420 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 28, NO. 3, APRIL 2010

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1 420 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 28, NO. 3, APRIL 2010 Statistica QoS Provisionings for Wireess Unicast/Muticast of Muti-Layer Video Streams Qinghe Du, Student Member, IEEE, and Xi Zhang, Senior Member, IEEE Abstract Due to e time-varying wireess channes, deterministic quaity of service QoS is usuay difficut to guarantee for rea-time muti-ayer video transmissions in wireess networks. Consequenty, statistica QoS guarantees have become an important aternative in supporting rea-time video transmissions. In is paper, we propose an efficient framework to mode e statistica deay QoS guarantees, in terms of QoS exponent, effective bandwid/capacity, and deay-bound vioation probabiity, for muti-ayer video transmissions over wireess fading channes. In particuar, a separate queue is maintained for each video ayer, and e same deay bound and corresponding vioation probabiity reshod are set up for a ayers. Appying e effective bandwid/capacity anayses on e incoming video stream, we obtain a set of QoS exponents for a video ayers to effectivey characterize is deay QoS requirement. We en deveop a set of optima adaptive transmission schemes to minimize e resource consumption whie satisfying e diverse QoS requirements under various scenarios, incuding video unicast/muticast wi and/or wiout oss toerance. Simuation resuts are aso presented to demonstrate e impact of statistica QoS provisionings on resource aocations of our proposed adaptive transmission schemes. Index Terms Mobie muticast, wireess networks, rate contro, ayered video streaming, statistica QoS guarantees. I. INTRODUCTION RECENTLY, supporting rea-time video services wi diverse QoS constraints has become one of e essentia requirements for wireess communications networks. Consequenty, how to efficienty guarantee QoS for video transmission attracts more and more research attention [1]- [14]. However, e unstabe wireess environments and e popuar ayer-structured video signas [2]-[4] impose a great dea of chaenges in deay QoS provisionings. Due to e highy-varying wireess channes, e deterministic deay QoS requirements are usuay hard to guarantee. As a resut, statistica deay QoS guarantees [9]-[14], in terms of effective bandwid/capacity and queue-eng-bound/deay-bound vioation probabiities, have been proposed and demonstrated as e powerfu way to characterize deay QoS provisionings for wireess traffics. Whie many reated existing research works mainy focused on e scenarios wi singe-ayer streams [11]-[14], e modern video coding techniques usuay Manuscript received 1 March 2009; revised 1 November The research reported in is paper was supported in part by e U.S. Nationa Science Foundation CAREER Award under Grant ECS As is paper was co-auored by a guest editor of is issue, e review of is manuscript was handed by senior editor Prof. Larry Mistein. The auors are wi e Networking and Information Systems Laboratory, Department of Eectrica and Computer Engineering, Texas A&M University, Coege Station, TX USA e-mais: duqinghe@tamu.edu; xizhang@ece.tamu.edu. Digita Object Identifier /JSAC /10/$25.00 c 2010 IEEE generate ayer-structured traffics [2]-[4]. Unfortunatey, how to design efficient schemes to support statistica deay QoS for ayered video traffics over wireess networks has been neier we understood nor oroughy studied. In video transmissions, video source is usuay encoded into a number of data ayers [2]-[4] in e appication protoco ayer. By appying ayered video coding, e receivers under poorer channe conditions can get ony ower video quaity, whie ose under better channe conditions can achieve higher video quaity. Aough e ayered coding techniques are efficient in handing diverse channe conditions, ey aso raise new chaenges for statistica deay QoS guarantees, which are not encountered in singe-ayer video transmissions. First, we need to keep e synchronous transmissions across different video ayers, impying e same deay-bound vioation probabiity for a ayers. Second, for muti-ayer video stream, it is a natura requirement at different video ayers can toerate different oss eves. Therefore, e scheduing and resource aocation need to be aware of e diverse oss constraints. Third, how to minimize e consumption of scarce wireess-resources whie satisfying e specified deay QoS requirements is a widey cited open probem. Besides e genera chaenges in statistica deay QoS guarantees for e unicast transmission of ayered video, muticasting ayered video over wireess networks furer compicates e probem significanty due to e heterogeneous channe quaities across muticast receivers at each time instant. Unike in e wireess muticast, ere are reativey more research resuts for e muticast over wireine networks. A number of muticast protocos were proposed over wireine networks. The auors of [3] deveoped e efficient receiver-driven ayered muticast over e Internet, where e video source is encoded to a hierarchica signa wi different ayers. Each ayer corresponds to a muticast group and muticast receivers can join/eave e group based on eir bandwids. In [5], we proposed a nove fow contro scheme for muticast services over e asynchronous transfer mode ATM networks. The kerne parts of is scheme incude e optima second-order rate contro agorim and e feedback soft-synchronization protoco [6], [7], which can achieve scaabe and adaptive muticast fow contro over bandwid and buffer occupancies and utiizations. The above designs are shown to be efficient in e wireine networks. However, e muticast strategies in wireine networks cannot be directy appied into wireess networks. This is because highy and rapidy time-varying wireess-channes quaities resut in unstabe bandwids and us unsatisfied oss and deay QoS. For wireess video muticast, at e muticast sender we need to design e transmission Auorized icensed use imited to: Texas A M University. Downoaded on May 12,2010 at 09:25:32 UTC from IEEE Xpore. Restrictions appy.

2 DU and ZHANG: STATISTICAL QOS PROVISIONINGS FOR WIRELESS UNICAST/MULTICAST OF MULTI-LAYER VIDEO STREAMS 421 Arriva processes Incoming ayered video stream Video ayer 1: A 1 [k] Video ayer 2: A 2 [k] Video ayer L: A L [k] Pr Statistica Deay QoS: D D P, Queue 1 Queue 2 Queue L pre-drop pre-drop pre-drop Time-sot aocation and rate adaptation across video ayers Loss constraint CSI feedback C 1 [k] C 2 [k] C L [k] Transmission at e PHY ayer Unicast scenario Wireess channes Signas from e sender CSI feedback Muticast scenario Signas from e sender CSI feedback a The base station sender b Unicast receiver c Muticast receiver Unicast receiver Wireess channes Wireess channes Muticast receiver 1 Muticast receiver N Fig. 1. The system modeing framework for ayered-video transmission over wireess networks; a The ayered-video arriva stream and e sender s processing. b Unicast scenario. c Muticast scenario. scheme to contro e oss and/or deay performance for a muticast receivers at each video ayer based on eir instantaneous channe quaities. In [8] and [14], we appied e effective capacity eory to propose and evauate rate-adaptation schemes for statistica deay QoS guarantees in mobie muticast. However, e anayses ony focused on singe-ayer stream. It remains one of e major chaenges to extend e statistica QoS eory into muti-ayer video muticast in deveoping QoSdriven transmission strategies. In [4], e auors proposed a cross-ayer architecture for adaptive video muticast over mutirate wireess LANs. In particuar, two-ayer video signas are considered, which incude e base ayer more important and enhancement ayer ess important. The auors derived e transmission rate for e base ayer according to e worst-case signa-to-noise ratio SNR among a receivers, whie dynamicay reguating e transmission rate for e enhancement ayer based on e best-case SNR to benefit receivers wi better channe quaities. However, under is strategy, e oss rate of e enhancement ayer wi vary significanty wi e statistica characteristics of wireess channes, and us is hard to contro. To overcome e above probems, in is paper we propose an efficient framework to mode e statistica deay QoS guarantees, in terms of QoS exponent, effective bandwid/capacity, and deay-bound vioation probabiity, for muti-ayer video transmission over wireess networks. In particuar, a separate queue is maintained for each video ayer, and e same deay bound and e corresponding vioation probabiity are set up for a video ayers. We en deveop a set of optima adaptive transmission schemes to minimize e resource consumption whie satisfying e diverse QoS requirements under various scenarios, incuding video unicast/muticast wi and/or wiout oss toerance. The rest of is paper is organized as foows. Section II describes e system mode. Section III proposes e framework of statistica deay QoS guarantees for muti-ayer video unicast and muticast. Section IV presents e design procedures for muti-ayer video by appying effective bandwid/capacity eory. Sections V and VI derive e optima adaptive transmission schemes for video unicast and muticast, respectivey. Section VII presents e simuation evauations. The paper concudes wi Section VIII. II. THE SYSTEM MODEL We consider e unicast/muticast system mode for mutiayer video distribution in wireess networks, as shown in Fig. 1. Specificay, e base station sender is responsibe for transmitting a muti-ayer video stream to a singe receiver unicast or mutipe receivers muticast over broadcast fading channes. The video stream generated by upper protoco ayers e.g., appication ayer consists of L video ayers, each having e specific QoS requirements. The L-ayer video stream wi be injected to e physica PHY ayer. Then, as depicted in Fig. 1a, we aim at deveoping strategies to efficienty aocate imited wireess resources for mutiayer video transmission whie satisfying e specified QoS requirements for each video ayer. At e PHY ayer, e sender uses a constant transmit power wi e signa bandwid equa to B Hz. The wireess broadcast channes are assumed to be fat fading. Then, we can use an SNR vector γ γ 1,γ 2,...,γ N to characterize e channe state information CSI of receivers, where N denotes e number of unicast/muticast receivers, γ n is e received SNR of e n receiver for n =1, 2,...,N,and γ n N n=1 are independent and identicay distributed i.i.d. for e cases of N>1. WhenN is equa to 1, e scenario reduces to video unicast, 1 as iustrated in Fig. 1b; whie N is arger an 1, we get e muticast scenario depicted in Fig. 1c. The CSI γ is modeed as an ergodic and stationary bock-fading process, where γ does not change wiin a timeframe wi e fixed eng T, but varies independenty from frame to frame. Moreover, γ foows Rayeigh fading mode, which is one e most generay used modes to characterize wireess fading channes. In addition, we assume at γ can 1 When N =1, we write SNR as γ instead of γ 1 to simpify notation. Auorized icensed use imited to: Texas A M University. Downoaded on May 12,2010 at 09:25:32 UTC from IEEE Xpore. Restrictions appy.

