the load balancing problem by afair load distribution. However, such approaches are not ableto maintain per-flow packet ordering. Furthermore, althoughthe least-loaded-based scheme [11] is one of the most well-known algorithms, it does not consider the order of packets.In the load distribution over multipath networks, a large delaydifference among different paths results in a high risk of PR,leading to large latency, buffer size, and PR processing power.To resolve the reordering problem, Prabhavat et al. [3] proposedthe effective delay-controlled load distribution (E-DCLD) al-gorithm, which minimizes the reordering risk by minimizingthe difference of delay in multipath networks. Recently, novelperformance analyses of probabilistic multipath transmission ofvideo streaming traffic were proposed in terms of the average

delay, delay jitter, and delay outage probability in [12]. In otherstudies [1], a novel distributed multiservice resource-allocationalgorithm in multihoming services was proposed. Here, bothconstant and variable bit-rate services were considered, aswell as different resource access priorities; however, the powerefficiency of load distribution over multiple interfaces was ig-nored. In this sense, in homogeneous wireless access networks,Zhao and Xie [13], [14] proposed a power-efficient design onthe upper network layers by considering power consumptioncaused by the location update procedure where an MT’s sleepand active mode are employed. Moreover, in heterogeneouswireless access networks, a power-minimized rate-allocationscheme was proposed in [15]; although this work suggests thepossibility of reducing power consumption of multi-interfaceddevices, detailed MAC operations (e.g., sleep mode) and PRwere not considered.

B. Sleep Mode in the MAC Layer

Sleep mode has been extensively studied in World Interoper-ability for Microwave Access (WiMAX) and wireless local areanetworks (WLANs). In WiMAX, sleep mode is specified differ-ently for different power saving classes, which vary by param-eter sets, procedures of sleep-mode activation/deactivation, andpolicies for data transmission of an MT [16]. Xiao evaluatedsleep-mode performance in WiMAX [17] in terms of averageenergy consumption and response delay. In [18], the sleep-stateduration is adjusted by considering the previous sleep-stateduration under light traffic conditions. Unfortunately, theseapproaches result in worse delay than the original sleep modewhen traffic is high, although power efficiency is improved.Han and Choi [19] numerically analyze the sleep mode usinga Markov chain and derive the packet delay and power con-sumption for sleep, listening, and waking-up states. Analyticalstudies have been carried out to find the optimal sleep dura-tion to minimize the power consumption while guaranteeingrequired QoS [5]–[7]. Unlike in WiMAX where sleep-stateduration can be changed [17], in WLANs, sleep-state durationis basically fixed. A WLAN is a shared medium communica-tion, requiring the sending of a polling message to retrieve thebuffered traffic. This results in competition among MTs thathave pending packets [8], [20]. This competition affects thedelay in accessing the medium and the power consumption.In [8], Lei and Nilson describe two models for WLAN powermanagement to achieve good energy efficiency with minimalQoS degradation: the M/G/1 queue with a bulk service modeland the D/G/1 queue model. Baek and Choi extended the studyof power saving mode in [8] to include a simple derivation ofthe mean and the variance of packet delay [20].

To the authors’ knowledge, no previous studies have ad-dressed the power efficiency and sleep mode in MAC in relationto load distribution for multihoming. The existing researchactivities on load distribution have been confined to the scope ofthe throughput or QoS optimization problem, although multipleinterfaces may have different MAC operations and thus affectthe power efficiency. This paper investigates both the loaddistribution problem and detailed sleep mode at each interfacefor multihoming conditions. In this paper, we stay within the

LEE et al.: PELD FOR MULTIHOMED SERVICES WITH SLEEP MODE OVER WIRELESS ACCESS NETWORKS 3

TABLE INOTATION FOR FORMULATION

Fig. 1. Description of PELD.

optimization framework for a power-efficient load distributionwith varying constraints and compare the performance of theproposed algorithms to that of previous approaches.

III. SYSTEM MODELS

Here, we present our scenarios and analytical models forpower consumption and delay for each interface in a multi-homed MT. In this paper, the analysis is restricted to downlinktraffic. The notation is summarized in Table I. Two sets of inter-faces are considered: I = {I1, I2}. Note that this interface setI can be classified into two categories, i.e., I1 (WiMAX) andI2 (WLAN). It is assumed that the holding rate μi at interface iis exponentially distributed and that packets arriving at an MTfollow a Poisson distribution with rate λ [3], [21]. The arrivalrate λ is then partitioned as rate λi over each interface i bya splitting vector ψi (λi = λψi), where an MT computes theoptimal splitting vector ψi over each interface i to minimizethe total power consumption of all interfaces while satisfyingdelay requirements. Fig. 1 shows a functional block diagram of

the proposed algorithms. Basically, our system design follows[22], [23], where the load distribution scheduler is located inan MT. The main difference is that the proposed algorithmsadditionally collect the estimated power consumption at eachinterface for a power-efficient load distribution. The detailedprocedures entail four steps. First, to check the required QoSand load λ, an application interface recognizes an applicationtype currently running on the MT. Second, a load information λof the application is passed on to the load distribution scheduler.Third, the load distribution scheduler calculates the optimalsplitting vector ψi according to the estimated power consump-tion and delay. Finally, the application service is requested fromthe server by splitting the load over each interface i using ψi. Amore detailed discussion of the system design can be found in[22] and [23].

