energy efficient cooperative video distribution with statistical qo s provisions over wireless...

Energy-Efficient Cooperative VideoDistribution with Statistical QoS

Provisions over Wireless NetworksAmin Abdel Khalek, Student Member, IEEE, and Zaher Dawy, Senior Member, IEEE

Abstract—For real-time video broadcast where multiple users are interested in the same content, mobile-to-mobile cooperation can

be utilized to improve delivery efficiency and reduce network utilization. Under such cooperation, however, real-time video

transmission requires end-to-end delay bounds. Due to the inherently stochastic nature of wireless fading channels, deterministic delay

bounds are prohibitively difficult to guarantee. For a scalable video structure, an alternative is to provide statistical guarantees using

the concept of effective capacity/bandwidth by deriving quality of service exponents for each video layer. Using this concept, we

formulate the resource allocation problem for general multihop multicast network flows and derive the optimal solution that minimizes

the total energy consumption while guaranteeing a statistical end-to-end delay bound on each network path. A method is described to

compute the optimal resource allocation at each node in a distributed fashion. Furthermore, we propose low complexity approximation

algorithms for energy-efficient flow selection from the set of directed acyclic graphs forming the candidate network flows. The flow

selection and resource allocation process is adapted for each video frame according to the channel conditions on the network links.

Considering different network topologies, results demonstrate that the proposed resource allocation and flow selection algorithms

provide notable performance gains with small optimality gaps at a low computational cost.

Index Terms—Scalable video coding, real-time video broadcast, statistical QoS guarantees, mobile-to-mobile cooperation.

Ç

1 INTRODUCTION

THE real-time nature of video broadcast demands quality-of-service (QoS) guarantees such as delay bounds for

end-user satisfaction. Given the bit rate requirements ofsuch services, delivery efficiency is another key objective.The H.264/AVC video coding standard [1] is designed toprovide high coding efficiency that is suitable for wirelessvideo transmission. To provide a network-friendly design,the scalable video coding (SVC) extension of H.264 [2]allows rate scalability at the bitstream level by generatingembedded bit streams that are partially decodable atdifferent bitrates with degrading quality. The basic levelof quality is supported by the base layer and incrementalimprovements are provided by the enhancement layers.Video source rate scalability can be achieved with temporal,spatial, or quality scalability [2].

Deterministic delay bounds are prohibitively expensiveto guarantee over wireless networks. Consequently, toprovide a realistic and accurate model for quality of service,statistical guarantees are considered as a design guidelineby defining constraints in terms of the delay-bound

violation probability. The notion of statistical QoS is tied

back to the well-developed theory of effective bandwidth

[3], [4], [5] and its dual concept of effective capacity [6], [7],

[8]. For scalable video transmission, a set of QoS exponents

for each video layer are obtained by applying the effective

bandwidth/capacity analyses on the incoming video stream

to characterize the delay requirement [9], [10]. The problem

of providing statistical delay bounds for layered video

transmission over single hop unicast and multicast links

was considered in [9]. For general multihop multicast

network scenarios, it is inefficient to allocate resources

independently among network links since the variation in

the supported service rates among different links affects the

end-to-end transport capability in the network.Cooperation among mobile devices in wireless networks

has the potential to provide notable performance gains in

terms of increasing the network throughput [11], [12], [13],

[14], [15], extending the network coverage [16], [17], [18],

decreasing the end-user communication cost [19], and

decreasing the energy consumption [20], [21], [22]. For

example, the ICAM architecture presents an integrated

cellular and ad hoc multicast scheme to increase the cellular

multicast throughput through the use of mobile stations

(MSs) as ad hoc relays [13]. In the UCAN architecture [12],

the MSs use their WLAN interface to enhance the

throughput and increase the coverage of a wireless wide

area network. In [19], MSs are assumed to be connected to

several wireless networks with different characteristics in

terms of bandwidth, packet loss probability, and transmis-

sion cost. A near optimal solution is shown to reduce end-

user cost while meeting distortion and delay constraints.

IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 11, NO. 7, JULY 2012 1223

. A. Abdel Khalek is with the Wireless Networking and CommunicationGroup (WNCG), Department of Electrical and Computer Engineering,University of Texas at Austin, 1 University Station C0803, Austin, TX78712-0240. E-mail: [email protected].

. Z. Dawy is with the Department of Electrical and Computer Engineering,Faculty of Engineering and Architecture, American University of Beirut,Riad El-Solh, PO BOX 11-0236, Beirut 1107 2020, Lebanon.E-mail: [email protected].

Manuscript received 2 Sept. 2010; revised 9 May 2011; accepted 14 May 2011;published online 7 June 2011.For information on obtaining reprints of this article, please send e-mail to:[email protected], and reference IEEECS Log Number TMC-2010-09-0416.Digital Object Identifier no. 10.1109/TMC.2011.127.

1536-1233/12/$31.00 � 2012 IEEE Published by the IEEE CS, CASS, ComSoc, IES, & SPS

http://ieeexploreprojects.blogspot.com

The advantages of cooperation among mobile devices inwireless networks have been also revealed for videostreaming applications [23], [24], [25], [26], [27]. For example,the CHUM architecture assumes that all mobile devices areinterested in the same video content that is divided intomultiple descriptions [23]; each mobile device randomlyselects and pulls a video description through a cellular linkand multicasts it to all members in its cooperation groupwhich is formed in an ad hoc manner. In [27], the authorspropose distributed video scheduling schemes for multi-radio multihop wireless networks to minimize videodistortion and ensure distortion-fairness sharing amongmultiple description video streams. The distortion model isconstructed to provide a balance between the selfishmotivation of minimizing video distortion and the globalperformance of minimizing network congestion.

Minimizing energy consumption in battery-operatedmobile devices is essential for the development of nextgeneration heterogeneous wireless communications sys-tems. Enhancement schemes and communication architec-tures with cooperation among mobile devices to reduceenergy consumption appear extensively in the literature,e.g., see [20], [22], [28], [29], [30]. In [22], a cooperativenetwork architecture is presented and experimentallyevaluated to reduce energy consumption in multiradiomobile devices for video streaming applications. In [30], acomprehensive experimental study is conducted whereresults presented demonstrate notable energy reductiongains by collaborative downloading. The problem ofresource allocation with statistical QoS guarantees andoptimized energy consumption over cooperative networkswith general topologies has not been tackled yet in theliterature. While the work in [27] addresses optimized rateallocation and routing over cooperative wireless networks,it is fundamentally different from our work since weconsider minimizing energy consumption in mobile term-inals as the central objective, providing statistical delayguarantees, and capturing layered video content with QoSrequirements per layer.

In this work, we develop optimized flow selection andresource allocation schemes that can provide end-to-endstatistical delay bounds and minimize energy consumptionfor video distribution over cooperative wireless networks.The network flow for video content distribution can be anysequential multihop multicast tree forming a directedacyclic graph that spans the network topology. We modelthe queuing behavior of the cooperative network accordingto the effective capacity link layer model. Based on thismodel, we formulate and solve the flow resource allocationproblem to minimize the total energy consumption subjectto end-to-end delay bounds on each network path. More-over, we propose two approximation algorithms to solvethe flow selection problem which involves selecting theoptimal flow in terms of minimizing energy consumption.The first algorithm uses negated signal-to-noise ratios(SNR) as link weights on the complete network graph,finds the minimum spanning tree using those weights tomaximize the sum rate, and performs optimal resourceallocation on the flow corresponding to the obtained treestructure. The second algorithm maintains a set ofdominant flows that are optimal for a potentially largepercentage of channel states under a certain networktopology and performs flow selection on that dominant

set. By updating the optimal allocation and flow selectioniteratively in each time frame according to the instanta-neous channel states, the Algorithms effectively reselect thebest network flow and reconfigure the service process oneach link to provide optimized end-to-end transport.

The cooperative network model is presented in Section 2.The procedure for providing end-to-end delay bounds foreach path in the network is described in Section 3. InSection 4, the problem of cooperative video distribution isformulated as a convex optimization problem and theoptimal solution is derived. In Section 5, two approximationalgorithms for flow selection are proposed and discussed interms of complexity. In Section 6, results of the proposedresource allocation and flow selection schemes are pre-sented and analyzed for different network topologies.Finally, conclusions are drawn in Section 7.