3 422 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 28, NO. 3, APRIL 2010 be perfecty estimated by e receivers and reiaby fed back to e sender wiout deay rough e dedicated feedback contro channes. III. MODELING FRAMEWORK FOR WIRELESS UNICAST/MUTICAST OF MULTI-LAYER-VIDEO We propose e foowing framework for transmitting mutiayer video over fading channes by integrating e adaptive resource aocations, statistica QoS guarantees, and oss constraints. A. Muti-Queue Mode for Muti-Layer Video Arriva Processes The modern video coding techniques [2] usuay encode e video source into a number of video ayers wi different reevance and importance. The most important ayer is caed based ayer and e oer ayers are caed enhancement ayers. Because of e diverse importance, different strategies need to be proposed for e corresponding video ayers in e PHY-ayer transmission, depending on e specified QoS requirements to be detaied in Sections III-B and III-D. Then, to achieve e efficient video transmission, e sender manages a separate queue for each video ayer. As shown in Fig. 1a, e data arriva rate of e video ayer is characterized by a discrete-time process, denoted by A [k] nats/frame, where = 1, 2,...,L,and[k], k = 1, 2,..., is e index of time frames; e service rate process departure process of e ayer is denoted by C [k] nats/frame. Moreover, we determine C [k] based on CSI, tota avaiabe wireess resources, and QoS constraints. B. Statistica Deay QoS Guarantees for Video Transmissions For video transmissions, deay is one of e most important QoS metrics. However, due to e highy varying wireess channes, usuay e hard deay bound cannot be guaranteed. Therefore, e statistica metric, namey deay-bound vioation probabiity [9]-[12], has been widey appied in QoS evauations for rea-time services. In our framework, we aso use e deay-bound vioation probabiity to statisticay characterize e deay QoS provisionings for each video ayer. In particuar, a queueing deay bound, denoted by D,is specified. Accordingy, over a video ayers, e deay-bound vioation probabiity cannot exceed e reshod denoted by P : PrD >D P, P 0, 1, 1 for a 1, 2,...,L,whereD denotes e queueing deay at e video ayer. The deay-bound vioation probabiity in Eq. 1 is evauated over e entire transmission process, which is assumed to be ong enough. Note at D and P are appication-dependent parameters. Moreover, e pair of D and P is set to be e same for a video ayers, because e synchronous transmission across different video ayers is usuay required. Aso note at e deay in wireess video transmissions may resut from mutipe factors such as transmissions, queueing, and decoding. In is paper, we mainy focus on queueing deay, which refects e capabiity of e wireess channe transmission botteneck in supporting video distributions. C. Adaptive Resource Aocation and Transmissions To efficienty use e imited wireess resources for video unicast/muticast, we empoy e adaptive transmission strategy based on e CSI, consisting of ree fods: transmission rate adaptation, dynamic time-sot aocation, and adaptive predrop queue management strategy, as detaied beow. 1 Time Sot Aocation for Video Layers: Each time frame is divided into L time sots, e engs of which are denoted by T [k] L =1,where0 T [k] T and L =1 T [k] T. The time sot wi eng T [k] is used for transmitting data of e video ayer. For convenience of presentation, we furer define time proportion t [k] T [k]/t, and us we have L =1 t [k] 1. Notice at our target is to minimize e wireess-resource consumption whie satisfying e QoS requirements imposed by video quaities. Thus, L =1 t [k] may be smaer an 1 for some γ. 2 Rate Adaptation of Unicast/Muticast: We denote e tota amount of transmitted data at e video ayer in e k time frame by R [k] wi e unit nats/frame. Moreover, we use e normaized transmission rate, denoted by R [k] nats/s/hz, to characterize e transmission rate adaptation, where R [k] R [k]/bt. We assume at capacity-achieving codes are used for transmission at e PHY ayer. Accordingy, for unicast, e normaized transmission rate of e video ayer is set equa to e Shannon capacity under e current SNR γ: R [k] = og1 + γ nats/s/hz. 2 Ceary, R [k] does not vary wi, and us we ony focus on time-sot aocation for unicast. For e muticast case, e rate adaptation becomes more compicated. In particuar, e time sot for video ayer is furer partitioned into N sub-sots. The eng of e n sub-sot, denoted by T,n [k], is equa to T [k]t,n [k], where 0 t,n [k] 1 and N n=1 t,n[k] =1. Wiin e n subsot, e transmission rate is set equa to e Shannon capacity under SNR γ n, and us e data transmitted in is sub-sot can be correcty decoded ony by receivers wi SNR higher an or equa to γ n. Then, e normaized transmission rate R [k] for e video ayer becomes R [k] = = N t,n [k]r,n [k] n=1 N t,n [k] og1 + γ n nats/s/hz, 3 n=1 where R,n [k] og1 + γ n is e normaized transmission rate for e n sub-sot of e video ayer. As a resut, we need to not ony adjust t [k] s for each ayer, but aso reguate t,n [k] s wiin every time sot. Unike e wireine muticast networks, in is paper we focus on e ayered video transmissions over wireess networks, which has a singe-hop ceuar network structure. Due to e broadcast nature of wireess channes, e sender ony needs to transmit a singe copy of data and a muticast receivers can hear e transmitted signa for each video ayer. Under is mode, our scheme empoys e sender-oriented muticast approach because e sender needs to dynamicay adjust e Auorized icensed use imited to: Texas A M University. Downoaded on May 12,2010 at 09:25:32 UTC from IEEE Xpore. Restrictions appy.