Fig. 2(a) and (b) shows the sleep modes in WiMAX andWLAN, respectively, where an MT repeatedly alternates be-tween sleep and wake modes to reduce power. In WiMAX,a sleep mode includes a number of sleep cycles, where eachsleep cycle is composed of a sleep-state duration Tl (l = 1,2, . . .) that is adjusted on a binary-exponentially basis [16]and a listening-state duration TL. In WLAN, a sleep cycle isbasically fixed as listen interval L, which is a multiple of beaconintervals B. In sleep mode, an MT alternately enters between asleep state, where it powers down most of its functions, and alistening state, where it powers up the receiver to check whetherthere were packets addressed to it while in the sleep state. Ifthere is a packet for that MT, the packet is put into the MT’sbase station (BS) queue. The MT then transits into wake mode;otherwise, the MT sleeps again. Specifically, in WLAN, due tothe competitive nature on a shared medium, to retrieve packets,an MT stays awake and sends a polling message [8], [20].

A. Models for WiMAX Interface

1) Power Consumption: We consider the case where inter-face i (i ∈ I1) transitions from sleep mode to wake modeafter k sleep cycles. This happens when there are no downlinkpackets arriving at interface i during the first (k − 1) sleepcycles and at least one packet arrives during the kth sleep cycle.Let Tl,i and TL,i be the sleep-state duration and listening-stateduration of the l th sleep cycle in sleep mode at interfacei, respectively. In WiMAX, Tl,i varies from the initial sleep-state duration Tmin,i to the final sleep-state duration Tmax,i

on a binary-exponentially basis [16]. Let Prk,i(λi) be theprobability of the sleep-to-wake transition with a given rate λi;then, Prk,i(λi) is determined such that

Prk,i(λi)=

{1−e−λi(TC1,i), with k=1

e−λi

∑k−1

l=1(TCl,i)

(1−e−λi(TCk,i)

), otherwise

(1)

where notation TCk,i is the duration of the kth sleep cycleand equal to Tk,i + TL,i. Note that e−λt is the probability thatthere is no packet arriving during t according to a Poissondistribution [24].

When interface i transitions from the kth sleep cycle to wakemode, it must spend an average amount of time TNk,i in wake

4 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY

Fig. 2. Description of sleep operation of (a) WiMAX and (b) WLAN interfaces.

mode to process all packets in its BS queue. Let Nk,i denotethe average number of packets arriving during interface i’s kthsleep cycle. Note that these packets include: 1) packets arrivingduring interface i’s sleep time, and 2) packets that newly arrivewhile the interface i is processing packets in the queue. prm(t)denotes the probability that there are m packets arriving duringtime t; then, according to a Poisson distribution, prm(t) isdetermined such that [24]

prm(t) = e−λit(λit)m/m!. (2)

Let nk,i be the number of packets arriving during the interfacei’s kth sleep cycle. Then, Nk,i is

Nk,i =E[nk,i|nk,i ≥ 1]

=

∞∑m=1

E[nk,i|nk,i = m,nk,i ≥ 1]

× P{nk,i = m|nk,i ≥ 1}

=

∞∑m=1

E[nk,i|nk,i = m]P{nk,i = m,nk,i ≥ 1}

P{nk,i ≥ 1}

=

∞∑m=1

m · prm(TCk,i)

1 − Pr0(TCk,i)(3)

where, m is the number of packets in the queue, andprm(TCk,i) is the probability that there are m packets duringthe interface i’s kth sleep cycle.

In (3), the MT wakes up after kth sleep cycle only if thereis at least one packet in the queue. Therefore, it is necessaryto take the conditional probability as in (3). Accordingly, thedenominator in (3) is used to guarantee that there is at least onepacket in the queue.

Let NEk,i be the average total number of newly arrivedpackets while interface i is in wake mode after the kth sleepcycle in sleep mode. Since the average processing rate is μi,TNk,i is given by

TNk,i =1μi

(Nk,i +NEk,i). (4)

By Little’s law [24], NEk,i = λi · TNk,i; we obtain

TNk,i(λi) =Nk,i

μi − λi. (5)

Let PS,i and PL,i be the consumed power at interface iduring sleep and listening states, respectively. In addition,assume that the power needed for an interface to transitionfrom one state to another can be negligible; the average powerconsumption of interface i (ξI1i ) (i ∈ I1) can be then calculatedas follows:

ξI1i (λi) =

∞∑k=1

Prk,i(λi)

k∑l=1

(PCl,i) + TNk,i(λi)PL,i

k∑l=1

(TCl,i) + TNk,i(λi)

(6)

where, Tl,i PS,i + TL,i PL,i = PCl,i is the energy consumptionduring the l th sleep cycle at interface i. In the kth term in (6),Prk,i(λi) is the probability that interface i is in sleep modefor k cycles, the numerator is the energy consumption in sleepmode including k cycles and in wake mode for duration TNk,i

to transmit all downlink packets, and the denominator is thetotal duration that interface i is in sleep and wake modes.

