Energy-Efficient Cooperative Video Distribution With Statistical QoS Provisions Over Wireless Networks

7/31/2019 Energy-Efficient Cooperative Video Distribution With Statistical QoS Provisions Over Wireless Networks

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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;lj denote the time slot duration allocated bynode k to layer l in the jth frame if flow Fn is used. We needto guarantee that

Pk2Pni

PLl1 T

nk;lj T 8 path i 8 frame j

where k 0 refers to the BS transmission and k > 0 refers to

MS Mks transmission. The time proportion tnk;lj Tnk;lj=Trepresents the normalized resource allocation, thus, theresource allocation bound reduces to

1

T

Xk2Pni

XLl1

Tnk;lj Xk2Pni

XLl1

tnk;lj 1 8i; j 1

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 ratios

are 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 j

4fk;k0 jg

K Kk0;k01

represents a fading state of the network for frame j wherek;k0 j 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 effective

SNR for the transmission of node k as follows:

kj mink02Mnk

k;k0 j 2

Assuming capacity-achieving codes are used to provide thecapability of operating at the Shannon capacity, the transmis-sion rate of node k is Rkj Bk log1 kj. The serviceprocess Ck;lj (bits/frame) of node k for the lth video layerand jth frame can be expressed as follows:

Cnk;lj Tnk;ljRkj BkT t

nk;lj log21 kj 3

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

3 STATISTICAL END-TO-END DELAY BOUNDS FORGENERAL 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;lgLl1 and

is determined by the scalable codec parameters and the

video content. Given this arrival process and the instanta-

neous SNRs fk;k0 gK Kk0;k01, we are interested in adaptively

configuring the service processes fCk;lgL Kl1;k0 such that the

following condition is satisfied:

PrXk2Pni

Dnk;l > Dth

8 Qthg :

elQth ; 0 k K; 0 l L; 5

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;ll and Ank;ll the effective capacity

and effective bandwidth functions, respectively, for thekth link and lth layer when flow Fn is used. Given anarrival process fAnk;lg, its effective bandwidth, denotedby Ank;ll (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;ll (bits/frame), is defined as themaximum constant arrival rate which can be supported byfCnk;lg subject to the specified QoS exponent l. Moreover,for a stationary and ergodic service process fCnk;lg that isuncorrelated across time frames, the effective capacity canbe expressed as follows [33]:

Cnk;ll 1

llog

IE

elCnk;l

6

1

llog

IE

elBk Tt

nk;l

log1k

7

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 guaranteel for the lth video layer, the effective capacity on thekth link should be equal to the effective bandwidth [34], i.e.,

Cnk;ll Ank;ll 8l 1; . . . ; L; k 0; . . . ; K: 8

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 Mnk ,i.e., fAnk;lg fC

nk0;lg 8k

0 2 Mnk . Thus, Ank;ll C

nk0;ll 8l; k

0; . . . ; 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;ll Cnk;ll 8k 1; . . . ; K: 9

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)

B0tn0;l log1 0 Bktnk;l log1 k 8k 1; . . . ; K: 10Intuitively, (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;lgLl1 at the BS has an average arrival

rate l IEA0;l=T for each video layer l. The per-layerarrival rate is determined by the parameters of the scalable

codec andby thevideocontent.Giventhis arrival process andthe instantaneous SNRs, we are interested in adaptivelyconfiguring the service processes fCnk;lg

L Kl1;k0 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 cutthrough. Considering constant ratefluid traffic, the total delay can be bounded as follows [7], [8]:

PrXk2Pni

Dnk;l > Dth

8: 32

where ~ni is obtained by solving the univariate function

niXLl1

tn0;l

; l ; ~ni

1: 33

Since (31) is strictly decreasing in ni , then if at ni 0, (24)

is not violated, this constraint will not be active for any niand ni 0 to satisfy (29). Otherwise, if at

ni 0, (24) is

violated, we could keep increasing ni until (24) is satisfiedfor some ni

~ni with equality so that (29) holds.Finally, since the Lagrangian function Ltnk;l;

nl ;

ni ;

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

nl nl

IEelB0T t

n0;l log210

elCl

; 34

where > 0 is a small positive constant. The estimationfor the expectation IEelB0T t

n0;l

log210 is obtained itera-tively for the jth time frame through a first-order low-pass filter as follows:

Sj 1 1 Sj elB0T tn0;l

j1 log210j1; 35

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 Ltnk;l;

nl ;

ni ;

n

; ni over where the solution satisfies (30). Other-

wise, (34) will not converge indicating that the delayconstraint cannot be satisfied, resulting in an infeasibleproblem. Plugging nl and

ni into (31), we obtain the

optimal first hop allocation tn0;l for any flow Fn. The optimalallocation by all nodes can then be computed as follows:

tnk;l B0 log21 0

Bk log21 k tn0;l

; nl ; ni

: 36

After the first few video frames, the process of tracking theoptimal Lagrange multipliers using (34) and (35) converges

and the network reaches the steady state. In this state, theresource allocation for frame j and flow Fn can be obtainedusing the following steps:

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

2. Use (32) to update the Lagrange multiplierni j for i 1; . . . ; pn.

3. Use (35) followed by (34) to update the Lagrangemultiplier nl j for l 1; . . . ; L.

4. Solve for the first hop resource allocation tn0;l for l

1; . . . ; L using (31) to minimize IE

PKk0P

Ll1 E

nk;l.

5. Obtain the instantaneous resource allocations foreach node tnk;l for k 1; . . . ; K; l 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 Rk, transmitpower Pk;t, and its set of multicast nodes M

nk . 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

PKk1 w

nk =Rk

as follows: Starting from the leaf nodes, each node Mk sums

the components it receives from its downstream nodes,adds wnk =Rk, 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=Rk tothe incremental value it receives and sends it to itsupstream node until it reaches the BS which scales it byR0 to obtain

ni . Next, steps 2-4 are performed at the BS

with the knowledge of n and ni for each path. Step 5 isperformed in a distributed fashion so that each node

computes 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 t

nk0;lRk0 =Rk. This procedure

does 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. Findingnj costs OK and finding ni j also costs OK for each

path. Since the number of paths in a DAG is upper boundedby the number of nodes, the operation cost is OKpn OK2. The complexity of steps 2-4 is dominated by thecomplexity of solving for tn0;l using (31) which is OK for

1228 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 11, NO. 7, JULY 2012

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each video layer. For all layers, the cost of obtaining the firsthop allocation becomes OKL. The final step also costsOKL to solve (36) 8k; l. Thus, the complexity of theoptimal resource allocation process for a single video frameand a predefined flow is OK2 KL.

4.4 Combinatorial Encoding of Network Flows

After solving for tn0;l over all flows, we can compute the

energy consumption of flow Fn as nP

Ll1 tn0;l. Finally, we

select the optimal flow as

nj argminn

nXLl1

tn0;l j

!; 37

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 mm2 [36]. For ournetwork of one base station and K mobile stations, weobtain the number of network flows as

N K 1K1: 38

Thus, the complexity of brute force flow selection isOK2 KL K 1K1. This complexity presents alimitation for the brute force approach as K increases. For

instance, in a network with one BS and 6 MSs, there are16,807 possible ways to distribute the content. We will

propose some approximation algorithms and provide

performance bounds for these algorithms under specificnetwork topologies.

Furthermore, Prufer devised a method for encoding anddecoding the set of spanning trees in a graph using what isknown as Prufer sequences. Given a tree with labeledvertices Mkj

Kk0, the Prufer encoding algorithm outputs a

unique 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 FLOWSELECTION

Finding the globally optimal distribution strategy requiresconverting each of the K 1K1 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 the

link, 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 statej

4fk;k0 jg

K Kk0;k01, we construct the complete network

graph with edge weights k;k0 j on the link between nodesMk and Mk0 . We then use Prims 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 that

flow 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 j. Instead, due to multicast, it isdetermined by the effective SNR on the worst link k mink02Mnk k;k0 which is not known beforehand because itdepends on the choice of n.

Using this approach, the flow selection problem isseparated from the resource allocation problem. Theflow selection process using Prims minimum spanningtree algorithm costs OE V logV OKK 1 K1 logK 1 OK2 where E KK 1 is the numberof edges in the complete graph and V K 1 is the numberof vertices. Thus, the total time complexity of the flowselection and resource allocation is OK2 OK2 KL OK2 KL as opposed to OK2 KL K 1K1 forthe optimal flow selection. Results presented in Section 6demonstrate that this significantdecrease in complexity costsa limited increase in the average energy consumption invarious network scenarios.

5.2 Dominant Set Flow SelectionThe second approximation algorithm is based on theobservation that most of the network flows can only beoptimal for a small percentage of the fading states

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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 M1through 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 can

estimate 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 the

dominant 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 long

training 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 OKa 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 OKa dominant flow to obtain thebest dominant flow, the time complexity of the flowselection and resource allocation is OK2 KL Ka.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 Mk1 make an angle for allk 1; . . . ; K 1 as shown in Fig. 2.