4 DU and ZHANG: STATISTICAL QOS PROVISIONINGS FOR WIRELESS UNICAST/MULTICAST OF MULTI-LAYER VIDEO STREAMS 423 transmissions rate in controing e oss rate to be detaied in Section III-D and guaranteeing e deay-qos requirements see Section III-B across different muticast receivers. 3 Pre-drop Strategy: In [14], for muticasting singe-ayerdata we deveoped e pre-drop strategy to gain a more robust queueing behavior. In is paper, we furer extend e predrop strategy to muti-ayer video transmission. Specificay, based on e CSI, in each time frame e sender can drop some data see Fig. 1a from e head of each queue, but treat em as if ey were transmitted. We denote e amount of dropped data in video ayer by Z [k] nats/frame and define e normaized drop rate, denoted by z [k], asz [k] Z [k]/bt nats/s/hz. Then, e service process C [k] of e video ayer is given by C [k] =BTt [k]r [k]+z [k] nats/frame. 4 Ceary, e pre-drop strategy suppresses e growing speed of e queue for a more robust queueing behavior, but is strategy aso causes data oss to a muticast receivers. As a resut, z [k] needs to be determined by not ony e CSI, but aso e oss constraints see Section III-D. D. Loss Rate Constraint Aough a certain oss is usuay toerabe for deaysensitive services, e oss eve cannot be arbitrariy high. Consequenty, we require e oss rate of e video ayer for each receiver to be imited ower an or equa to an appication-dependent reshod, denoted by q. The oss rate of e video ayer for e n receiver, denoted by q,n,is defined as e ratio of e amount of data correcty received by is receiver to at of e data transmitted at is video ayer. Data oss for unicast wi be caused ony by e predrop strategy, whie data oss for muticast wi be introduced by bo pre-drop operation and heterogeneous channe fading across muticast receivers. Since various efficient forward-error contro FEC codes [16]-[18] at upper protoco ayers were proposed and widey appied to muticast communications in wired/wireess networks, in our framework we suppose at FEC mechanisms are aready empoyed at e upper protoco ayers. The errorcontro redundancies added in e FEC codes at different video ayers are inherenty reated among video ayers and are jointy determined by e targeted video-deivery quaities at different video ayers. Correspondingy, e toerabe oss-rate eves q s for different video ayers indexed by are jointy specified based on e video deivery quaity requirements and e error contro redundancy degrees across different video ayers. Under is framework, we en mainy focus on how to use e minimum wireess resources wi QoS guarantees to unicast/muticast muti-ayer video over wireess channes. IV. STATISTICAL DELAY QOS GUARANTEES THROUGH EFFECTIVE BANDIWDTH/CAPACITY A. Preiminary for Statistica Deay QoS Guarantees The eory on statistica deay QoS guarantees [9]-[11] provides a powerfu approach in anayzing e queueing behavior for time-varying arriva and/or service processes. Specificay, consider a stabe queueing system wi e stationary and ergodic arriva and service processes. Asymptotic anayses [9] show at wi sufficient conditions, e queue eng process Q[k] converges to a random variabe Q[ ] in distribution such at og Pr Q[ ] >Q im = θ 5 Q Q for a certain θ>0, whereq is e queue-eng bound. Moreover, e queue-eng bound vioation probabiity can be approximated by PrQ >Q e θq, 6 where we remove e index[k] for Q[k] to simpify notations. In e above two equations, θ is caed QoS exponent and can be used to characterize deay QoS. The arger θ corresponds to e more stringent QoS requirement, whie e smaer θ imposes e ooser deay constraint. When e QoS metric of interest becomes deay-bound, e simiar expressions can be obtained. B. Preiminary for Effective Bandwid/Capacity Effective bandwid [10] and effective capacity [11] are a pair of dua concepts. Given an arriva process A[k], effective bandwid of A[k], denoted by Aθ nats/frame, is defined as e minimum constant service rate required to guarantee a specified QoS exponent θ, i.e., Eqs. 5-6 are satisfied for e given θ. In contrast, given a service process C[k], effective capacity of C[k], denoted by Cθ nats/frame, is defined as e maximum constant arriva rate which can be supported by C[k] subject to e specified QoS exponent θ. Moreover, effective bandwid [10] and effective capacity [11] can be expressed as Aθ = im k 1/kθ og E e θsa[k] and Cθ = im k 1/θk og E e θsc[k], respectivey, where E denotes e expectation, S A [k] k i=1 A[i], and S C [k] k i=1 C[i]. In addition, for effective capacity and effective bandwid scenarios, e deay-bound vioation probabiity can be approximated [10], [11] as: and PrD >D e θcθd, for effective capacity; 7 PrD >D e θaθd, for effective bandwid. 8 Equations 6, 7, and 8 are good approximations for reativey arge Q and D asshownin[11],[22].whenq and D are reativey sma, e more accurate approximations expressions an Eqs. 6, 7, and 8 are given in [11], [22] as foows: PrQ >Q ϱe θq ; PrD >D ϱe θcθd ; PrD >D ϱe θaθd, where ϱ denotes e probabiity at e queue is nonempty. These approximations are upper-bounded by e corresponding approximations given in Eqs Thus, directy using Eqs. 6-8 for e system design often guarantees more stringent QoS an e specified requirements. For wireess video transmissions, e deay bound D is typicay hundreds of miiseconds ms, which are us much arger an e Auorized icensed use imited to: Texas A M University. Downoaded on May 12,2010 at 09:25:32 UTC from IEEE Xpore. Restrictions appy.

5 424 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 28, NO. 3, APRIL 2010 Statistica Deay QoS: D D e D P L Arriva processes Layer 1: Layer 2: A 1[k] A 2[k] Virtua constant service processes A 1 1 A 2 2 Virtua constant arriva processes 1 1 = A = A 2 2 Service processes C 1[k] C 2[k] Step 1: Determine effective bandwid functions A θ for e arriva processes A [k], =1, 2,...,L. Step 2: Appy Eq. 7 or Eq. 8 to find e soution θ to e equation PrD > D = P and get e corresponding effective bandwid A θ. Step 3: Set e target effective capacity C = A θ for e service processes of each video ayer. Step 4: Jointy design adaptive service process C [k] for each video ayer, such at C θ C is satisfied whie minimizing e tota consumed wireess resources. Layer L: A L[k] A L L L L = A L L C L[k] Fig. 3. The design procedures to provide statistica deay QoS guarantees for transmitting muti-ayer video stream. Deay-bound D and vioation probabiity P Obtained effective bandwid A Target effective capacity Reguate C [k] Fig. 2. Iustration of design procedures to guarantee statistica deay QoS by using effective capacity and effective bandwid eories. adaptive-transmission period scae e.g., e physica-ayer time-frame eng of e wireess transmission system, where e adaptive-transmission period typicay varies from a few miiseconds ms to tens of miiseconds ms. Therefore, Eqs. 6-8 are good approximating expressions in designing efficient wireess video-transmission schemes wi statistica QoS guarantees. C. Design Procedures for Transmitting Layered Video wi Statistica QoS Guarantees For a dynamic queueing system, in order to guarantee e QoS exponent θ given in Eqs. 5-6, e foowing equation need to be satisfied [10], [12]: Cθ =Aθ. 9 Inspired by is property, e statistica deay QoS guarantees can be characterized rough e arriva process and service process separatey. As shown in Fig. 2, e queueing system for e video ayer can be decomposed to two virtua queueing systems. The one on e eft-hand side of Fig. 2 is composed by e true arriva process A [k] and one virtua constant-rate service process, e rate of which is equa to e effective bandwid A θ of A [k]; e right one consists of e true service process C [k] and one constantrate virtua arriva process, e rate of which is equa to e effective capacity C θ of C [k]. Using e above concept, we deveop e design procedures to provide statistica deay QoS guarantees for transmitting muti-ayer video stream as shown in Fig. 3. Among e procedures in Fig. 3, Steps 1 and 2 first identify e effective bandwid A θ and QoS exponent θ required to satisfy e deay-bound D and its vioation probabiity P. Then, to satisfy e deay QoS in Eq. 1, we need to eier satisfy Eq. 9 or guarantee at e effective capacity is arger an e effective bandwid, which resuts in Steps 3 and 4. The anaytica expressions of effective bandwid for many typica arriva processes, such as constant-rate process, autoregressive AR process, and Markovian process, can be found in [10]. Note at if A [k] is time varying, in Step 2 θ can be determined rough Eq. 8. However, if A [k] is a constant-rate process equa to A,wehaveA θ =A for a θ, impying at e deay-bound vioation probabiity of e virtua queueing system on e eft-hand side of Fig. 2 is aways equa to 0. Therefore, we cannot derive θ directy rough Eq. 8. In contrast, e QoS exponent θ to guide e adaptive transmission needs to be determined by using Eq. 7 under e condition of C θ =A θ =A. V. UNICASTING MULTI-LAYER VIDEO STREAM Assuming at e target effective capacity L C and =1 QoS exponent θ have been determined, we next focus on deveoping e optima adaptive time-sot aocation and pre-drop strategy to satisfy e QoS requirements whie minimizing e wireess-resource consumption. Uness oerwise mentioned, we drop e time-frame index [k] for e corresponding variabes in e rest of is paper to simpify notations. Based on our previous work [13], if a stationary and ergodic service rate process C is uncorreated across different time frames, we can write its effective capacity as foows: C θ = 1 og E e θ C nats/frame. 10 θ Since e bock-fading channe mode described in Section II satisfies e time-uncorreated condition, we can appy Eq. 10 for our framework to derive e adaptive unicast/muticast schemes wi e statistica QoS guarantees. A. Unicasting Layered Video Stream Wiout Loss Toerance We first consider e cases wiout oss toerance for mutiayer video transmissions, i.e., q = 0 for a and e pre-drop strategy wi not be appied. Thus, we ony need to focus on reguating e time-sot proportion t L =1 for each video ayer. Foowing e design target and QoS constraints characterized in Sections III and IV, we derive e adaptive transmission strategy by soving e foowing optimization probem. Probem 1: P 1 L min t E γ t 11 =1 s.t.: C θ C,, 12 L t 1 0, 0 t 1, γ, 13 =1 where t t 1,t 2,...,t L and E γ denotes e expectation over e random variabe γ. Auorized icensed use imited to: Texas A M University. Downoaded on May 12,2010 at 09:25:32 UTC from IEEE Xpore. Restrictions appy.