2) Delay: The mean service delay at interface i caused bysleep mode includes two kinds of delay: 1) mean delay TD1,i

for interface i to transition from sleep mode to wake mode and2) mean queuing delay TD2,i that a given packet needs to waitto process all its previous packets in the BS queue.

LEE et al.: PELD FOR MULTIHOMED SERVICES WITH SLEEP MODE OVER WIRELESS ACCESS NETWORKS 5

Fig. 3. Average power consumption and delay of WiMAX.

Suppose that the MT spends k sleep cycles in sleep mode,which happens with probability Prk,i(λi). We divide the ksleep-state duration TCk,i into K small equal subintervals,where K is sufficiently large. Then, the duration that a packetarriving during the lth subinterval has to wait for an MTto transition from sleep mode to wake mode is (TCk,i −l(TCk,i/K)). In this case, the mean transition delay is

1K

K∑l=1

(TCk,i − l

TCk,i

K

)=

TCk,i

2− TCk,i

2K. (7)

Since limK→∞(TCk,i/(2K)) = 0, (7) becomes TCk,i/2, andTD1,i is determined as follows:

TD1,i(λi) =∞∑

k=1

Prk,i(λi)TCk,i

2. (8)

Now, we assume that there are l packets in the queue;this event happens with probability (prl(TCk,i))/(

∑∞m=1

prm(TCk,i)). For the jth packet (1 ≤ j ≤ l), the time neededto process (j − 1) previous packets is ((j − 1)/μi). The meantime that each packet needs to wait is

∑li=1(j − 1/2μi). There-

fore, TD2,i is given by

TD2,i(λi) =∞∑

k=1

Prk,i(λi)∞∑l=1

l − 12μi

prl(TCk,i)∞∑

m=1prm(TCk,i)

. (9)

Let ϕI1i be the total mean delay of a packet at interface i

caused by sleep mode; then, it is determined such that

ϕI1i (λi) = TD1,i(λi) + TD2,i(λi). (10)

3) Numerical Results: We evaluate the average power con-sumption and delay for the WiMAX interface using our an-alytical model. Fig. 3 shows the average power consumptionand delay in the WiMAX interface as a function of networkloading (λi/μi, where i ∈ I1), which is defined as the ratioof the packet arrival rate divided by the packet departure rate(or the MT processing rate) at the WiMAX interface. Thefigure shows that power consumption at interface i increasesas loading increases. This is because, when the processingrate is fixed, an increase in loading means that there are more

arriving packets, forcing the MT to more frequently transitionfrom sleep mode to wake mode. Furthermore, the MT requiresmore time in wake mode to process those packets. Since powerin wake mode is higher than that in the sleep state or thelistening state, the power consumption increases. It is alsoshown in Fig. 3 that delay decreases with the increase innetwork load (packet arrival rate increases). It is due to that,as the packet arrival rate increases, TD1,i becomes smaller dueto shorter sleep-cycle duration. In addition, because the sleep-cycle duration becomes smaller, the required time to processthe arrived packets during the sleep-cycle duration is negligiblein a moderate arrival region. Consequently, TD2,i can be alsonegligible. In a high arrival rate, the processing time could notbe negligible. However, this is outside the scope of this paper.

B. Models for WLAN Interface

We consider beacon interval Bi in access point (AP) i (notethat index i for the AP is same as for the interface); then,the listen interval of an MT in AP i is Li = kBi, where k =1, 2, 3. The following clarifies the differences between WLANand WiMAX sleep modes.

• The sleep window (listen interval L in the case of WLAN)is of fixed duration. (In case of WiMAX, it changes on abinary-exponentially basis.)

• An MT with shared medium communications (e.g.,WLANs) has to send a polling message to retrieve thebuffered traffic using carrier sense multiple access withcollision avoidance. This means that the MTs that havepending packets are competitors [8], [20], [25], thus af-fecting the average delay and the power consumption.

Assumptions of power consumption and delay models re-lated to WLAN basically follow those in [8] and [20]. Thus, weassume that there are mtotal,i MTs downloading traffic throughinterface i (i ∈ I2). All MTs employ sleep mode and have thesame priority and packet arrival rates. Let mi be the numberof MTs sharing the same beacon interval in AP i; then, mi

is obtained by mi = mtotali ·Bi/Li. Since packets arrive toa certain interface i of the MT with rate λi, the total numberof packet arrivals in the AP i toward the MT sharing the samebeacon interval also follows a Poisson process with rate miλi.

1) Power Consumption: The upper and lower bounds of theaverage sleep ratio of interface i are obtained by [25]

qi(λi) =

{qi(λi)upper = 1 − miλi

kμi

qi(λi)lower = 1 − miλi

2kμi− λi

2μi.