2 COOPERATIVE NETWORK MODEL

The proposed system model consists of a base station (BS),denoted by M0, and K MSs M1; . . . ;MK which are capableof transmitting, receiving, or relaying a scalable videobitstream. The BS is responsible for distributing the samemultilayer video stream to the MSs over wireless fadingchannels. We define a flow as a tree of adjacent links thatrepresents consecutive unicast/multicast transmissions. Weare given a set of N candidate flows where the nth flow isdefined by a set of links Fn which form a directed acyclictree (DAG).

Fig. 1a shows an example network with seven MSs and afixed network flow used to explain the system model. Thisnetwork flow consists of four distinct paths leading to M4,M7, M6, and M3 and traversing all MSs. We define Pni as theset of nodes traversed by the ith path of the nth flow. For thefirst path in the given example network, Pn1 ¼ fM0;M1;M4g.We refer to pn as the number of paths in flow Fn. Thus,pn ¼ 4 for the fixed network flow n. The set of unicast/multicast receivers for MSMk in the nth flow is denotedMn

k .For example, the set of multicast receivers for the BStransmission is Mn

0 ¼ fM1;M2;M3g and jMn0 j ¼ 3. Note

that jMnk j ¼ 1 characterizes a unicast transmission by Mk.

The video stream generated by the scalable video codecconsists of L video layers. Each layer maintains a separatequeue at each node and has specific QoS requirementsaccording to its relevance in the decoding process.

The time frame T is defined as the difference between theplayback time of two video frames at the receiver, i.e., thereciprocal of the video frame rate. Within this duration T ,the video frame contents corresponding to the L layersshould be transmitted as per the construction of flow F n toall K receivers to avoid playback buffer starvation. Fig. 1bshows the time frame structure corresponding to the fixednetwork flow in Fig. 1a for explanation purposes. We treateach path of the multicast tree separately by allowing thecontent to be streamed simultaneously (in parallel) ondifferent paths of the network flow. This is based on theassumption that channels are readily available for all MSs inthe network. Note that the number of channels required isupper bounded by the number of paths in the network. Forexample, the 4-path network flow in Fig. 1 requires onlytwo channels to support the simultaneous transmission byM1 and M2. The number of paths is typically significantly

1224 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 11, NO. 7, JULY 2012


lower than the network size K, and in realistic scenarios,the network size is much less than the number of availablechannels in the wireless technology utilized for the shortrange transmissions. For instance, Bluetooth uses frequencyhopping for multiple access with a carrier spacing of 1 MHzand a total bandwidth of 80 MHz [31].

Let Tnk;l½j� denote the time slot duration allocated bynode k to layer l in the jth frame if flow F n is used. We needto guarantee that

Pk2Pni

PLl¼1 T

nk;l½j� � T 8 path i 8 frame j

where k ¼ 0 refers to the BS transmission and k > 0 refers toMS Mk’s transmission. The time proportion tnk;l½j� ¼ Tnk;l½j�=Trepresents the normalized resource allocation, thus, theresource allocation bound reduces to

1

T

Xk2Pni

XLl¼1

Tnk;l½j� ¼Xk2Pni

XLl¼1

tnk;l½j� � 1 8i; j � ð1Þ

In general, different links may be employing differenttechnologies, and thus having different bandwidths. Thesignal bandwidth for the transmission of node k isdenoted Bk Hz. The wireless channels are assumed to beflat fading. Then, the instantaneous signal to noise ratiosare used to characterize the channel state information(CSI) under the assumption that the SNR is perfectlyestimated by all MSs and reliably fed back to the BSwithout delay. The SNR vector ��½j� ¼4 f�k;k0 ½j�gK K

k¼0;k0¼1

represents a fading state of the network for frame j where�k;k0 ½j� is the instantaneous SNR on the link between nodesMk and Mk0 . Moreover, �� is modeled as an ergodic andstationary block-fading process invariant within the dura-tion of the time frame and uncorrelated among consecu-tive frames.

We consider a network with no loss tolerance, that is,multicast is limited by the supported rate on the link withthe lowest SNR [9]. For this purpose, we define the effectiveSNR for the transmission of node k as follows:

�k½j� ¼ mink02Mn

k

�k;k0 ½j� � ð2Þ

Assuming capacity-achieving codes are used to provide thecapability of operating at the Shannon capacity, the transmis-sion rate of node k is Rk½j� ¼ Bk logð1þ �k½j�Þ. The serviceprocess Ck;l½j� (bits/frame) of node k for the lth video layerand jth frame can be expressed as follows:

Cnk;l½j� ¼ Tnk;l½j�Rk½j� ¼ BkTt

nk;l½j� log2ð1þ �k½j�Þ � ð3Þ

In the sequel, we drop the frame index j for convenience.

3 STATISTICAL END-TO-END DELAY BOUNDS FOR

GENERAL NETWORK FLOWS

In this section, we describe the procedure for providing end-

to-end delay guarantees by characterizing link-level QoS

metrics according to the effective capacity link layer model.

3.1 Queuing Network Model for Multihop LayeredVideo Transmission

A separate queue is maintained for each video layer at each

node. The arrival process at the BS is denoted fA0;lgLl¼1 and

is determined by the scalable codec parameters and the

video content. Given this arrival process and the instanta-

neous SNRs f�k;k0 gK Kk¼0;k0¼1, we are interested in adaptively

configuring the service processes fCk;lgL Kl¼1;k¼0 such that the

following condition is satisfied:

PrXk2Pni

Dnk;l > Dth

8<:

9=; � Pth 8l; i; ð4Þ

where Dnk;l is the queuing delay at node k for layer l if

flow Fn is used, Dth is the end-to-end statistical delay-

bound, Pth is the target delay-bound violation probability,

Pni is the set of nodes along the ith path of flow F n.The behavior of the queue-length process in queuing-

based communication networks is extensively treated in

[32]. In an acyclic network, the queue length at time t of

each queue can be bounded exponentially as t!1

ABDEL KHALEK AND DAWY: ENERGY-EFFICIENT COOPERATIVE VIDEO DISTRIBUTION WITH STATISTICAL QOS PROVISIONS OVER... 1225

Fig. 1. System model.


PrfQk;lðtÞ > Qthg ¼: e��lQth ; 0 � k � K; 0 � l � L; ð5Þ

where Qk;l is the queuing delay at MS Mk for video layer land Qth is the queue-length threshold. The parameter �l,termed the QoS exponent, is used to characterize delay.More stringent QoS requirements are characterized bylarger �l while looser QoS requirements require smaller �l.

3.2 Effective Bandwidth/Capacity Model

The effective capacity channel model captures a generalizedlink-level capacity notion of the fading channel bycharacterizing wireless channels in terms of functions thatcan be easily mapped to link-level QoS metrics, such asdelay-bound violation probability. Thus, it is a convenienttool for designing QoS provisioning mechanisms [6], [9].