6 DU and ZHANG: STATISTICAL QOS PROVISIONINGS FOR WIRELESS UNICAST/MULTICAST OF MULTI-LAYER VIDEO STREAMS 425 Using Eq. 10, e constraint in 12 can be equivaenty rewritten as E γ e β t og1+γ V 0, 14 where β θ TB is termed normaized QoS exponent and V e θ C. It is not difficut to see: 1 e objective function in P 1 is convex over t; 2 e functions on e eft-hand side of a inequaity constraints Eqs. 13 and 14 are convex over t. Therefore, P 1 is a convex probem [20] and e optima soution can be obtained by using e Lagrangian meod and e Karush-Kuhn-Tucker KKT conditions [20], which is summarized in Theorem 1. Theorem 1: The optima soution t to probem P 1, if existing, is determined by 1+ψ og + γ t = t γ,λ,ψ γ β λ og1+γ, 15 β og1 + γ where [ ] + max, 0. The parameters ψγ and λ L =1 are e optima Lagrangian mutipiers associated wi Eqs. 13 and 14, respectivey. Given SNR γ in a fading state and λ L =1,if L t γ,λ, =1 hods, ψ γ is e unique soution to L t γ,λ,ψ γ =1, ψ γ 0; 17 =1 oerwise, we get ψ γ =0. 18 Under e above strategy to determine t and ψγ, e optima are seected to satisfy λ L =1 E γ e β t og1+γ V =0,. 19 Proof: We construct e Lagrangian function for P 1, denoted by J, as foows: L L J = E γ t + E γ ψ γ t 1 + =1 L =1 =1 λ E γ e β t og1+γ V, 20 where ψ γ 0 and λ 0, =1, 2,...,L, are Lagrangian mutipiers associated wi Eqs. 13 and 14, respectivey. Then, e optima t and Lagrangian mutipiers of optimization probem P 1 satisfy e foowing KKT conditions [20]: J t t =0,, γ =t ψγ 0 and λ 0; L ψγ =1 t 1 21 =0,, γ; Eγ e β t og1+γ V =0,. λ Taking e derivative of J wi respect to w.r.t. t,weget J = 1+ψ γ λ β 1 + γ β t og1 + γ f Γ γdγ 22 t where f Γ γ is e probabiity density function pdf of γ. Pugging Eq. 22 into e first ine of Eq. 21 and soving for t under e boundary condition t 0, wegeteq.15. According to Eq. 15, t γ,λ,ψ γ is a stricty decreasing function of ψ γ for t γ,λ,ψ γ > 0, andψγ eads to t 0. Therefore, if Eq. 16 hods, we can aways find e unique ψγ to satisfy Eq. 18; oerwise, e inequaity L =1 t γ,λ,ψ γ 1 < 0 foows for any ψ γ 0, impying ψγ = 0 by appying e ird ine of Eq. 21. Through Eq. 15, λ =0resuts in t =0for a γ, and us e constraint in Eq. 12 wi be vioated, impying an infeasibe soution. Therefore, λ has to be positive. Then, to satisfy e four ine of Eq. 21, Eq. 19 must hod and us Theorem 1 foows. Note at given λ L =1, ψ γ is easy to sove because t γ,λ,ψ γ is a decreasing function of ψ γ. However, how to find λ L =1 is sti unknown. Moreover, Theorem 1 does not state wheer e optima soution exists. Next, we discuss how to get λ L =1 and examine e existence of e optima soution, which can be performed eier off-ine or on-ine. Based on e optimization eory [19], [20], e Lagrangian dua probem to P 1 is given by Jλ,ψγ, 23 max λ,ψ γ where λ λ 1,λ 2,...,λ L and Jλ,ψ γ is e Lagrangian dua function defined by Jλ,ψ γ min t J = J t =t γ,λ,ψ γ. We can furer convert Eq. 23 into max λ,ψγ Jλ,ψγ = max λ Jλ,ψγ λ, where ψ γ λ denotes e maximizer of Jλ,ψ γ given λ. Moreover, we can obtain ψ γ λ by using e same procedures as ose used in determining ψγ, which are given by Eqs in Theorem 1. Since probem P 1 is convex, ere is no duaity gap between P 1 and its dua probem given by Eq. 23 if e optima soution exists. Thus, e optima Lagrangian mutipiers λ L =1 and ψ γ to probem P 1 aso maximize e objective function Jλ,ψ γ in Eq. 23. Consequenty, we can obtain λ L =1 rough maximizing Jλ,ψ γ. Foowing convex optimization eory [20], Jλ,ψγ λ is a concave function over λ, and us we can track e optima λ by using e subgradient meod [21]: λ := λ + ɛ E γ e β t og1+γ V t =t γ,λ,ψ γλ 24 where ɛ is a positive rea number cose to 0. and Eγ e β t og1+γ V in e above equation is a subgradient of Jλ,ψ γ λ w.r.t. λ [19] see e definition of subgradient in Section VI-B. If e optima soution to P 1 exists, e above iteration wi converge to e optima λ wi propery seected ɛ because of e concavity of Jλ,ψ γ λ. Correspondingy, E γ e β t og1+γ V wi converge to 0. If e optima soution to P 1 does not exist, we cannot Auorized icensed use imited to: Texas A M University. Downoaded on May 12,2010 at 09:25:32 UTC from IEEE Xpore. Restrictions appy.