(11)

Based on the given equations, the user can decide the averagesleep ratio of an interface for the power efficiency metric ac-cording to two different cases: 1) low battery power, and 2) highbattery power. In case 1, the user prefers to use the lower boundto save more power consumption. On the other hand, in case 2,the user prefers to use the upper bound. The average powerconsumption of WLAN at interface i (i ∈ I2) of an MT isdetermined as follows:

ξI2i (λi) =PS,i · qi(λi) + PL,i (1 − qi(λi))

=PL,i − (PL,i − PS,i) · qi(λi). (12)

6 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY

Fig. 4. Average power consumption and delay of WLAN.

2) Delay: To obtain the mean delay of a packet caused bysleep mode, the total waiting time of a packet includes fourkinds of delay: 1) the time between the arrival of the packet(kBi/2); 2) the waiting time caused by other packets in thesame batch ((λiBi)/(2μi)); 3) packet processing time (1/μi);and 4) the waiting time experienced by a batch in the queue.However, the fourth type of delay can be negligible becauseit is very small [8]. Therefore, the mean delay of a packet atinterface i (i ∈ I2) is determined as

ϕI2i (λi) =

kBi

2+

λiBi

2μi+

1μi

. (13)

3) Numerical Results: Fig. 4 shows the average power con-sumption and delay with respect to network loading (λi/μi,where i ∈ I2) in the WLAN interface where sleep mode isemployed. The actual power consumption is bounded by theupper and lower limits of power consumption. Furthermore,the power does not dramatically increase as the arrival rate λi

increases due to the constant sleep interval (beacon interval). Inaddition, the delay increases as network loading increases. Thisis because when μi is fixed, network loading can be consideredthe arrival rate λi. Here, delay increases with λi because thewaiting time caused by other packets coming during Bi/2 (thetime between the arrival instant of the packet and the beginningof the next listen interval) increases.

IV. POWER-EFFICIENT LOAD DISTRIBUTION ALGORITHMS

FOR MULTIHOMED SERVICES WITH SLEEP MODE

Using analytical models for power consumption and delayfor different interface types on an MT given earlier, we addressthe problem of load distribution over multiple access networksfrom several perspectives. We first introduce the optimizationproblem for solving the power minimization with delay con-straints. This is a basic approach to minimizing power con-sumption at an MT with a minimal constraint. Based on theformulation, we can also gain insight into the rate-allocationbehavior at multiple networks with a simple condition. InSection IV-B, the reordering effect is considered an importantconstraint. This problem can be used as an efficient tool tominimize power consumption while satisfying the requiredreordering delay. In Section IV-C, we briefly discuss the con-vergence of the proposed algorithms.

A. PELD Without PR

We investigate the load distribution (in packets/s) that min-imizes the summation of the average power consumption (inwatts) at each interface in a multihomed device. As the firststep to formulating the optimization problem, we assumed thatthere is only a single stream over interface i. The optimizationproblem of minimizing the summation of power consumptionat each interface (total power consumption) is then formulatedas follows:

minψi

∑i∈I

ξtypei (ψi · λ) (14)

s.t. ψi ≥ 0 for ∀ i ∈ I (15)

ψi · λ ≤ μi for ∀ i ∈ I (16)∑i∈I

ψi = 1 for ∀ i ∈ I (17)

ϕtypei (ψi · λ) ≤ δi for ∀ i ∈ I. (18)

where type refers to I1 or I2 (WiMAX or WLAN), andψi · λ = λi.

In (14), the objective function is considered the summation ofthe power consumption at each interface i (i ∈ I) according tothe distributed allocated load (ψi · λ), where the average powerconsumption metric at interface i (ξtypei ) can be decided byeach interface i’s type from (6) and (12). Thus, for the givenoptimization problem, we seek an optimal splitting vector ψi

that minimizes the objective function with given constraints(15)–(18) and other system parameters (e.g., μi, Tmin,i, Tmax,i,PS,i, PL,i, etc). Specifically, the constraints in (15) and (17)represent the feasible region of splitting vectors. This meansthat the splitting vector at interface i (i ∈ I) should be greaterthan or equal to zero to guarantee a nonnegative load distribu-tion. Note that the summation of the splitting vector equals 1.In addition, allocated load to a certain interface i cannot exceedthe service rate of interface i (i ∈ I), as expressed in (16).The constraint in (18) expresses the delay requirement δi foreach interface i (i ∈ I) where the mean delay of a packet atinterface i (ϕtype

i ) can be decided by each interface i’s typefrom (10) and (13).

For the analysis, we first deal with a simple multihomedhomogeneous case. In particular, a multihomed MT has a set ofWLAN interfaces. We then extend our analysis to a multihomedheterogeneous case where the MT has two types of interfaces(WiMAX and WLAN). In the first case, the optimization prob-lem can be classified as a hard or soft optimization problembased on the upper and lower bounds of the average sleepratio (qi(λi)).

• Hard optimization problem. An MT is very sensitive topower consumption due to limited battery. We can directlychoose the lower bound of the average sleep ratio metricin the case of WLAN.

• Soft optimization problem. An MT chooses the upperbound of the average sleep ratio metric in the case ofWLAN.