We denote by Cnk;lð�lÞ and Ank;lð�lÞ the effective capacityand effective bandwidth functions, respectively, for thekth link and lth layer when flow F n is used. Given anarrival process fAn

k;lg, its effective bandwidth, denotedby Ank;lð�lÞ (bits/frame), is defined as the minimum constantservice rate required to guarantee a specified QoS exponent�l. In contrast, for a given service process fCn

k;lg, its effectivecapacity, denoted by Cnk;lð�lÞ (bits/frame), is defined as themaximum constant arrival rate which can be supported byfCn

k;lg subject to the specified QoS exponent �l. Moreover,for a stationary and ergodic service process fCn

k;lg that isuncorrelated across time frames, the effective capacity canbe expressed as follows [33]:

Cnk;lð�lÞ ¼ �1

�llog�IE�e��lC

nk;l��

ð6Þ

¼ � 1

�llog�IE�e��lBkT ðtnk;l logð1þ�kÞÞ�� ð7Þ

The target QoS exponent �l for a given layer l should be thesame for all transmissions to guarantee the same level ofquality over the entire path. To provide the QoS guarantee�l for the lth video layer, the effective capacity on thekth link should be equal to the effective bandwidth [34], i.e.,

Cnk;lð�lÞ ¼ Ank;lð�lÞ 8l ¼ 1; . . . ; L; k ¼ 0; . . . ; K: ð8Þ

Moreover, we assume that, at the link layer, the serviceprocess of the kth queue is input instantaneously as thearrival processes to all its multicast nodes k0 2 Mn

k ,i.e., fAn

k;lg ¼ fCnk0;lg 8k0 2 Mn

k . Thus,Ank;lð�lÞ ¼ Cnk0;lð�lÞ 8l; k ¼0; . . . ; K; k0 2 Mn

k and each end-to-end path of the networkflow can be treated separately. By induction, we deduce thatthe service processes should be designed to guarantee thatthe effective capacity is the same for the multicast/unicasttransmissions by each node in the network, i.e.,

Cn0;lð�lÞ ¼ Cnk;lð�lÞ 8k ¼ 1; . . . ; K: ð9Þ

Since all links satisfy the same QoS requirement �l and using(7), it is sufficient to ensure that the service processes on alllinks are equal. We deduce that the following condition onthe resource allocation tnk;l will implicitly satisfy (9)

B0

�tn0;l logð1þ �0Þ

�¼ Bk

�tnk;l logð1þ �kÞ

�8k ¼ 1; . . . ; K: ð10Þ

Intuitively, (10) can be described as an adaptive allocationstrategy that guarantees that the video frame data (inbits/frame) are delivered reliably over all multihop paths.

Since individual links support different rates according tothe instantaneous fading state, the required time slotallocations are weighted inversely by the supported rates.

3.3 End-to-End Delay Bounds on Network Paths

The arrival process fA0;lgLl¼1 at the BS has an average arrivalrate �l ¼ IE½A0;l=T � for each video layer l. The per-layerarrival rate is determined by the parameters of the scalablecodec and by the video content. Given this arrival process andthe instantaneous SNRs, we are interested in adaptivelyconfiguring the service processes fCn

k;lgL Kl¼1;k¼0 such that the

end-to-end delay bounds are satisfied for every path. Tomodel the end-to-end delay bound for each path in thenetwork, we consider a fluid model of traffic such that theservice at each node is cut through. Considering constant ratefluid traffic, the total delay can be bounded as follows [7], [8]:

PrXk2Pni

Dnk;l > Dth

8<:

9=; � Pth ¼: e��lC

ni;lð�lÞDth 8l; i; ð11Þ

where Dnk;l is the queuing delay at node k for layer l if flow

Fn is used, Dth is the end-to-end statistical delay bound,and Pth is the delay-bound violation probability, and Cni;lð�lÞis the effective capacity function of the equivalent channelfor path Pni . Also, Cni;lð�lÞ can be conveniently upperbounded by the effective capacity of the worst link alongthe path, i.e., Cni;lð�lÞ � mink2Pni Ck;lð�lÞ.

Thus, we can guarantee the statistical delay constraint byrequiring that Cni;lð�lÞ ¼ Cnk;lð�lÞ � Cl8k 2 Pni where Cl isselected to satisfy the delay constraint with equality, thatis, Cl ¼ Al ¼ �l � T for each video layer. The serviceprocesses fCn

k;lg are then designed such that the end-to-end statistical delay bound is satisfied. Since Cnk;lð�lÞ is afunction of �l, for a given Dth and Pth, we use (11) to find therequired QoS exponent �l for each layer. For the constant-rate arrival process fAlg, the expression is

�l ¼ �logPth

T�lDth: ð12Þ

4 ENERGY-EFFICIENT RESOURCE ALLOCATION AND

FLOW SELECTION

In this section, we formulate and solve the problem ofhybrid unicast/multicast resource allocation over multihopcooperative networks with statistical end-to-end delaybounds. Moreover, we present a procedure for time slotadaptation and flow selection over the multihop links toobtain the optimal solution.

4.1 Problem Formulation

The cooperative content distribution problem can besubdivided into two components: The first component is acontinuous component that involves finding the optimalallocation of time slots for all multicast transmissions alongall paths of a given network flow. The second component isa combinatorial component that involves selecting the flowthat minimizes energy consumption among all other flowsin the network independently for each video frame. Theinterdependence of the two components is clear: Theminimum energy consumption on any flow is determinedby solving the first component, and the optimal resource



allocation will take place on the network flow selected by

the second component.We are given the delay bound Dth, the delay bound

violation probability Pth, and the arrival rates ��. The QoS

exponent �l is specified according to (12). The variables of

the problem are the time slot allocation variables

ttnn ¼4 ftnk;lgL Kl¼1;k¼1. It will also be of interest to focus on the

first hop (BS) allocation defined as ttnn00 ¼4 ftn0;lg

Ll¼1.

LetP0;t be the constant transmit power of the BS,Pk;t be the

constant transmit power of MS Mk, and Pr be the power

consumed by each MS during reception. The energy con-

sumed for the BS transmission is ðP0;t þ jMn0 jPrÞ

PLl¼1 t

n0;l ¼

wn0PL

l¼1 tn0;l where jMn

0 j is the number of multicast receivers.

Similarly, the energy consumed for the transmission by MS

Mk is ðPk;t þ jMnk jPrÞ

PLl¼1 t

nk;l ¼ wnk

PLl¼1 t

nk;l where we define

weights wnk as follows:

wnk ¼P0;t þ jMn

0 jPr if k ¼ 0;Pk;t þ jMn

k jPr if 1 � k � K:

�ð13Þ

The objective of minimizing energy consumption per flow

can now be formulated in terms of the first hop allocation

as follows:

minttnn

XKk¼0

XLl¼1

IE�Enk;l

�ð14Þ

¼ minttnn

IE T wn0XLl¼1

tn0;l þXKk¼1

wnkXLl¼1

tnk;l

!" #ð15Þ

¼ minttnn

00

IE T wn0XLl¼1

tn0;l þXKk¼1

wnkR0ð�ÞRkð�Þ

XLl¼1

tn0;l

!" #ð16Þ

¼ minttnn

00

IE T wn0 þR0ð�ÞXKk¼1

wnkRkð�Þ

!XLl¼1

tn0;l

" #; ð17Þ

where Rkð�Þ ¼ Bk log2ð1þ �kÞ is the transmission rate of

Mk. Based on this formulation, we define

�n ¼ T wn0 þR0ð�ÞXKk¼1

wnkRkð�Þ

!: ð18Þ

We further want to satisfy (1) for all paths in the flow. Thus,

we write the resource allocation constraint in terms of the

first hop allocation as follows:

Xk2Pni

XLl¼1

tnk;l � 1 8i; ð19Þ

Xk2Pni

R0ð�ÞRkð�Þ

0@

1AXL

l¼1

tn0;l � 1 8i; ð20Þ

where we define �ni as follows:

�ni ¼Xk2Pni

R0ð�ÞRkð�Þ

: ð21Þ

The statistical delay bound constraint is Ck;lð�lÞ � Cl.Additionally, we require that the allocation variables areinversely weighted by the instantaneous service rates asdescribed by (10). Now, we formulate the problem ofadaptive resource allocation for general flows in terms ofthe first hop allocation vector ttnn00 ¼

4 ftn0;lgLl¼1 as follows:

minttnn

00

IE �nXLl¼1

tn0;l

" #ð22Þ

s:t: IE e��lB0Ttn0;l

log2ð1þ�0Þh i

� e��lCl 8 l ð23Þ

�niXLl¼1

tn0;l � 1 8 i ð24Þ

tn0;l � 0 8 l: ð25Þ

The objective function (22) represents the total energyconsumption in the network to transmit one video frame toall receivers using flow Fn. Using (15) through (17), werepresented this in terms of the first hop allocation tn0;l.Moreover, the statistical delay constraint (23) is writtenstrictly in terms of tn0;l. Since there is a linear relation amongthe instantaneous time-slot allocation as evident in (10), thedegrees of freedom in choosing ttn is reduced to L ratherthan KL. Thus, writing the optimization problem in termsof tn0;l enables obtaining all the allocations by substituting(10) to obtain tnk;l. Note also that if (23) is satisfied for thefirst hop and tnk;l are computed using (10), then Ck;lð�lÞ � Clis satisfied for all links k. The path allocation constraint (24)is also written in terms of tn0;l using (19) and (20).