7 426 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 28, NO. 3, APRIL 2010 support such a statistica QoS requirement even we use up a time sots. Then, E γ e β t og1+γ V is aways arger an 0 for some. As a resut, λ wi approach infinity. So, if any λ does not converge and keeps increasing, we can concude at e optima soution does not exist and current wireess resources are not enough to support e specified statistica deay QoS for e incoming muti-ayer video stream. To find e optima λ, we need e pdf of γ. In reaistic systems, aough e pdf of γ is usuay unknown, we can sti appy Eq. 24 to impement onine tracking. In particuar, e iterative update of Eq. 24 wi be performed in each time frame. However, e expectation of e β t og1+γ in Eq. 24 needs to be substituted by its estimation obtained based on e statistics from previous time frames. Denoting e estimation of E γ e β t og1+γ in e k time frame by S [k], we obtain S [k+1] rough a first-order autoregressive fiter owpass fiter as foows: S [k +1]:=1 αs [k]+αe β t [k+1] og1+γ[k+1], 25 where = 1, 2,..., L and α 0, 1 is a sma positive number cose to 0. If e optima soution exists, e onine tracking meod converges wi propery seected α and ɛ. Section VII wi present some exampes of tracking e optima Lagrangian mutipiers rough simuations. B. Unicasting Layered Video Stream Wi Loss Toerance When q > 0, e transmission strategy becomes more compicated, but wi use ess wireess resources. After integrating e pre-drop strategy, e oss rate q of e ayer is derived as q =1 BTE γt R E γ C =1 E γt R E γ t R + z. 26 Next, we identify e adaptive transmission poicy by soving optimization probem P 2: Probem 2: P 2 L min t,z =1 E γ t 27 s.t.: E γ e β z +t og1+γ V 0, z 0,, 28 q q, 29 L t 1, 0 t 1, γ, 30 =1 where z z 1,z 2,...,z. Appying Eq. 26, we can rewrite Eq. 29 as foows: 1 q E γ z q E γ t og1 + γ 0,. 31 It is aso not hard to prove at probem P 2 is sti a convex probem and e Lagrangian meod is sti effective in finding e optima soutions, which is summarized in Theorem 2. Theorem 2: The optima soution t, z, if existing, is expressed by a set of functions of γ, λ L =1, φ L =1,and ψ γ as foows:: t = t γ,λ,φ,ψ γ, z = z γ,λ,φ,ψ γ,, 32 where t γ,λ,φ,ψ γ, if < 1+ψγ og1+γ φ q [ ] + 1 β og1+γ og 1+ψ γ q φ og1+γ β λ og1+γ, if φ q < 1+ψγ og1+γ <φ ; 0, if φ 1+ψγ og1+γ <, and ; 33 z γ,λ,φ,ψ γ 0, if < 1+ψγ og1+γ <φ ; [ φ 1 q ]+ 1 β og β λ, if φ 1+ψγ og1+γ <. 34 Given γ, λ L =1,andφ L =1,if L =1 t γ,λ,φ, 0 1, ψγ is seected such at e equation L =1 t γ,λ,φ,ψ γ= 1 hods; oerwise, we have ψγ =0. The optima λ L =1 and φ L =1 need to be jointy seected such at = hods in bo Eqs. 28 and 31. Proof: The proof of Theorem 2 can be readiy obtained by using e standard Lagrangian-mutipier based meod and KKT conditions, and us is omitted due to ack of space. The detaied proof of Theorem 2 is provided onine in [24]. In order to search for e optima Lagrangian mutipiers and check e existence of e optima soution, we can aso design e adaptive tracking meod simiar to probem P 1. VI. QOS GUARANTEES FOR MULTICASTING LAYERED-VIDEO STREAM We consider e muticast scenario in is section. If no oss is toerated, e transmission rate in each time frame is imited by e worst-case SNR among a muticast receivers. Thus, e system roughput wi be degraded very quicky as e muticast group size increases. Therefore, we mainy focus on e muticast scenario wi oss toerance. A. Probem Formuation for Muticast Scenario Under e muticast rate-adaptation strategy given in Section III, e oss rate of e n receiver at e video ayer becomes E γ t N i=1 t,i og1 + γ i δ γn γ i q,n =1, 35 E γ z + t R where E γ denotes e expectation over a fading states of e random vector variabe γ, δ γn γ i is e indication function for a given statement ϖ, δϖ =1if ϖ is true, and δϖ =0oerwise, and R = N i=1 t,i og1 + γ i is e tota normaized transmission rate in a time frame see Eq. 3. Accordingy, e foowing oss-rate constraint needs to be satisfied for each muticast receiver at every video ayer, which is specified by e inequaity as foows: q,n q, n,. 36 Auorized icensed use imited to: Texas A M University. Downoaded on May 12,2010 at 09:25:32 UTC from IEEE Xpore. Restrictions appy.

8 DU and ZHANG: STATISTICAL QOS PROVISIONINGS FOR WIRELESS UNICAST/MULTICAST OF MULTI-LAYER VIDEO STREAMS 427 To simpify e derivations, we first use a reaxed constraint to repace Eq. 36 by: q,0 1 N N n=1 q,n q, 37 where q,0 is caed group oss rate average oss rate over receivers at e video ayer. We wi show ater at e optima adaptation poicy derived under e group-oss-rate constraint given in Eq. 37 does not vioate Eq. 36, and us is aso optima under e origina oss-rate constraint given by Eq. 36. Pugging Eq. 35 into Eq. 37, we have N E γ t i=1 t,im i og1 + γ i q,0 =1, 38 NE γ z + t R where m i is e number of receivers wi SNR higher an or equa to γ i. In addition, it is cear at R fas in e foowing range: R [ R πn,r π1 ], 39 where R πn min 1 n N og1 + γ n and R π1 max 1 n N og1+γ n. Note at when we attempt to use a normaized transmission rate equa to R in a time frame, ere are many different choices for t,n N n=1 to get e same R. In order to minimize e oss for e entire muticast group, among a ese choices we need to seect e one which maximizes e numerator of e second term on e righand side of Eq. 38, which represents e sum rate of data correcty received by each muticast receiver. Accordingy, we define N g s R Pmax t,i m i og1 + γ i t : Ni=1 t,i =1 i=1 N s.t.: t,i og1 + γ i =R 40 i=1 where t t,1,t,2,...,t,n. Therefore, g s R denotes e maximum sum of achieved rates over a muticast receivers under e given normaized transmission rate R.In our previous work [15], where we studied e tradeoff between e average roughput and oss rate for singe-ayer muticast, we showed at g s R can be derived rough e concept of convex hu [20]. Using e properties of convex hu, in [15] we proved at g s R is a continuous, piecewise inear, and concave function over R. Thus, we can obtain g s R as foows: g s r i +η i R r i, if R [r i,r i 1, g s R = 2 i N; 41 g s r 2 +η 2 r 1 r 2, if R = r 1, where R π1 = r 1 >r 2 > >r N = R πn.fig.4depicts an exampe for e function g s R. As shown in Fig. 4, wiin each interva [r i,r i 1, g s R is a inear function of R wi e sope equa to η i,andn 1 is equa to e number of such intervas. Note at r i, g s r i N i=1 are actuay e vertices on e upper boundary of e convex hu of e 2-dimensiona point set og1 + γ i,m i og1 + γ i N i=1 see [15]. For e compete procedures to identify g s R gsr nats/s/hz r 5 η 5 R, gs R η 4 5 r η 3 N =6 N =5 η 2 The transmission rate R nats/s/hz Fig. 4. An exampe for e function eg sr against R,whereN =6and γ =1.98, 6.07, 18.71, 29.63, 45.43, and e corresponding time sot aocation poicy, pease refer to our previous work [15]. The above discussions impy at we need to consider ony e transmission poicies yieding g s R, because ony ese poicies can minimize e tota oss for e entire muticast group. Moreover, Eqs suggest at we can focus on reguating e scaar R instead of e N-dimension time-proportion vector t.afterr is determined, we can use Eq. 40 to obtain t. Foowing previous anayses in is section, we formuate probem P 3 to derive e adaptation poicy for muti-ayer video muticast as foows: Probem 3: P 3 L min t,r,z =1 E γ t 42 s.t.: E γ e β z +t R V 0, z 0,, 43 N 1 q E γ t R + z E γ t g s R 0,, 44 L t 1 0, 0 t 1, γ, 45 =1 where R R 1,R 2,...,R L and Eq. 44 is e grouposs-rate constraint equivaent to Eq. 37 for e poicies corresponding to g s R. B. Derivation of e Optima Soution for Muticast Video Notice at Probem P 3 is not convex, because e functions on e eft-hand side of Eqs. 43 and 44 are not convex over t, R, z. However, we show in e foowing at e optima soution can sti be obtained rough Lagrangian dua probem. B.1 Lagrangian Characterization of Probem P 3 The Lagrangian function of P 3, denoted by W, is constructed as W = E γ w 46 Auorized icensed use imited to: Texas A M University. Downoaded on May 12,2010 at 09:25:32 UTC from IEEE Xpore. Restrictions appy.