LEE et al.: PELD FOR MULTIHOMED SERVICES WITH SLEEP MODE OVER WIRELESS ACCESS NETWORKS 7

Because the objective and inequality constraint functions areconvex and the equality constraint functions are linear (or moregenerally, affine), the problem is a convex optimization problem(or convex program) [26]. The basic idea in Lagrange dualityis to relax the original problem (14)–(18) by transferring theconstraints to the objective in the form of a weighted sum. Wethen define a Lagrangian associated with the given problemto be

L(ψ, χ, γ, σ, ) =∑i∈I

ξtypei (ψi · λ)−∑i∈I

χiψi

+∑i∈I

γi (ψi · λ− μi) + σ

(∑i∈I

ψi − 1

)

+∑i∈I

i

(ϕtypei (ψi · λ)− δi

)(19)

where type is restricted at I2, and (χ, γ, σ, ) is the set of dualvariables.

We use one of the distributed algorithms to solve (14)–(18),which is a Lagrangian algorithm based on a dual decomposition[27]. The Lagrangian algorithm for this problem is given by

ψ(h+1)i =ψ

(h)i − α

{∇iξ

I2,(h)i − χ

(h)i + γ

(h)i λ

+ σ(h) +(h)i

}(20)

χ(h+1)i =

[χ(h)i − β · ψ(i)

i

]+

(21)

γ(h+1)i =

[γ(h)i + θ(ψi · λ− μi)

]+

(22)

σ(h+1) =

[σ(h) + ν

(∑i∈I

ψi − 1

)]+ (23)

(h+1)i =

[

(h)i + o

(ϕI2i (ψi · λ)− δi

)]+

(24)

where [·]+ = max{0, ·}, h is the time index, and α, β, θ, ν, ando are fixed step sizes.

The update equation for dual variables is a projected gradientalgorithm for maximizing the Lagrangian with respect to itsdual variable argument. The reason for the projection is thatthe Karush–Kuhn–Tucker (KKT) multiplier vector is requiredto be nonnegative to satisfy the KKT condition [28].

In the next step for the optimization problem, an MT hastwo types of interfaces (WiMAX or WLAN) and is thus amultihomed heterogeneous case. Due to the nonconvexity ofthe average power metric of WiMAX in (6), this optimizationcan be solved by an exhaustive search algorithm. However, thecomplexity is considered very low due to the limited numberof interfaces. Specifically, the computational complexity of theoptimization problem linearly increases with the number ofavailable access networks K on the order of O(K). The PELDwithout PR is shown as Algorithm 1. Let ξ(t) be the total powerconsumption at the t th iteration and λ be the total packet arrivalrate. In addition, we define ε as the bound of optimal points. Forthe first step of the proposed algorithm, we input the interfacetype (e.g., WiMAX or WLAN). According to the interface type,

various system parameters should be defined. The algorithmstarts with an initial splitting vector and power consumption(steps 1–6) and then iteratively finds the optimal PELD pointfor an MT (steps 7–23). We have two main constraints forfinding the optimal point: packet delay and power consumption.Before checking the power consumption, we check the averagepacket delay (step 10). To minimize the total average powerconsumption, Algorithm 1 should satisfy ξ(t) ≤ ξ(t−1). Afterchecking the delay and power consumption conditions, we set anew splitting vector for distribution of the load to each interfacei (steps 19–22). This algorithm will stop after reaching theoptimal load distribution point |ξ(t) − ξ(t−1)| ≤ ε; otherwise,it keeps searching for the optimal point.

Algorithm 1 Greedy PELD without PR for a multiinterfacemobile node

Input: type at interface i, ∀ i ∈ IEnsure: type ∈ {I1, I2}Ensure: If type = I1 then

system parameters: μi, Tmin,i, Tmax,i, PS,i, PL,i

Ensure: If type = I2 thensystem parameters: qi(λi), PS,i, PL,i, Bi

1:Initialize ψi = 1/|I|∀ i ∈ I2:Initialize Δψ = constant3:Initialize t = 04:Initialize kbest = argmini∈I ξ

typei (ψi ∗ λ)

5:Initialize kworst = argmaxi∈I ξtypei (ψi ∗ λ)

6:Initialize ξ(t) = ∞7:repeat8: t = t+ 19: Send stream traffic.10: if

∨i∈I(ϕ

typei > δi) then,

11: ibest = argmini∈I(ϕtypei − δi)

12: iworst = argmaxi∈I(ϕtypei − δi)

13: Δψ = Δψ/214: else if ξ(t) > ξ(t−1) then,15: ibest = argmini∈I ξ

typei (ψi ∗ λ)

16: iworst = argmaxi∈I ξtypei (ψi ∗ λ)

17: Δψ = Δψ/218: end if19: Δψ′ = min(Δψ, μk/λ− ψibest

)20: Δψ′ = min(Δψ′, ψiworst

)21: ψibest

= ψibest+Δψ′

22: ψiworst= ψiworst

−Δψ′

23:until |ξ(t) − ξ(t−1)| ≤ ε

B. PELD With PR

To develop the first-step optimization problem, we considerdelay difference with multiple paths tightly connected with thePR performance. PR is important for a multipath load distribu-tion because PR due to delay difference can induce additionaldelay, processing buffer, and processing power consumption.To simplify the problem, we assume that, if the differencebetween maximum and minimum delays of the interfaces is