Throughout this section, we consider a two layer videostream with constant arrival rates 2 105 bps; 1 105 bps. The signal bandwidth Bkj

Kk1 1 MHz and the

time frame duration T 33 ms corresponding to a video


TABLE 1Complexity of the Flow Selection Algorithms

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



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frame rate of 30 fps. We define a delay bound Dth 3T

100 ms and a delay bound violation probability Pth 103.The transmit power by the BS is P0;t 0:5 W, the transmitpower of each MS is Pk;t 0:05 W 8k and the power(energy per second) consumed by each MS during receptionis Pr 0:05 J/sec. For channel modeling, we derive theaverage SNRs "k;k0 from the distances dk;k0 as follows:

"k;k0 10 log10Pk;tKdB 10log10dk;k0 10logN0Bk; 39

where KdB is the pathloss constant, is the pathlossexponent, and N0 is the power spectral density of theAWGN noise. In the simulations, KdB 21:36 dB, 3:52,and N0 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 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 approximation

algorithms, 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 in

flow F11 (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, 0:03 and 0:03.

In Fig. 4a, we compute the energy consumption for eachframe from tn0;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 .



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configuration represented by dand has a key effect on theenergy consumption in the network. At d 200 m and 10o, we require around 0.6 mJ/frame, while at d 1;500m and 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 tn0;l to find the end-to-end normalizedresource allocation for the most resource consuming path

which can be written as IEmaxifniPL

l1 tn0;lg. We thenaverage the end-to-end normalized resource allocation over

all frames for different values of d and . The trend of theresource allocation variation is similar to the energyconsumption, but shows a steeper slope of increase. Resultsshow that at d 200 m and 10o, we require only5 percent of the wireless resources, whereas the wirelessresources are almost fully utilized at d 1;500 m and 40o. This implies that increasing d or further willprohibit maintaining the statistical delay bound guarantee.

6.2 Flow Selection Analysis

We are further interested in finding the probability ofselecting a certain flow Fn for a given network topology. Wedefine the probability of using flow Fn as the number offrames transmitted through Fn as implied by (37) dividedby the total number of transmitted frames. For a networkwith K 3, Fig. 5a shows all the 42 16 candidate flows.The flows are ordered according to their Prufer encoding,that is, the first flow is generated from the Prufer sequence1; 1 up to the last flow corresponding to the sequence 4; 4.

In Fig. 5b, we compute the percentage of flow usage forthe three flow selection algorithms with d 1;000 m, 10o,and K 3 corresponding to 42 16 possible network flows.

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

uM1

uM2

uM3, BS

uM2

mM1; M3, and

BS u

M3 u

M2 u

M1, 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 channelconditions among MSs and the lower transmit power. Also,sequential unicast through M1 and M3 are two goodcandidates depending on the channel conditions on the firsthop links. Note that the traditional noncooperative flowinvolving 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 1;000 m, 10o,and K 5 corresponding to 64 1;296 possible networkflows. Despite the large number of flows, we can see that

only 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 Ecoop divided by theenergy consumption without cooperation Enocoop, that is,

Ecoop

Enocoop ; 40

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


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



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Enocoop 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, i s al way s l ess t ha n o r equ al t o 1 , t hat i s, i f thenoncooperative flow is the most energy efficient, resourcesare allocated on that flow to minimize energy consumption.

Fig. 7a shows the normalized energy consumption while

varying 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 Ecoopincreases as K increases, the rate at which Enocoop increasesis faster which explains this desirable behavior. Also, forlarger , Enocoop does not change, while E

coop increases, thus

reducing 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

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 willrequire 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 5 using optimal flow selection.



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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 energy

consumption at a much lower computational cost.Finally, to verify that the dominant set size is polynomial

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

that the decay rate is indeed an exponential regardless of thenetwork topology and the decay rate does not decrease as

K increases. For instance, with K 6, the total number ofcandidate flows is 16,807, however, the dominant set size isat most 155 for 30o. This shows that the flow selectionand resource allocation complexity is reduced fromOK2 KL K 1K1 to OK2 KL Ka where ais a constant that depends on the network topologycharacteristics and the mobility level.

6.4 Case Study: A Large Scattered Network

We consider a large network with 10 MSs scattered

randomly 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 2:35 109 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 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.



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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 to

M8. 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.

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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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Energy-Efficient Cooperative Video Distribution With Statistical QoS Provisions Over Wireless Networks