4.2 Problem Solution for General Network Flows

We represented the problem formulation in terms of thefirst hop allocation while maintaining the end-to-endstatistical delay bound for each path. Solving for tn�0;l, wecan find the minimal energy consumption in the networkusing flow F n as �n

PLl¼1 t

n�0;l. We explain how to solve for

the optimal first hop allocation tn�0;l.The objective function (22) is linear in ttnn00 , the delay

bound constraint (23) is exponentially decaying in ttnn00 , andthe resource allocation constraints (24) and (25) are linear inttnn00 . As a result, the optimization problem is a convexoptimization problem [35] and the solution comes with aquality certificate as the global optimal solution.

The Lagrangian function Lðtnk;l; �nl ;�ni ; �

n; �ni Þ of thevideo distribution problem can be written as

L ¼ IE �nXLl¼1

tn0;l

" #þ IE

Xpni¼1

�ni �ni

XLl¼1

tn0;l � 1

!" #

þXLl¼1

�nl�IE�e��lB0Tt

n0;l

log2ð1þ�0Þ�� e��lCl�;ð26Þ

where �nl and �ni are the Lagrange multipliers. Based on

optimization theory, the KKT conditions are

@L

@tn0;l

tn0;l¼tn�

0;l

¼ 0 8l; 8�; ð27Þ



�n�i � 0; �n�l � 0; ð28Þ

�n�i �ni

XLl¼1

tn0;l � 1

!¼ 0; ð29Þ

�n�l�IE�e��lB0Tt

n0;l

log2ð1þ�0Þ�� e��lCl� ¼ 0 8l; 8�: ð30Þ

Substituting @L@tn

0;l

tn0;l¼tn�

0;l

¼ 0 into (26), we obtain the expres-

sion for the optimal solution ttnn� in terms of the Lagrange

multipliers �� and � as

tn�0;l ¼ tn0;lð��; �n�l ;�n�i Þ ¼ �

log�nþPpn

i¼1�n�i �

ni

�n�l�lB0T log2ð1þ�0Þ

��lB0T log2ð1þ �0Þ

2664

3775þ

: ð31Þ

The optimal allocation in (31) depends on the Lagrange

multipliers �nl and �ni . We use the subgradient method to

track these Lagrange multipliers and solve for the optimal

solution. First, given instantaneous link SNRsf�k;k0 ½j�gK Kk¼1;k0¼1,

we obtain f�k½j�gKk¼1 from (2). Given flow F n, we find �n and

�ni using (18) and (21), respectively. Given the optimal

Lagrangian multipliers f�n�l gLl¼1 obtained from the previous

frame, we find �n�i as follows:

�n�i ¼

~�ni if �ni

XLl¼1

tn�0;lð��; �n�l ; 0Þ � 1

0 otherwise;

8><>: ð32Þ

where ~�ni is obtained by solving the univariate function

�niXLl¼1

tn0;l��; ��l ;

~�ni

�¼ 1: ð33Þ

Since (31) is strictly decreasing in �ni , then if at �n

i ¼ 0, (24)is not violated, this constraint will not be active for any �n

i

and �n�i ¼ 0 to satisfy (29). Otherwise, if at �n

i ¼ 0, (24) isviolated, we could keep increasing �n

i until (24) is satisfiedfor some �n�

i ¼ ~�ni with equality so that (29) holds.

Finally, since the Lagrangian function Lðtnk;l; �nl ;�ni ;

�n; �ni Þ is concave, we use the subgradient method [9] totrack the optimal �� and maximize the Lagrangian asfollows:

�nl ¼ �nl þ ��IE�e��lB0Tt

n�0;l

log2ð1þ�0Þ�� e��lCl�; ð34Þ

where � > 0 is a small positive constant. The estimationfor the expectation IE½e��lB0Tt

n0;l

log2ð1þ�0Þ� is obtained itera-tively for the jth time frame through a first-order low-pass filter as follows:

S½jþ 1� ¼ ð1� ÞS½j� þ e��lB0Ttn0;l½jþ1� log2ð1þ�0½jþ1�Þ; ð35Þ

where > 0 is a small positive constant. If the solutionexists, that is, the wireless resources are enough to satisfythe delay constraint, then the convergence of (34) to theoptimal �� is guaranteed due the concavity of Lðtnk;l; �nl ;�ni ; �

n; �ni Þ over �� where the solution satisfies (30). Other-wise, (34) will not converge indicating that the delayconstraint cannot be satisfied, resulting in an infeasibleproblem. Plugging �n�l and �n�

i into (31), we obtain the

optimal first hop allocation tn�0;l for any flow F n. The optimalallocation by all nodes can then be computed as follows:

tn�k;l ¼B0 log2ð1þ �0ÞBk log2ð1þ �kÞ

� tn0;l��; �n�l ;�

n�i

�: ð36Þ

After the first few video frames, the process of tracking theoptimal Lagrange multipliers using (34) and (35) convergesand the network reaches the steady state. In this state, theresource allocation for frame j and flow F n can be obtainedusing the following steps:

1. For the instantaneous fading state �, obtain �n½j�using (18) and �ni ½j� for i ¼ 1; . . . ; pn using (21).

2. Use (32) to update the Lagrange multiplier�n�i ½j� for i ¼ 1; . . . ; pn.

3. Use (35) followed by (34) to update the Lagrangemultiplier �n�l ½j� for l ¼ 1; . . . ; L.

4. Solve for the first hop resource allocation tn�0;l for l ¼1; . . . ; L using (31) to minimize IE½

PKk¼0

PLl¼1 E

nk;l�.

5. Obtain the instantaneous resource allocations foreach node tn�k;l for k ¼ 1; . . . ; K; l ¼ 1; . . . ; L using (36).

4.3 Distributed Implementation

We describe a distributed approach to implement theresource allocation procedure above where we assume thateach node knows only its own transmit rate Rkð�Þ, transmitpower Pk;t, and its set of multicast nodesMn

k . Additionally,to avoid added complexity, nodes are only allowed to sendfeedback to their direct upstream node.

For step 1, �n can be computed in a distributed fashionby incrementally updating its second term

PKk¼1 w

nk=Rkð�Þ

as follows: Starting from the leaf nodes, each node Mk sumsthe components it receives from its downstream nodes,adds wnk=Rkð�Þ, and sends the incremental value to itsupstream node. The BS can linearly transform the receivedincremental information to obtain (18) using knowledge ofits multicast tree and transmit rate. Now, �ni is easier tocompute because it is path dependent. On each path,starting from the leaf node, each node Mk adds 1=Rkð�Þ tothe incremental value it receives and sends it to itsupstream node until it reaches the BS which scales it byR0ð�Þ to obtain �ni . Next, steps 2-4 are performed at the BSwith the knowledge of �n and �ni for each path. Step 5 isperformed in a distributed fashion so that each nodecomputes its resource allocation and transmits accordingly.Each node knows the rate at which it receives from itsupstream node Mk0 and its own transmit rate. In addition,the receiver can easily find the resource allocation of itsupstream node by sensing the time it takes to receive allvideo layers. Thus, Mk allocates resources for its transmis-sion according to tnk;l ¼ tnk0;lRk0 ð�Þ=Rkð�Þ. This proceduredoes not require the BS or MSs to be aware of the entirenetwork topology or of the SNR on other links.

The complexity of the operations described in steps 1-5 isobtained as the sum of the individual operations. Finding�n½j� costs OðKÞ and finding �ni ½j� also costs OðKÞ for eachpath. Since the number of paths in a DAG is upper boundedby the number of nodes, the operation cost is OðKpnÞ �OðK2Þ. The complexity of steps 2-4 is dominated by thecomplexity of solving for tn�0;l using (31) which is OðKÞ for



each video layer. For all layers, the cost of obtaining the firsthop allocation becomes OðKLÞ. The final step also costsOðKLÞ to solve (36) 8k; l. Thus, the complexity of theoptimal resource allocation process for a single video frameand a predefined flow is OðK2 þKLÞ.