8 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY

bounded by threshold values, the effects of PR can be negligible[3]. The optimization problem of minimizing the total powerconsumption is then formulated as follows:

minψi

∑i∈I

ξtypei (ψi · λ) (25)

s.t. ψi ≥ 0 for ∀ i ∈ I (26)

ψi · λ ≤ μi for ∀ i ∈ I (27)∑i∈I

ψi = 1 for ∀ i ∈ I (26)

R(ψi · λ) ≤ Rth for ∀ i ∈ I (28)

where R(ψi · λ) = max(ϕtypei (ψi · λ))−min(ϕtype

i (ψi · λ)).Equation (29) is considered an important constraint to guar-

anteeing that there is no PR risk. The detailed procedure forobtaining the optimal solution of (25)–(29) is described inAlgorithm 2. In this algorithm, we consider PR due to delaydifference at multiple paths. Note that Algorithm 2 checks thedifference between maximum delay and minimum delay overmultiple paths bounded in the threshold value Rth (step 5). Thealgorithm will converge to the optimal point of minimum powerconsumption without PR risk.

Algorithm 2 Greedy PELD with PR for a multiinterfacemobile node

1:Same procedure of Algorithm 1 until line 62:repeat3: t = t+ 14: Send stream traffic.5: if

∨i∈I(

∨i′∈I\{i}(max(ϕtype

i )−min(ϕtypei′ )>Rth) then,

6: ibest = argmini∈I(ϕtypei )

7: iworst = argmaxi∈I(ϕtypei )

8: Δψ = Δψ/29: else if ξ(t) > ξ(t−1) then,10: ibest = argmini∈I ξ

typei (ψi ∗ λ)

11: iworst = argmaxi∈I ξtypei (ψi ∗ λ)

12: Δψ = Δψ/213: end if14: Δψ′ = min(Δψ, μi/λ− ψibest

)15: Δψ′ = min(Δψ′, ψiworst

)16: ψibest

= ψibest+Δψ′

17: ψiworst= ψiworst

−Δψ′

18:until |ξ(t) − ξ(t−1)| ≤ ε

C. Proposed Algorithms Complexity

The convergence time of Algorithms 1 and 2 increases withthe number of: 1) available access networks I, and 2) iteration tdecided by the step size Δψ. Since we reduce the Δψ value byhalf for each iteration, we need log(Δψ) iterations. The com-putational complexity of this algorithm is then O(K log(Δψ)).Moreover, the proposed greedy algorithms will regardless con-verge because of the fixed criteria and reduction of the step size

Fig. 5. NS-2 simulation model for the proposed PELD.

for each iteration. (The size of fixed criteria may influence thequality of the solution.)

In real communication systems, the power consumption be-havior cannot be easily modeled as a convex or linear func-tion. It is therefore difficult to search the optimal distributionpoint mathematically from an exact power consumption model.Our proposed heuristic algorithms can be easily adopted anddeployed to find the optimal point with low complexity andconvergence time, although various nonlinear or nonconvexperformance functions are considered. Thus, the algorithmscan be considered a promising solution with load distributionover heterogeneous wireless access networks and wired accessnetworks.

V. PERFORMANCE EVALUATION

Here, we evaluate how much the proposed load distributionalgorithms reduce the power consumption while other impor-tant performances such as packet loss rate and delay (e.g.,maximum delay and minimum delay, and delay difference) arereasonably guaranteed. Specifically, we compare the perfor-mance of the proposed algorithms to other existing schemesusing an NS-2 simulation of practical configurations as follows:

• Proposed PELD algorithm with/without PR;• RR-based load distribution scheme [2];• Least-loaded-first (LLF) scheme [11];• E-DCLD scheme [3].

A. Simulation Methodology

1) Simulation Scenario and Setup Description: Fig. 5 showsour new wireless node architecture where we changed the struc-ture of the MAC, the interface queue, the link layer, the networkinterface, Address Resolution Protocol (ARP), and the routingagent to support NS-2 mobile nodes with multiple interfaces.

LEE et al.: PELD FOR MULTIHOMED SERVICES WITH SLEEP MODE OVER WIRELESS ACCESS NETWORKS 9

Fig. 6. Optimal point convergence time of the PELD algorithm.