9 428 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 28, NO. 3, APRIL 2010 where L L L w t + ψ γ t 1 + λ e β z +t R V =1 =1 =1 =1 L + φ N 1 q t R + z t g s R. 47 In Eq. 47, ψ γ 0, φ 0, and λ 0 are e Lagrangian mutipiers associated wi e constraints given by Eqs. 45, 44, and 43, respectivey. The Lagrangian dua function, denoted by U, is en determined by Uλ, φ,ψ γ min t,z,r W = E γ uλ, φ,ψ γ, 48 where φ φ 1,φ 2,...,φ L and uλ, φ,ψ γ min t,z,r w. 49 It is cear at uλ, φ,ψ γ is a concave function over λ, φ,ψ γ,andsoisuλ, φ,ψ γ Moreover, e Lagrange dua probem is defined as: P 3-Dua : U Uλ, φ,ψ γ= max λ,φ,ψ γ Uλ, φ,ψ γ, 50 where λ, φ,ψγ is e maximizer. We en sove for e optima adaptation strategy to P 3 rough e dua probem. If e optima soution to P 3 exists, we wi show ater at ere is no duaity gap between e prima probem P 3 and e dua probem P 3-Dua. As a resut, e optima soution to P 1 must minimize e Lagrangian function W under e optima Lagrangian mutipiers λ, φ,ψγ. B.2 Derivation of e Lagrangian Dua Function Uλ, φ,ψ γ =E γ uλ, φ,ψγ Since g s R is nondifferentiabe at some R as shown in Fig. 4, w is aso nondifferentiabe at some R. Aternativey, we need to use e subgradient and subdifferentia [19] instead of gradient to derive e minimizer to Eq. 49, which is denoted by t, z, R. Definition 1: Consider a convex function h : D R, where R denotes e set of rea numbers and D R n is a convex set. Then, an n 1 vector ξ, forξ R n, is caed a subgradient [19] at d Dif hd hd+ξ T d d for a d D,where T represents e transpose. The coection of subgradients at d form a set caed e subdifferentia [19] of h at d, denoted by hd. Ifh is differentiabe at d, e subgradient at d is unique and becomes e gradient. Moreover, e sufficient and necessary condition at d minimizes hd is at 0 hd.whenh is a concave function, e subgradient and subdifferentia at hd is defined in e simiar way as e convex case, except at e required inequaity becomes hd hd+ξ τ d d. Then, using Eq. 40 and Definition 1, we obtain [ ηn, ], if r = r N ; ηi, if ri <r<r i 1, 2 i N; g s r = [ ] 51 ηi,η i+1, if r = ri, 2 i N 1; [ ],η1, if r = r1. Appying Eq. 47 into Definition 1, we get e subdifferentia of w w.r.t. R, denoted by w R,as: w R = y y = t φ N 1 q λ β e β z +t R φ x, x g s R,, γ. 52 It is cear at w is differentiabe w.r.t. t and R.Takinge derivative of w w.r.t. t and z, respectivey, we get w =1+ψ γ λ β R e β z +t R t w z φ g s R +φ N 1 q R,, γ; 53 = φ N 1 q λ β e β z +t R,, γ. 54 Ceary, e minimization of w can be performed separatey for each video ayer. Now consider e video ayer. Since e function w is not convex over e 3-tupe t,z,r,e equations w/t =0, w/z =0,and0 w R are ony e necessary conditions for t,z,r.however,ift is given, w becomes a convex function over e 2-tupe z,r.using is property, we can decompose e minimization of w into severa easier sub-probems. Appying e above principe, we discuss e cases wi e fixed t = 0 and t > 0, respectivey, as foows. 1 t = 0: The variabe R vanishes in Eq. 47 when t =0. Then, we ony need to find e minimizer z.by soving w/ z =0under e condition z 0, weget ] + z [ = 1 φ N 1 q β og λ β t > 0: We jointy sove w/ z =0and 0 w R under e condition z 0 and R 0, and en get e minimizer, which is summarized in Eqs as foows: if R > R, en R = R; z = if R R, en R = R ; z = 0, [ 1 β og where R is e unique soution to φ N 1 q ]+ λ β t R ; w R z =0 58 under e given t,and R arg max gs r. 59 r The detaied derivations for Eqs. 56 and 57 are omitted due to ack of space, but are provided onine in [24]. Note at R depends ony on gs r, but not on t. Then, rough Eqs , we can see at wi t > 0, e minimizer must satisfy eier z =0or R = R. Furer note at e above resuts provide not ony e maematica convenience, but aso e insightfu observations for e adaptive muticast transmission. For muticast, zero oss can be achieved ony Auorized icensed use imited to: Texas A M University. Downoaded on May 12,2010 at 09:25:32 UTC from IEEE Xpore. Restrictions appy.

10 DU and ZHANG: STATISTICAL QOS PROVISIONINGS FOR WIRELESS UNICAST/MULTICAST OF MULTI-LAYER VIDEO STREAMS 429 when setting transmission rate R = R πn, which is determined by e worst-case SNR over a muticast receivers. The higher e transmission rate or e higher e drop rate we use, e higher e oss rate we get observed from Eq. 38. Therefore, when not vioating e statistica deay QoS guarantees, we need to choose e transmission rate R and e drop rate z as sma as possibe. Moreover, R and z need to be jointy derived for performance optimization. Foowing e above strategies, we first derive R which optimizes e system performance equivaenty, minimizes e Lagrangian function given e zero drop rate. However, if R > R, we can see at e achieved sum rate g s R over a muticast receivers under R = R decreases when R increases, as depicted in Fig. 4. When is happens, we need to set R = R and appy e nonzero drop rate to avoid e degradation of g s R whie supporting e satisfied service rate. Based on e above resuts for t =0and t > 0, e minimizer t,r,z at e video ayer must fa into one of e foowing ree Sub-domains: Sub-domain 1: t =0, R 0, z 0; Sub-domain 2: t 0, R = R, z 0; 60 Sub-domain 3: t 0, R 0, z =0. In Eq. 60, Sub-domain 1 is associated wi e case of t =0. For e case wi t > 0, Sub-domains 2 and 3 correspond to e conditions R R and R < R, respectivey. In order to get e minimizer t,r,z of w, we can first find e minimizer wiin each Sub-domain, which is denoted by t j,r j,z j, j =1, 2, 3. After identifying e minimizers of each Sub-domain, t,r,z can en be obtained rough t,r,z = t j,r j,z j, 61 where j =arg min j=1,2,3 w t,r,z = t j,r j,z j. In Sub-domains 1, 2, and 3, e variabes t, R, and z are fixed, respectivey, impying at ere are ony two optimization variabes in each Sub-domain. Therefore, e minimization probem wiin each Sub-domain becomes tractabe. For Sub-domain 1, e minimizer 0,R 1,z 1 is given in Eq. 55. For Sub-domain 2, since R is fixed, deriving e minimizer t 2,R 2,z 2 is equivaent to soving a convex probem. For Sub-domain 3, e optimization probem can be readiy soved by appying e piecewise inear property of gr. The detaied derivations for t 2,R 2,z 2 and t 3,R 3,z 3 are omitted due to ack of space, but are provided onine in [24]. B.3. The Optima Soution to P 3. In Section VI-B.2, we have obtained e minimizer t, z, R for w. Then, based on e optimization eory [19], e necessary and sufficient conditions for zero duaity gap are as foows: ere exists e feasibe poicy t, z, R φγ=φ γ,λ =λ,φ =φ,,γ such at L ψγ =1 t 1 =0,, γ; λ Eγ e β z +t R V =0, ; φ E γ N 1 q t R + z t g sr =0, ; ψγ 0, λ 0, φ Then, e optima poicy to P 3 is given by t, z, R φγ=φ γ,λ =λ,φ =φ,,γ. 63 We can sove for e optima Lagrangian mutipiers by using e simiar arguments in e proof of Theorem 1. Specificay, for each channe reaization if L =1 t ψ γ=0 1, wehave ψγ =0;oerwise,ψγ is e unique soution to L =1 t =1. Moreover, φ L =1 and λ L =1 wi be seected such at = hods for constraints given in Eqs Furermore, we can design e adaptive tracking meod simiar to probem P 1 to examine e existence of e optima soution and find e optima Lagrangian mutipiers. Note at under e above optima soution, different γ n N n=1, which have e same ordered permutation, wi generate e same function g s R defined by Eq. 40 and us e same adaptation poicy. Then, since γ n s are i.i.d. as assumed in Section II, is poicy wi benefit a receivers eveny, impying q,0 = q,1 = q,2 = = q,n = q. Therefore, e origina oss-rate constraint is not vioated for a muticast receivers. Moreover, since e group-oss-rate constraint given by Eq. 44 in probem P 3 is a reaxed version of e origina oss-rate constraint for each muticast receiver given by Eq. 36, e optima soution to probem P 3 is aso optima even if we repace Eq. 44 by using e origina oss-rate constraint given in Eq. 36. VII. SIMULATION EVALUATIONS We use simuation experiments to evauate e performances of our proposed optima adaptive transmission schemes and to investigate e impact of QoS requirements on resource aocations. Note at e metric deay investigated/simuated in simuations represents e queueing deay, as addressed previousy in Section III-B for e framework of is paper. In simuations, we set e signa bandwid B and timeframe eng T equa to Hz and 10 ms, respectivey. The arriva video stream incudes two ayers, bo of which have constant arriva rates, where A 1 [k] = 250 Kbps and A 2 [k] = 150 Kbps. Then, e effective bandwids of A 1 [k] and A 2 [k] are determined by A 1 θ 1 = nats/frame A 2 θ 2 = nats/frame, respectivey. The vaues of θ 1 and θ 2 can be derived from soving Eq. 7, depending on e QoS requirements specified by D and P, =1, 2,...,L. The wireess channe foows e Rayeigh fading mode and we denote e average SNR by γ. Fig.5 pots e iterative on-ine tracking of e optima Lagrangian mutipiers λ s based on e meod used in Section V-A wi ɛ =0.01 and α =0.02. As shown in Fig. 5, e Lagrangian mutipiers quicky converge to e optima vaue and osciate sighty wiin e sma dynamic ranges, which demonstrates e effectiveness of our tracking meod. Auorized icensed use imited to: Texas A M University. Downoaded on May 12,2010 at 09:25:32 UTC from IEEE Xpore. Restrictions appy.