4.4 Combinatorial Encoding of Network Flows

After solving for tn�0;l over all flows, we can compute theenergy consumption of flow F n as �n

PLl¼1 t

n�0;l. Finally, we

select the optimal flow as

n�½j� ¼ argminn

�nXLl¼1

tn�0;l½j� !

; ð37Þ

where we use the frame index j to stress that the optimalflow may be different in each frame based on theinstantaneous fading state �.

We provide a methodology to count and enumerate allpossible network flows. Since we define a network flow as adirected acyclic graph (DAG), we deduce that there is a one-to-one correspondence between the set of network flowsand the set of spanning trees for the network graph. Given aspanning tree, we can obtain the DAG by starting at thebase station and assigning unicast and multicast directedlinks for selected edges such that all nodes are covered.Conversely, each DAG is clearly a spanning tree. Thenumber of spanning tree in a complete graph withm vertices was devised by Cayley as mm�2 [36]. For ournetwork of one base station and K mobile stations, weobtain the number of network flows as

N ¼ ðK þ 1ÞK�1: ð38Þ

Thus, the complexity of brute force flow selection is

OððK2þKLÞ � ðKþ 1ÞK�1Þ. This complexity presents a

limitation for the brute force approach as K increases. For

instance, in a network with one BS and 6 MSs, there are

16,807 possible ways to distribute the content. We will

propose some approximation algorithms and provide

performance bounds for these algorithms under specific

network topologies.Furthermore, Prufer devised a method for encoding and

decoding the set of spanning trees in a graph using what isknown as Prufer sequences. Given a tree with labeledvertices MkjKk¼0, the Prufer encoding algorithm outputs aunique Prufer sequence of length K � 1. The Pruferdecoding algorithm provides the inverse function, that is,given a Prufer sequence of K � 1 elements, we can find theset of edges that construct the unique spanning treecorresponding to the Prufer sequence [36]. This provides ahandy tool for implementing the brute force approachcombinatorially to obtain insight into the optimal flowselection and analyze the performance of other approxima-tion algorithms.

5 APPROXIMATION ALGORITHMS FOR FLOW

SELECTION

Finding the globally optimal distribution strategy requiresconverting each of the ðK þ 1ÞK�1 Prufer sequences into aspanning tree and finding the minimal energy consumptionusing that tree structure, then choosing the tree that

minimizes energy consumption among all candidates, andallocating resources accordingly. In this section, we proposetwo approximation algorithms to reduce the complexityinvolved in choosing the best flow for a given fading state.The objective of the proposed algorithms is to avoidsearching through the exponential number of possible treestructures. The first algorithm uses negated SNRs as linkweights on the complete network graph, and finds theminimum spanning tree using these weights. The secondalgorithm is based on selecting a set of dominant flows thatare optimal for a large percentage of fading states for agiven network topology.

5.1 Minimum Spanning Tree Flow Selection

To find a suitable flow without using brute force, we shoulddeal with network variables that are independent of theflow structure so that the flow choice is done independentlyand prior to resource allocation. While it is tempting toconstruct the spanning tree using link weights that take intoaccount the energy consumption required to transmit on thelink, this is not possible because the energy consumptionrequirement is a function of the resource allocation strategyand the set of multicast receivers on that link, which areboth specific to the choice of the network flow. The networkvariable that can be readily used is the instantaneouslink SNR. For video frame j, given the fading state��½j� ¼4 f�k;k0 ½j�gK K

k¼0;k0¼1, we construct the complete networkgraph with edge weights ��k;k0 ½j� on the link between nodesMk and Mk0 . We then use Prim’s algorithm [37] to obtain theminimum spanning tree. The spanning tree is mapped tothe corresponding directed acyclic graph representing thenetwork flow, and wireless resources are allocated on thatflow according to the convex problem in (22) through (25) tominimize total energy consumption. The chosen flow underthis strategy maximizes the sum SNR over the networklinks, or equivalently the sum rate because the shannon rateis a concave function of the SNR. Note that the chosen flowis not necessarily throughput optimal because the actualrate on the link between nodes Mk and Mk0 is notdetermined by �k;k0 ½j�. Instead, due to multicast, it isdetermined by the effective SNR on the worst link �k ¼mink02Mn

k�k;k0 which is not known beforehand because it

depends on the choice of n.Using this approach, the flow selection problem is

separated from the resource allocation problem. Theflow selection process using Prim’s minimum spanningtree algorithm costs OðE þ V logðV ÞÞ ¼ OðKðK þ 1Þ þ ðK þ1Þ logðK þ 1ÞÞ ¼ OðK2Þ where E ¼ KðK þ 1Þ is the numberof edges in the complete graph and V ¼ K þ 1 is the numberof vertices. Thus, the total time complexity of the flowselection and resource allocation is OðK2Þ þOðK2 þKLÞ ¼OðK2 þKLÞ as opposed to OððK2 þKLÞ � ðK þ 1ÞK�1Þ forthe optimal flow selection. Results presented in Section 6demonstrate that this significant decrease in complexity costsa limited increase in the average energy consumption invarious network scenarios.

5.2 Dominant Set Flow Selection

The second approximation algorithm is based on theobservation that most of the network flows can only beoptimal for a small percentage of the fading states



corresponding to extreme instantaneous SNRs on thenetwork links. For instance, if MS M1 lies between the BSand MS M2, it is very unlikely that the transmission to M1

through M2 is more energy efficient than the transmissionto M2 through M1. We thus attempt to reduce the number ofcandidates by taking into account the network flows thatcollectively correspond to a large percentage of the fadingstates. We refer to this set of network flows as the dominantset. Since we employ a block-fading model, the flows thatare optimal in a percentage p of the fading states are alsooptimal in a percentage p of the video frames for anasymptotically large number of video frames. Thus, we canestimate the dominant set using an offline simulation of thebrute force algorithm. After running the offline brute forcesimulation for a large number of frames, we obtain statisticson the flow usage. We sort the flows by percentage of usageand select the sorted flows in descending order such thatthe total usage of the selected set is greater than a threshold.In our simulations, we use a threshold of 90 percent, andcall this the 90th percentile dominant set. As the thresholdincreases, the dominant set solution approaches the optimalsolution but the complexity of flow selection increases. Onthe other hand, a smaller threshold corresponds to a looserapproximation, but reduced complexity.

Using this approximation scheme, we can achievesolutions asymptotically close to the optimal solution. Infact, we will show that this algorithm exhibits betterperformance than the first one at a higher computationalcost. Despite the asymptotic performance, one majorlimitation in this approach is that it is topology dependent,that is, we have different dominant sets for differentinstances of the MS locations. This makes the algorithmsuitable for low mobility scenarios. However, it is worthnoting that the variation of the dominant set as a function ofthe MS locations is smooth, so that the same set can be usedfor a well-defined set of network topologies. A mobilitymodel can also be used in the process of populating thedominant flow set to obtain more accurate statistics on flowuse and better approximations. In general, the moreclustered the network topology and the lower the mobility,the smaller the size of the dominant set. Finally, we shouldnote that although the dominant set construction is not areal-time process, this offline simulation might not alwaysbe computationally feasible if K is somewhat large. In thiscase, we may consider the following alternative approachesto make the dominant set construction feasible:

1. Populate the dominant set using the minimumspanning tree algorithm: After running the mini-mum spanning tree algorithm for a sufficiently longtraining period, all the flows selected at least oncewill be used to form the dominant set. This trainingphase is computationally very efficient and it mightend up with a superset of the 90th percentile set due

to the frequent reuse of the “good” flows, thus itmay perform better.

2. Use a clustering algorithm to group the mobilestations according to the physical MS locations: Aftergrouping the mobile stations, choose the cluster-heads as the closest MS in each cluster to the BS,perform an optimal flow selection on each groupseparately using the clusterhead as the source, usethe BS to multicast to all clusterheads and use theoptimal flow within each cluster/group.