The MT is equipped with both WLAN and WiMAX interfaces,where each interface employs sleep mode. The current MACmodules for NS-2 include 802.11, Ethernet, time-division mul-tiple access, and satellite; however, no 802.16 MAC module isavailable. Thus, we use WiMAX extensions from [29] for ourstudy. In the simulations, a single WiMAX BS and two WLANAPs are placed in the center of an area of 300 ∗ 300 m2. Thesource of the streaming service is a so-called mobile networkoperator (MNO) placed in the fixed Internet portion of thenetwork. The MNO is connected to WiMAX and IEEE 802.11APs via error-free wired links. User data are transmitted overthe downlink direction (APs to MT). For the uplink direction(MT to APs), a probing packet is transmitted every 2 s, andstandard communication packets (e.g., AP association, ARP,etc.) use both uplink and downlink channels. The simulationtime is 600 s. Our simulation design is simple and has lowcomplexity. Fig. 6 shows how fast the proposed algorithmconverges to the optimal point. Here, with an initial step size of50 kb/s, the proposed algorithm converged to the optimal loaddistribution point within eight iterations. However, to check thedelay and the holding rate for optimal distribution, the MT hasto send the probing packet (if the MT sends the probing packetmore frequently, the distribution vector will converge to a moreaccurate optimal vector), and this causes additional delay andpower consumption.

2) Simulation Parameters: The system parameters used inthe simulation are configured based on the IEEE 802.11 and802.16 recommendations, respectively [16], [30], [31]. Detailedparameters are presented in Tables II and III. For the transportlayer protocol, we use the Transmission Control Protocol Renomodel. In addition, for power consumption measurement, eachaccess network is assigned different power consumption pa-rameters for each state (e.g., sleep, listening, or active states).Then, focusing on interface power consumption, we measureand calculate the average power consumption in the receivingmode from the interface state corresponding to the trafficarrival rate.

3) Simulation Assumptions: For the simulation, we basi-cally assume that there is no barrier between the BS (or AP)

TABLE II802.16 (WIMAX) SYSTEM PARAMETERS

TABLE III802.11 (WLAN) SYSTEM PARAMETERS

and an MT. An MT has no mobility as a static user. We alsoassume that the queue size of the BS (or AP) is large enoughto accommodate the maximum packet arrival rate. Therefore,packet loss is only caused by late packets. For the channelmodel, we use two ray ground propagation models [32]. Thepacket arrival is modeled as a Poisson process, and a packetlength of 3040 bits is used in the simulation [15].

B. Simulation Results

In Fig. 7, the normalized power consumption of the proposedalgorithms, which is defined as the actual power consumptionper maximum power consumption, is less than that of otherconventional schemes, particularly for higher data rates. Here,at 300 kb/s, PELD can achieve 7% power consumption re-duction compared with E-DCLD. In the case of PELD withPR, although it consumes more power than that without PR, itcompensates the risk of PR by tightly controlling the allowabledelay difference between each interface. In Fig. 8, at 300 kb/s,we checked the power consumption behavior with a varyingnumber of WLAN devices. As the number of WLAN usersincreases, there is greater power consumption due to severecompetition to retrieve the buffered traffic.

10 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY

Fig. 7. Power consumption dependence on data rate (200 and 300 kb/s).

Fig. 8. Power consumption with a varying number of WLAN devices.

In Fig. 9, we changed the value of the deadline constraint(from 250 to 500 ms), and compared the packet loss ratio. Sincethe short deadline constraint means the tight delay requirement,the packet loss ratio decreased with the deadline constraint.Here, we can check that PELD with PR has less packet lossrate than PELD by controlling the load distribution to satisfy thedelay requirement. Then, we can also observe that the proposedalgorithms (PELD and PELD with PR) have similar packetloss rate to others at 500-ms deadline constraint. In a multipathload distribution, PR is very important since it causes additionalreordering recovery delay and power consumption. In addition,the possibility of PR could be indirectly predicted by the delaydifference between the maximum delay and minimum delay[3]. In this case, if the difference is lower than the packetinterarrival time, the risk of PR could be negligible. Hence,to illustrate the risk of PR, we first present in Fig. 10(a) themaximum delay of the proposed algorithms in comparison toothers. Note that the minimum delay of various schemes hasa very small value (less than 10−5 s) and a minor impact on

Fig. 9. Packet loss rate with varying deadline constraints.

Fig. 10. (a) Maximum delay and (b) minimum delay with varying data rate.

LEE et al.: PELD FOR MULTIHOMED SERVICES WITH SLEEP MODE OVER WIRELESS ACCESS NETWORKS 11

Fig. 11. Delay difference with varying data rate.

the delay difference for the risk of PR, as shown in Fig. 10(b).Here, we observe that the maximum delay of the proposed algo-rithms (PELD and PELD with PR) has similar behavior to RRand E-DCLD. This observation is also related to delay differ-ence. Hence, with regard to delay difference, the conventionalE-DCLD has the lowest delay difference because it focuses onminimizing this parameter, as shown in Fig. 11. Thus, E-DCLDis suitable for eliminating the risk of PR. On the other hand,the LLF scheme causes a high delay difference due to lack ofconsideration of the significant variation in the packet delayof different paths. In comparison with E-DCLD, the proposedalgorithms also achieve reasonable delay difference.