11 430 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 28, NO. 3, APRIL 2010 The Lagrangian mutipier λ Tracking λ 1 Tracking e optima λ 1 = Tracking e optima λ 2 = CCDF Wi oss toerance Modeing resuts Our scheme Fixed aocation CCDF Modeing resuts Our scheme Fixed aocation Video ayer 1 Video ayer 2 Wi oss toerance Tracking λ Time frame index x Deay d ms Deay d ms Fig. 5. Iustration of tracking e optima Lagrangian mutipier λ for unicast wi zero oss, where e average SNR is γ =10dB, e required deay bound is P =10 4, and e required reshod for e deay-bound vioation probabiity is D = 250 ms. Fig. 7. The compementary cumuative distribution function PrD >d of e queueing deay for e unicast scenario wi oss toerance for video ayer 1 and video ayer 2, respectivey, where γ =15dB, P =10 4, D = 250 ms, and q 1,q2 =0.01, Modeing resuts Adaptive scheme Fixed aocation 10 0 Modeing resuts Adaptive scheme Fixed aocation 10 0 Modeing resuts Adaptive scheme FDP scheme 10 0 Modeing resuts Adaptive scheme FDP scheme CCDF 10 2 Video ayer 1 CCDF 10 2 Video ayer 2 CCDF 10 2 Video ayer 1 CCDF 10 2 Video ayer Wi zero oss 10 3 Wi zero oss 10 3 Wi oss toerance 10 3 Wi oss toerance Deay d ms Deay d ms Deay d ms Deay d ms Fig. 6. The compementary cumuative distribution function CCDF PrD >d of e queueing deay for e unicast scenario wi zero oss for video ayer 1 and video ayer 2, respectivey, where γ =15dB, P =10 4, and e required deay-bound is D = 250 ms. We aso investigate some straightforward time-sot aocation schemes as e baseine schemes for comparative anayses. We wi compare e average resource consumption between our derived optima schemes and ese baseine schemes under e same QoS satisfactions. 1 Fixed time-sot aocation for unicast wiout oss: This scheme uses constant time-sot eng t [k] =t, k =1, 2,..., in a fading states. The normaized transmission rate is set to R =og1+γ nats/s/hz for e video ayer. The parameters t, =1, 2, are seected such at e effective capacity C θ of e video ayer s service process is just equa to C : C θ = 1 og E e θ t BT og1+γ = C, 64 θ Fig. 8. The compementary cumuative distribution function PrD >d of e queueing deay for muticast scenario wi oss toerance for video ayer 1 and video ayer 2, respectivey, where N =20receivers, γ =20dB, q 1,q2 =0.01, 0.05, P =10 4,andD = 250 ms. where C = A θ and = 1, 2,...,L. We can obtain e unique t s by numericay soving e above equation. If we get L =1 t > 1, is scheme cannot guarantee e QoS requirements under current channe conditions, even using up a time-sot resources. 2 Fixed time-sot aocation for unicast wi oss toerance: This scheme uses bo e constant time-sot eng t [k] =t and e constant per-drop rate z [k] =z in a fading states. The normaized transmission rate is aso set to R = og1 + γ nats/s/hz for e video ayer. The parameters t and z can be obtained by soving C θ = 1 og E e θ t BT og1+γ+btz =C 65 θ and q = q for a video ayers, where =1, 2,...,L. Auorized icensed use imited to: Texas A M University. Downoaded on May 12,2010 at 09:25:32 UTC from IEEE Xpore. Restrictions appy.

12 DU and ZHANG: STATISTICAL QOS PROVISIONINGS FOR WIRELESS UNICAST/MULTICAST OF MULTI-LAYER VIDEO STREAMS Normazied time sot resources Muticast, 6 receivers Unicast wi zero oss, optima scheme Unicast wi zero oss, fixed aocation Unicast wi oss toerance, optima scheme Unicast wi oss toerance, fixed aocation Muticast wi oss toerance, optima scheme Muticast wi oss toerance, FDP scheme Unicast Normazied time sot resources Muticast, 6 receivers Unicast wi zero oss, optima scheme Unicast wi zero oss, fixed aocation Unicast wi oss toerance, optima scheme Unicast wi oss toerance, fixed aocation Muticast wi oss toerance, optima scheme Muticast wi oss toerance, FDP scheme Unicast Deay bound requirement ms n PL o Fig. 9. The normaized time-sot resource consumption E γ =1 t versus deay-bound requirement D,whereγ =15dB, P =10 4,and q 1,q2 =0.01, Threshod for deay bound voation probabiity n PL o Fig. 10. The normaized time-sot resource consumption E γ =1 t versus e reshod P for e deay-bound vioation probabiity, where γ =15dB, D = 250 ms, and q 1,q2 =0.01, Fixed dominating position scheme for muticast wi oss toerance: The fixed dominating position FDP scheme aways sets R = og1 + γ πi nats/s/hz, where γ πi denotes e i argest instantaneous SNR among a muticast receivers. The index i is fixed at i = N 1 q such at e oss-rate QoS is not vioated. Moreover, e FDP scheme aso adopts e constant time-sot eng t [k] =t and e constant per-drop rate z [k] =z, which can be obtained by soving C θ = 1 og E e θ t BT og1+γ πi +BTz =C θ 66 and q,0 = q for a video ayers, where =1, 2,...,L. Figures 6, 7, and 8 depict e compementary cumuative distribution function CCDF of e queueing deay, i.e., e probabiity PrD >d given a reshod d, for unicast wi zero oss, unicast wi oss toerance, and muticast wi oss toerance, respectivey. We can observe from Figs. 6-8 at e CCDF s of a schemes agree we wi e modeing resuts see Eqs. 7-8 at each video ayer, where e deaybound vioation probabiity decreases exponentiay against e deay bound. Moreover, for e required deay bound D = 250 ms, e vioation probabiity of a schemes can be upper-bounded by e targeted P =10 4 for each video ayer, which demonstrates e vaidity of a schemes in terms of statistica deay-qos guarantees. Having shown at a schemes can meet e same QoS requirements, we en focus on e performance of e average time-sot consumption. Figures 9 and 10 iustrate e impact of deay-bound D and its vioation probabiity P on e resource consumption, respectivey. As shown in Figs. 9 and 10, eier smaer D or P wi cause more resource consumption, which is expected because e smaer D or P impies e more stringent deay QoS requirement. Moreover, under various QoS conditions, our proposed optima schemes aways use much ess wireess resources an e baseine schemes. For muticast services, our derived optima scheme consumes at east 15% of tota resources ess an e FDP scheme. For unicast services, more resources can be saved by using e optima scheme when deay QoS becomes ooser, whie ess resources are saved under e more stringent QoS constraints. After demonstrating e superiority of our proposed optima schemes over e baseine schemes, Fig. 11a pots e average time-sot consumption versus e average SNR for muti-ayer video unicast and muticast. We observe from Fig. 11a at under e same channe conditions, video unicast uses much ess time-sot resources an muticast. When e average SNR is reativey ow around 7-8 db, video unicast does not need to consume a avaiabe timesot resources. In contrast, video muticast amost uses up a resources even wi γ = 13.5 db for e 6-receiver case. For e 10-receiver case, e average SNR needs to be arger an 15 db to provide e QoS-guaranteed muticast services. The above observations refect e key chaenges on wireess muticast. In wireess broadcast channes, since a receivers can hear e sender, it is idea at ony one copy of data is transmitted such at sizabe resources can be saved. However, due to e heterogeneous fading channes across muticast receivers, e transmission rate has to be imited wiin e reativey ow range to avoid too much data oss for receivers wi poorer instantaneous channe quaities. As a resut, more time-sot resources are consumed to meet e QoS requirements. In addition, more muticast receivers resut in more resource consumption, as depicted in Fig. 11a. But note at aough e wireess muticast faces many chaenges, it sti uses much ess wireess resources an e strategy which uses mutipe unicast inks to impement wireess muticast. For exampe, if using mutipe unicast inks to impement muticast, we need e time-sot resources at east N times as much as e resource consumption for a unicast ink. Ceary, for environments simuated in Fig. 11a, even wi γ = 18 db, we sti do not have enough resources for such a unicast-based muticast scheme wi just 6 receivers. Fig. 11b shows e resource consumption for each video ayer. We can see at video ayer 1 requires more resources Auorized icensed use imited to: Texas A M University. Downoaded on May 12,2010 at 09:25:32 UTC from IEEE Xpore. Restrictions appy.