3. Place restrictions on the number of flows: Limit thesearch space for dominant set construction, e.g., bylimiting the maximum number of hops of themulicast group size.

We will show that the number of dominant flows ispolynomial in K unlike the total number of flows becausethe percentage of dominant flows decays exponentially asK increases (See Fig. 8b). For general topologies, thedominant set has size OðKaÞ where the exponent a is aconstant that depends on the network topology andmobility dynamics. A good fit typically yields a betweentwo and three. Since the resource allocation problem issolved for each of the OðKaÞ dominant flow to obtain thebest dominant flow, the time complexity of the flowselection and resource allocation is OððK2 þKLÞ �KaÞ.The complexity of the different flow selection algorithmsis summarized in Table 1.

6 RESULTS AND ANALYSIS

The network model consists of a base station and K mobilestations M1;M2; . . . ;MK . We assume all K mobile stationsare interested in the same content and the requirement is toselect the best flow for each video frame to be delivered toall receivers reliably based on the current fading state. Togain insight into the flow selection behavior, we consider abasic model where all MSs are at a distance d from the BS,the BS link to Mk and to Mkþ1 make an angle � for allk ¼ 1; . . . ; K � 1 as shown in Fig. 2.

Throughout this section, we consider a two layer videostream with constant arrival rates �� ¼ ½2� 105 bps; 1 �105 bps�. The signal bandwidth BkjKk¼1 ¼ 1 MHz and thetime frame duration T ¼ 33 ms corresponding to a video


TABLE 1Complexity of the Flow Selection Algorithms

Fig. 2. Simulation model with one BS and K MSs.


frame rate of 30 fps. We define a delay bound Dth ¼ 3T ¼100 ms and a delay bound violation probability Pth ¼ 10�3.The transmit power by the BS is P0;t ¼ 0:5 W , the transmitpower of each MS is Pk;t ¼ 0:05 W 8k and the power(energy per second) consumed by each MS during receptionis Pr ¼ 0:05 J/sec. For channel modeling, we derive theaverage SNRs ��k;k0 from the distances dk;k0 as follows:

��k;k0 ¼10 log10ðPk;tÞ�KdB�10 log10ðdk;k0 Þ�10 logðN0BkÞ; ð39Þ

where KdB is the pathloss constant, is the pathlossexponent, and N0 is the power spectral density of theAWGN noise. In the simulations, KdB ¼ 21:36 dB, ¼ 3:52,and N0 ¼ 4� 10�21 W/Hz.

6.1 Resource Consumption Analysis

The cooperative resource allocation algorithm is executedfor 10;000 frames on the network described above withK ¼ 3. In each frame, we solve for the optimal resourceallocation using (31) for the optimal flow and the flowselected by the approximation algorithms. Fig. 3a (Top)shows the instantaneous energy consumption in the net-work for a period of 2,500 video frames for the optimal flowselection algorithm.

To demonstrate the effectiveness of the approximationalgorithms, Fig. 3a (Middle and Bottom) show theiroptimality gap in energy consumption with respect tooptimal flow selection. Optimal flow selection requires anaverage of 1.366 mJ/frame. The minimum spanning treealgorithm requires only an additional 0.0576 mJ/frame,whereas dominant set flow selection requires an additional0.0064 mJ/frame. Furthermore, it can be seen that there is atransient period at the beginning of each simulation, whichcorresponds to the time required for the Lagrangianmultipliers to stabilize. To confirm the convergence of theLagrangian multipliers to the optimal solution, we presentthe tracking process in Fig. 3b for the two video layers inflow F 11 (See Fig. 5a). The convergence of the Lagrangianmultipliers to the optimal solution is controlled by the twovariables � and defined in Section 4.2. In this simulation,� ¼ 0:03 and ¼ 0:03.

In Fig. 4a, we compute the energy consumption for eachframe from tn�0;l using (17) and (18) where n is selectedaccording to (37). Then, the energy consumption isaveraged over all frames and result is shown for differentvalues of d and �. Results show that the network


Fig. 3. Analysis of the adaptive resource allocation process.

Fig. 4. Resource consumption analysis under the optimal flow versus d and �.


configuration represented by d and � has a key effect on theenergy consumption in the network. At d ¼ 200 m and� ¼ 10o, we require around 0.6 mJ/frame, while at d ¼ 1;500m and � ¼ 40o, we require around 4.3 mJ/frame. Althoughthe transmit powers are fixed, smaller distances provide alarger SNR, thus requiring a lower resource allocation in(31) to satisfy the same statistical delay bound. Eventually,the energy consumption per frame will be reduced due tothe unused time resources.

In Fig. 4b, we use tn�0;l to find the end-to-end normalized

resource allocation for the most resource consuming path

which can be written as IE½maxif�niPL

l¼1 tn�0;lg�. We then

average the end-to-end normalized resource allocation overall frames for different values of d and �. The trend of the

resource allocation variation is similar to the energy

consumption, but shows a steeper slope of increase. Results

show that at d ¼ 200 m and � ¼ 10o, we require only5 percent of the wireless resources, whereas the wireless

resources are almost fully utilized at d ¼ 1;500 m and

� ¼ 40o. This implies that increasing d or � further will

prohibit maintaining the statistical delay bound guarantee.

6.2 Flow Selection Analysis

We are further interested in finding the probability of

selecting a certain flow F n for a given network topology. Wedefine the probability of using flow Fn as the number of

frames transmitted through F n as implied by (37) divided

by the total number of transmitted frames. For a network

with K ¼ 3, Fig. 5a shows all the 42 ¼ 16 candidate flows.The flows are ordered according to their Prufer encoding,

that is, the first flow is generated from the Prufer sequence

ð1; 1Þ up to the last flow corresponding to the sequence ð4; 4Þ.In Fig. 5b, we compute the percentage of flow usage for

the three flow selection algorithms with d¼ 1;000 m, �¼ 10o,

and K ¼ 3 corresponding to 42 ¼ 16 possible network flows.

We can see that, in this scenario, three out of 16 flowsdominate the flow usage in the network. These three flows

are BS �!u M1 �!uM2 �!

uM3, BS �!u M2 �!

m ðM1;M3Þ, and

BS �!u M3 �!uM2 �!

uM1, and correspond to multihop

flows that use intermediate MSs M1, M2, and M3, respec-

tively. This is explained by the fact that the multicast fromM2 can be done efficiently because of the good channel

conditions among MSs and the lower transmit power. Also,sequential unicast through M1 and M3 are two good

candidates depending on the channel conditions on the firsthop links. Note that the traditional noncooperative flow

involving three node multicast by the BS is rarely usedbecause it limits the data rate according to the worst SNR,

which in turn requires higher resource allocation to providethe same end-to-end transport capacity, thus causing high-

energy consumption.We also compare the flow usage under the three flow

selection algorithms. The minimum spanning tree approachbalances the flow usage among dominant flows due to thefact that the flow construction does not differentiate unicastand multicast links. For the dominant set approach, wenotice that the dominant set consists of only three flowsfrom which the flow is selected for each video frame. InFig. 6, we compute the percentage of flow usage for theoptimal flow selection algorithms with d ¼ 1;000 m, � ¼ 10o,and K ¼ 5 corresponding to 64 ¼ 1;296 possible networkflows. Despite the large number of flows, we can see thatonly the best 25 flows collectively form 90 percent of theflow usage. In fact, this provides the motivation behind thedominant set flow selection approach.

6.3 Energy Consumption Gain Analysis

In this section, we assess the gain in energy consumptionfor the three flow selection algorithms for differenttopologies and network sizes. To evaluate the cooperationgain, we define the normalized energy consumption as thecooperative energy consumption E�coop divided by theenergy consumption without cooperation Eno�coop, that is,

¼E�coopEno�coop

; ð40Þ

where E�coop is obtained by allocating resources on the flowselected using one of the flow selection algorithms, and


Fig. 5. Analysis of flow usage for K ¼ 3 using the optimal and the approximation flow selection algorithms.