VI. CONCLUSION

This paper has dealt with the problem of data stripping loaddistribution across multiple interfaces, where each interfaceemploys sleep mode, of a multihomed MT over a heterogeneouswireless access network to minimize its power consumption.We first presented analytical models for power consumptionand delay for different types of interfaces i.e., WiMAX andWLAN in the MT. Based on these models, we proposed apower-efficient load distribution algorithm without PR, whichminimizes the overall MT power consumption under delayconstraint. The algorithm was then extended by taking intoaccount the delay and PR risk. The analytical and simulationresults under various practical configurations (e.g., WLAN andWiMAX standards) demonstrate that the proposed algorithmcan significantly reduce power consumption while guaranteeingQoS requirements.

ACKNOWLEDGMENT

The authors would like to thank H. Oh for his helpful supportof the simulation, Dr. C. Randy Giles at Bell Labs for his reviewand proofreading, and Dr. S. H. Shah Newaz at KAIST for histechnical discussion of this paper.

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Joohyung Lee received the B.S. and M.S. degreesfrom the Korea Advanced Institute of Science andTechnology (KAIST), Daejeon, Korea, in 2008 and2010, respectively. He is currently working towardthe Ph.D. degree with KAIST.

From June 2012 to March 2013, he was a Vis-iting Researcher with the Information EngineeringGroup, Department of Electronic Engineering, CityUniversity of Hong Kong, Hong Kong. Since 2010,he has contributed several articles to the Interna-tional Telecommunication Union Telecommunica-

tion Standardization Sector Study Group 13 Questions 9 and 22. His currentresearch interests include resource allocation and optimization, with a focus onresource management for broadband wireless networks, green networks, smartgrids (future power grids), and network economics.

Dr. Lee has been an active member of the GreenTouch Consortium. Hehas been a Technical Reviewer for several conferences and journals, suchas the IEEE COMMUNICATIONS LETTERS, the IEEE TRANSACTIONS ON

VEHICULAR TECHNOLOGY, and Elsevier Computer Communications. Hereceived a Best Paper Award at the Integrated Communications, Navigation,and Surveillance Conference in 2011.

Nga T. Dinh received the M.S. and Ph.D. degreesfrom the Korea Institute of Science and Technology,Daejeon, Korea, in 2005 and 2009, respectively.

From September 2009 to June 2010, she was aPostdoctoral Researcher with the Gwangju Instituteof Science and Technology, Gwangju, Korea. Sincethen, she has been a technical staff member with BellLabs Seoul, Seoul, Korea. Her current research inter-ests include energy efficiency of telecommunicationnetworks, dynamic bandwidth allocation, networkoptimization, wired/wireless convergence networks,

and quality-of-user experience/quality of service.

Ganguk Hwang (M’03) received the B.Sc., M.Sc.,and Ph.D. degrees in mathematics (applied probabil-ity) from the Korea Advanced Institute of Scienceand Technology (KAIST), Daejeon, Korea, in 1991,1993, and 1997, respectively.

From February 1997 to March 2000, he was withthe Electronics and Telecommunications ResearchInstitute, Daejeon. From March 2000 to February2002, he was a Visiting Scholar with the School ofInterdisciplinary Computing and Engineering, Uni-versity of Missouri, Kansas City, MO, USA. Since

March 2002, he has been with the Department of Mathematical Sciences,KAIST, where he is currently a Professor. From August 2010 to July 2011, hewas a Visiting Scholar with the Department of Electrical Engineering, Uni-versity of Washington, Seattle, WA, USA. His research interests includeteletraffic theory, performance analysis of communication systems, quality-of-service provisioning for wired/wireless networks, and cross-layer design andoptimization for wireless networks.

Jun Kyun Choi (SM’00) received the M.S. (Eng.)and Ph.D. degrees in electronic engineering from theKorea Advanced Institute of Science and Technol-ogy (KAIST), Daejeon, Korea, in 1985 and 1988,respectively.

From June 1986 to December 1997, he was withthe Electronics and Telecommunication ResearchInstitute, Daejeon. In January 1998, he joined theInformation and Communications University (nowknown as, KAIST) as a Professor. His research in-terests include broadband network architecture and

technologies, with particular emphasis on performance and protocol problems.Dr. Choi was an active member of the International Telecommunication

Union Telecommunication Standardization Sector Study Group 13 as either aRapporteur or an Editor focusing on the asynchronous transfer model, multi-protocol label switching, and next-generation network issues, in January 1993.He has also submitted more than 30 drafts in the International Engineering TaskForce over the past few years.

Chimoon Han (M’98) received the B.S. degree inelectronic engineering from Kyungpook NationalUniversity, Daegu, Korea, in 1977; the M.S. degreein electronic engineering from Yonsei University,Seoul, Korea, in 1983; and the Ph.D. degree in in-formation and communication engineering from TheUniversity of Tokyo, Tokyo, Japan, in 1990.

From 1977 to 1983, he was with the Korea Insti-tute of Science and Technology, Seoul. From 1983 to1997, he was with the Electronics and Telecommu-nications Research Institute, Daejeon, Korea. Since

March 1997, he has been with Hankuk University of Foreign Studies, Seoul,where he is currently a Professor with the Department of Electronic Engineer-ing and served as the Dean for the College of Engineering from 2002 to 2003and the Vice President in 2007. His research interests include next-generationnetworks, green information technology, network security, and performanceanalysis.