Eno�coop is obtained by allocating resources on the single-hop non-cooperative multicast flow to minimize energyconsumption and guarantee the statistical delay bound. If < 1, the scheme yields some cooperation gain. Otherwise,cooperation does not provide gains in terms of energyconsumption. With the proposed flow selection algorithm, is always less than or equal to 1, that is, if thenoncooperative flow is the most energy efficient, resourcesare allocated on that flow to minimize energy consumption.

Fig. 7a shows the normalized energy consumption whilevarying the network size and the angle � for the three flowselection algorithms. An interesting observation is that as Kincreases, the normalized energy consumption decreases,thus increasing the cooperation gain. Although E�coopincreases as K increases, the rate at which Eno�coop increasesis faster which explains this desirable behavior. Also, forlarger �, Eno�coop does not change, while E�coop increases, thusreducing the cooperation gain. Most importantly, note thesmall optimality gap of the approximation algorithms as

compared to an optimal flow selection. The dominant set

flow selection has a very small optimality gap. For

� ¼ 30o; 20o, and 10o, the optimality gaps are 0.008, 0.005,

and 0.002, respectively. The minimum spanning tree

algorithm has optimality gaps of 0.06, 0.03, and 0.015,

respectively, for the three values of �. Furthermore, the

optimality gap dependence on K is minor.Fig. 7b presents the end-to-end resource allocation on the

most resource consuming path averaged over video frames

versus K. As the number of nodes increase, unicasting will

require more hops to deliver the content, thus larger end-to-

end resource consumption. Also, the larger multicast group

size further limits supported rates, thus increasing resource

consumption. This places a physical limitation on the

maximum number of MSs that can be accommodated while

satisfying the statistical delay bound on all the flow paths.

Moreover, changing the network topology by increasing �

will decrease the average SNR on the mobile-to-mobile


Fig. 7. (a) Cooperation gain versus K for the optimal and approximation flow selection algorithms using different network topologies represented by�, (b) Average end-to-end normalized resource allocation for the most resource consuming path in the optimal flow versus K for different values of �.

Fig. 6. Percentage of flow usage for each of the 1,296 network flow for K ¼ 5 using optimal flow selection.


links, thus increasing the average resource allocationrequirement.

Fig. 8a shows the percentage of video frames in whicheach of the two approximation algorithms selected theglobally optimal flow. By our construction of the dominantset from the 90th percentile flow use, the dominant setalgorithm will use the optimal flow at least 90 percent of thetime for a simulation long enough. On the other hand, thepercentage drops almost linearly with the minimumspanning tree. But, it is known from Fig. 7a that theoptimality gap only slightly increases with K whichsuggests that the minimum spanning tree algorithm,although seldom uses the globally optimal flow, picks anetwork flow very close to the optimal in terms of energyconsumption at a much lower computational cost.

Finally, to verify that the dominant set size is polynomialin the number of flows, it is sufficient to confirm that thepercentage of dominant network flows decays exponentially

in K. We present the percentage of dominant flows as K

increases for different topologies in Fig. 8b. Results show

that the decay rate is indeed an exponential regardless of the

network topology and the decay rate does not decrease as

K increases. For instance, with K ¼ 6, the total number of

candidate flows is 16,807, however, the dominant set size is

at most 155 for � ¼ 30o. This shows that the flow selection

and resource allocation complexity is reduced from

OððK2 þKLÞ � ðK þ 1ÞK�1Þ to OððK2 þKLÞ �KaÞ where a

is a constant that depends on the network topology

characteristics and the mobility level.

6.4 Case Study: A Large Scattered Network

We consider a large network with 10 MSs scatteredrandomly around the BS as shown in the configuration inFig. 9. For this network, it is not feasible to apply bruteforce to populate the dominant set since there are 119 ¼2:35� 109 candidate flows. Instead, we apply the approach


Fig. 8. (a) Percentage of frames using the globally optimal network flow for both approximation algorithms versus K for � ¼ 10o, (b) The percentageof dominant flows showing exponential decay in K for different network topologies along with the dominant set cardinality for each topology.

Fig. 9. Scattered network case study. Percentages correspond to the end-to-end normalized resource allocation per path.


proposed in Section 5.2. That is, we use the minimumspanning tree algorithm to populate the dominant set.After running the minimum spanning tree algorithm for10,000 training frames, we obtain the flows selected at leastonce to be 597. After populating the dominant set, weapply the dominant set flow selection algorithm for 10,000frames to select the best flow in terms of an energyefficiency for each video frame according to the instanta-neous fading state. Results show that the two mostdominant flows are collectively used for 38 percent of thetime. These two flows are shown in Figs. 9a and 9b alongwith the average energy consumption per frame for eachflow and the average end-to-end resource allocation oneach path of the flow.

For the best network flow, an average energy consump-tion of 1.3652 mJ per frame is required and the worstaverage end-to-end resource allocation is 19.47 percent onthe path leading to M8 and M10. For the second-bestnetwork flow, an average energy consumption of 1.3995 mJper frame is required and the worst average end-to-endresource allocation is 14.22 percent on the path leading toM8. Note that the end-to-end resource consumption islarger in the best flow than the second-best flow since it hasa larger average end-to-end hop length. Furthermore, thelarger multicast group size by the BS for the second-bestflow limits the data rate and increases the first hop resourceallocation requirement. Since the BS transmit power istypically larger than that of the MSs, this dominates thetotal energy consumption, and the first flow becomes abetter candidate.

7 CONCLUSION

We derived the optimal resource allocation solution forscalable video distribution over cooperative multihop net-works to minimize the total energy consumption subject toend-to-end statistical delay bounds per network path. Thesolution is used to identify optimized energy-efficient flowsconsisting of hybrid unicast/multicast links to ensurereliable delivery of the video content to all requesting mobileterminals. Two low complexity approximation algorithmsfor flow selection are proposed and studied in terms ofperformance and complexity. Results demonstrate notablereductions in energy consumption and the performance ofthe approximation algorithms is close to optimal for variousnetwork topologies.

ACKNOWLEDGMENTS

This work was partially supported by an NPRP grant fromthe Qatar National Research Fund (a member of the QatarFoundation). The statements made herein are solely theresponsibility of the authors.

REFERENCES

[1] T. Wiegand, G. Sullivan, G. Bjontegaard, and A. Luthra, “Over-view of the H.264/AVC Video Coding Standard,” IEEE Trans.Circuits and Systems for Video Technology, vol. 13, no. 7, pp. 560-576,July 2003.

[2] H. Schwarz, D. Marpe, and T. Wiegand, “Overview of the ScalableVideo Coding Extension of the H.264/AVC Standard,” IEEETrans. Circuits and Systems for Video Technology, vol. 17, no. 9,pp. 1103-1120, Sept. 2007.

[3] A. Kumar, D. Manjunath, and J. Kuri, Communication Networking:An Analytical Approach. Morgan Kaufmann, 2004.

[4] C.-S. Chang, Performance Guarantees in Communication Networks.Springer-Verlag, 2000.

[5] C.-S. Chang and J. Thomas, “Effective Bandwidth in High SpeedDigital Networks,” IEEE J. Selected Areas in Comm., vol. 13, no. 6,pp. 1091-1100, Aug. 1995.

[6] D. Wu and R. Negi, “Effective Capacity: A Wireless Link Modelfor Support of Quality of Service,” IEEE Trans. Wireless Comm.,vol. 2, no. 4, pp. 630-643, July 2003.

[7] D. Wu and R. Negi, “Effective Capacity-Based Quality of ServiceMeasures for Wireless Networks,” Mobile Networks and Applica-tions, vol. 11, no. 1, pp. 91-99, June 2006.

[8] D. Wu, “Providing Quality-of-Service Guarantees in WirelessNetworks,” PhD thesis, Carnegie Mellon Univ., 2003.

[9] Q. Du and X. Zhang, “Statistical QoS Provisionings for WirelessUnicast/Multicast of Layered Video Streams,” Proc. IEEE IN-FOCOM, Apr. 2009.

[10] X. Zhang and Q. Du, “Cross-Layer Modeling for QoS-DrivenMultimedia Multicast/Broadcast over Fading Channels in MobileWireless Networks,” IEEE Comm. Magazine, vol. 45, no. 8, pp. 62-70, Aug. 2007.

[11] H. Wu, C. Qiao, S. De, and O. Tonguz, “Integrated Cellular andAd Hoc Relaying Systems: iCAR,” IEEE J. Selected Areas in Comm.,vol. 19, no. 10, pp. 2105-2115, Oct. 2001.

[12] H. Luo, R. Ramjeey, P. Sinha, L.E. Li, and S. Lu, “UCAN: AUnified Cellular and Ad Hoc Network Architecture,” Proc. ACMMobiCom, Sept. 2003.

[13] R. Bhatia, L.E. Li, H. Luo, and R. Ramjee, “ICAM: IntegratedCellular and Ad Hoc Multicast,” IEEE Trans. Mobile Computing,vol. 5, no. 8, pp. 1004-1015, Aug. 2006.

[14] L. Popova, T. Herpel, W. Gerstacker, and W. Koch, “CooperativeMobile-to-Mobile File Dissemination in Cellular Networks withina Unified Radio Interface,” Int’l J. Computer and Telecomm.Networking, vol. 52, no. 6, pp. 1153-1165, Jan. 2008.

[15] M. Peng and W. Wang, “Investigation of Cooperative Relay NodeSelection in Heterogeneous Wireless Communication Systems,”Proc. IEEE Int’l Conf. Comm., May 2008.

[16] J.-C. Chen, S.-H. Chan, J.-Y. He, and S.-C. Liew, “Mixed-ModeWLAN: The Integration of Ad Hoc Mode with Wireless LANInfrastructure,” Proc. IEEE GlobeCom, Dec. 2003.

[17] Z. Dawy, S. Davidovic, and I. Oikonomidis, “Coverage andCapacity Enhancement of CDMA Cellular Systems via MultihopTransmission,” Proc. IEEE GlobeCom, Dec. 2003.

[18] J. Chen, S. Li, S.-H.G. Chan, and J. He, “WIANI: WirelessInfrastructure and Ad-Hoc Network Integration,” Proc. IEEE Int’lConf. Comm., May 2005.

[19] K.-J. Peng and Z. Tsai, “Distortion and Cost Controlled VideoStreaming in a Heterogeneous Wireless Network Environment,”Proc. IEEE Int’l Symp. Personal, Indoor and Mobile Radio Comm.,Sept. 2006.

[20] F. Fitzek and M. Katz, Cooperation in Wireless Networks: Principlesand Applications. Springer, 2006.

[21] Q. Zhang, F.H.P. Fitzek, and V.B. Iversen, “Design and Perfor-mance Evaluation of Cooperative Retransmission Scheme forReliable Multicast Services in Cellular Controlled P2P Networks,”Proc. IEEE Int’l Symp. Personal, Indoor and Mobile Radio Comm.,Sept. 2007.

[22] M. Ramadan, L. Zein, and Z. Dawy, “Implementation andEvaluation of Cooperative Video Streaming for Mobile Devices,”Proc. IEEE Int’l Symp. Personal, Indoor, and Mobile Radio Comm.,Sept. 2008.

[23] S. Kang and M. Mutka, “A Mobile Peer-to-Peer Approach forMultimedia Content Sharing Using 3G/WLAN Dual ModeChannels,” J. Wireless Comm. and Mobile Computing, vol. 5, no. 6,pp. 633-645, Sept. 2005.

[24] M.F. Leung and S.-H. Gary Chan, “Broadcast-Based Peer-to-PeerCollaborative Video Streaming Among Mobiles,” IEEE Trans.Broadcasting, vol. 53, no. 1, pp. 50-61, Mar. 2007.

[25] Q. Zhang and Y. Zhang, “Cross-Layer Design for QoS Support inMultihop Wireless Networks,” Proc. IEEE, vol. 96, no. 1, pp. 64-76,Jan. 2008.

[26] L. Zhou, X. Wang, Y. Li, B. Zheng, and B. Geller, “OptimalScheduling for Multiple Description Video Streams in WirelessMultihop Networks,” IEEE Comm. Letters, vol. 13, no. 7, pp. 534-536, July 2009.



[27] L. Zhou, X. Wang, W. Tu, G. Muntean, and B. Geller, “DistributedScheduling Scheme for Video Streaming over Multi-ChannelMulti-Radio Multi-Hop Wireless Networks,” IEEE J. Selected Areasin Comm., vol. 28, no. 3, pp. 409-419, Apr. 2010.

[28] D. Zhu and M. Mutka, “Cooperation among Peers in an Ad HocNetwork to Support an Energy Efficient IM Service,” J. Pervasiveand Mobile Computing, vol. 4, no. 3, pp. 335-359, June 2008.

[29] B.J. Oh and C.W. Chen, “Energy Efficient H.264 Video Transmis-sion over Wireless Ad Hoc Networks Based on Adaptive 802.11eEDCA MAC Protocol,” Proc. IEEE Int’l Conf. Multimedia and Expo,June 2008.

[30] G. Ananthanarayanan, V. Padmanabhan, and L. Ravindranath,“COMBINE: Leveraging the Power of Wireless Peers throughCollaborative Downloading,” Proc. Int’l Conf. Mobile Systems,Applications, and Services (MobiSys ’07), June 2007.

[31] A.J. Goldsmith, Wireless Communications. Cambridge Univ., 2005.[32] C.-S. Chang, “Stability, Queue Length, and Delay of Deterministic

and Stochastic Queueing Networks,” IEEE Trans. AutomaticControl, vol. 39, no. 5, pp. 913-931, May 1994.

[33] J. Tang and X. Zhang, “Quality-of-Service Driven Power and RateAdaptation for Multichannel Communications over WirelessLinks,” IEEE Trans. Wireless Comm., vol. 6, no. 8, pp. 3058-3068,Aug. 2007.

[34] X. Zhang, J. Tang, H.-H. Chen, S. Ci, and M. Guizani, “Cross-Layer-Based Modeling for Quality of Service Guarantees inMobile Wireless Networks,” IEEE Comm. Magazine, vol. 44,no. 1, pp. 100-106, Jan. 2006.

[35] S. Boyd and L. Vandenberghe, Convex Optimization. CambridgeUniv., 2004.

[36] B. Wu and K. Chao, Spanning Trees and Optimization Problems.Chapman & Hall, 2004.

[37] T. Cormen, C. Leiserson, R. Rivest, and C. Stein, Introduction toAlgorithms. McGraw-Hill: MIT Press, 2001.

Amin Abdel Khalek received the BE degree incomputer and communication engineering withhighest distinction from Notre Dame Universityin 2008 and the ME degree in electrical andcomputer engineering from the American Uni-versity of Beirut in 2010. He is currently workingtoward the PhD degree in electrical and compu-ter engineering at the University of Texas atAustin. His general research interests are at theintersection of wireless communications, video

coding, and optimization. In 2010, he became a member of the WirelessSystems Innovation Laboratory (WSIL) and the Wireless Networkingand Communications Group (WNCG) at The University of Texas atAustin, where he is currently working on perceptual optimization ofwireless video networks. He is a student member of the IEEE.

Zaher Dawy received the BE degree in compu-ter and communications engineering from theAmerican University of Beirut (AUB) in 1998 andthe ME and Dr-Ing degrees in communicationsengineering from the Munich University ofTechnology (TUM) in 2000 and 2004, respec-tively. He joined the Department of Electrical andComputer Engineering at AUB in September2004, where he is currently an associateprofessor. He was the recipient of the AUB

2008 teaching excellence award, the best graduate award from TUM in2000, the youth and knowledge Siemens scholarship for distinguishedstudents in 1999, and the distinguished graduate medal of excellencefrom the Harriri Foundation in 1998. His research interests are in thegeneral areas of computational biology, information theory, and wirelesscommunications with a focus on genomic coding theory, gene networkmodeling, distributed and cooperative communications, cellular technol-ogies, radio network planning and optimization, and multimediatransmission over communication networks. He is a senior member ofthe IEEE, the chair of the IEEE Communications Society LebanonChapter, and a member of the Lebanese Order of Engineers.

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