13 432 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 28, NO. 3, APRIL 2010 Normazied time sot resources Upper bound of time sot resources Unicast Muticast 0.5 Unicast wi zero oss Unicast wi oss toerance 0.4 Muticast wi oss toerance, 6 receivers Muticast wi oss toerance, 10 receivers Average SNR db Normazied time sot resources Layer 2 Layer 1 Unicast wi zero oss, Layer 1 Unicast wi zero oss, Layer 2 Unicast wi oss toerance, Layer 1 Unicast wi oss toerance, Layer 2 Muticast wi oss toerance, N = 6, Layer 1 Muticast wi oss toerance, N = 6, Layer Average SNR db a b n PL o Fig. 11. a The normaized time-sot resource consumption E γ =1 t versus γ, wherep =10 4, D = 250 ms, b E γ t for each video ayer versus γ, wherep =10 4, D = 250 ms, q 1,q2 =0.01, q 1,q2 =0.01, an video ayer 2, which is because in our settings e traffic oad of ayer 1 is higher and e oss-rate QoS of ayer 1 is more stringent. Furermore, in muticast e difference of resource consumption between e two video ayers is arger an e difference in unicast. Figure 12 shows e impact from oss-rate constraints on video muticast. As shown in Fig. 12, even sighty increasing q can significanty reduce e tota consumed wireess resources. This is because e higher oss-toerance eve wi enabe arger muticast transmission rate and us consume ess time-sot resources. The above observations suggest at ere exists a tradeoff between oss-rate contro at e physica ayer and error recovery at e upper protoco ayers. As mentioned previousy, e oss-rate q depends argey on e capabiity of erasure-correction codes used at upper protoco ayers, especiay for muticast services. Thus, Fig. 12 suggests at using more redundancy for forward error-contro at upper protoco ayers can effectivey decrease e tota wireessresource consumption wi QoS guarantees, whie enabing e repair of more data osses at e physica ayer. VIII. CONCLUSIONS We proposed a framework to mode e wireess transmission of muti-ayer video stream wi statistica deay QoS guarantees. A separate queue is maintained for each video ayer and e same statistica deay QoS-requirement needs to be satisfied by a video ayers, where e statistica deay QoS is characterized by e deay-bound and its corresponding vioation probabiity rough e effective capacity bandwid/capacity eory. Under e proposed framework, we derived a set of optima rate adaptation and time-sot aocation schemes for video unicast/muticast wi and/or wiout oss toerance, which minimizes e time-sot resource consumption. We aso conducted extensive simuation experiments to demonstrate e impact of statistica QoS provisionings on wireess resource aocations by using our derived optima adaptive transmission schemes. Average SNR db Nomaized time sot resources q 1 =0.01, q2 =0.05 q 1 =0.02, q2 =0.05 q 1 =0.03, q2 =0.06 n PL o Fig. 12. The normaized time-sot resource consumption E γ =1 t versus γ for muticast wi N =6, P =10 4,andD = 250 ms. REFERENCES [1] J. Shin, J.-W. Kim, C.-C.J. Kuo, Quaity-of-service mapping mechanism for packet video indifferentiated services network, IEEE Trans. Mutimedia, vo. 3, no. 2, pp , Jun [2] H. Schwarz, D. Marpe, and T. Wiegand, Overview of e scaabe video coding extension of e H.264/AVC standard, IEEE Trans. Circuits and Systems for Video Technoogy, vo. 17, no. 9, pp , Sep [3] S. McCanne, M. Vetteri, and V. Jacobson, Low-compexity video coding for receiver-driven ayered muticast, IEEE J. Se. Areas Commun., vo. 15, no. 6, pp , Aug [4] J. Viaon, P. Cuenca, L. L. Orozco-Barbosa, Y. Seok, and T. Turetti, Cross-ayer architecture for adaptive video muticast streaming over mutirate wireess LANs,, IEEE J. Se. Area. Commun., vo. 25, no. 4, pp , May [5] X. Zhang and K. G. Shin, D. Saha, and D. Kandur, Scaabe fow contro for muticast ABR services in ATM networks, IEEE/ACM Trans. on Netw., vo. 10, no. 1, pp , Feb [6] X. Zhang and K. G. Shin, Deay anaysis of feedback-synchronization signaing for muticast fow contro, IEEE/ACM Trans. on Netw., vo. 11, no.3, pp , Jun [7] X. Zhang and K. G. Shin, Markov-chain modeing for muticast signaing deay anaysis, IEEE/ACM Trans. on Netw., vo. 12, no. 4, pp , Aug Auorized icensed use imited to: Texas A M University. Downoaded on May 12,2010 at 09:25:32 UTC from IEEE Xpore. Restrictions appy.

14 DU and ZHANG: STATISTICAL QOS PROVISIONINGS FOR WIRELESS UNICAST/MULTICAST OF MULTI-LAYER VIDEO STREAMS 433 [8] X. Zhang and Q. Du, Cross-ayer modeing for QoS-driven mutimedia muticast/broadcast over fading channes, IEEE Commun. Mag., vo. 45, no. 8, pp , Aug [9] C.-S. Chang, Stabiity, queue eng, and deay of deterministic and stochastic queueing networks, IEEE Trans. Auto. Contro, vo 39, no. 5, pp , May [10] C.-S. Chang, Performance Guarantees in Communication Networks, Springer-Verag London, [11] D. Wu and R. Negi, Effective capacity: A wireess ink mode for support of Quaity of Service, IEEE Trans. Wireess Commun., vo. 2, no. 4, pp , Ju [12] X. Zhang, J. Tang, H.-H. Chen, S. Ci, and M. Guizni, Cross-ayer-based modeing for quaity of service guarantees in mobie wireess networks, IEEE Commun. Mag., pp , Jan [13] J. Tang and X. Zhang, Quaity-of-service driven power and rate adaptation over wireess inks, IEEE Trans. Wireess Commun., vo. 6, no. 8, pp , Aug [14] Q. Du and X. Zhang, Effective capacity of superposition coding based mobie muticast in wireess networks, in Proc. IEEE Internationa Conference on Commun., ICC 09, Dresden, Germany, Jun [15] Q. Du and X. Zhang, Cross-ayer design based rate contro for mobie muticast in ceuar networks, in Proc. IEEE GLOBECOM 2007, Washington DC, USA, Nov , 2007, pp [16] J. Nonenmacher, E. Biersack, and D. Towsey, Parity-based oss recovery for reiabe muticast transmission, IEEE/ACM Trans. Networking, vo. 6, no. 4, pp , Aug [17] J. W. Byers, M. Luby, and M. Mitzenmacher, A digita Fountain approach to asynchronous reiabe muticast. IEEE J. Seect. Areas Commun., vo. 20, no. 8, pp , Oct [18] X. Zhang and Q. Du, Adaptive Low-Compexity Erasure-Correcting Code Based Protocos for QoS-Driven Mobie Muticast Services Over Wireess Networks, IEEE Trans. Veh. Techno., vo. 55, no. 5, pp , Sep [19] M. S. Bazaraa, H. D. Sherai, and C. M. Shetty, Noninear Programming: Theory and Agorims, 3rd ed., John Wiey & Sons, Inc., [20] S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, [21] Stephen Boyd, Lin Xiao, and Amir Mutapcic, Subgradient Meods, meod.pdf. [22] G. L. Choudhury, D. M. Lucantoni, and W. Whitt, Squeezing e most out of ATM, IEEE Trans. Commun., vo. 44, pp , Feb [23] T.H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Agorims, 2nd ed. Cambridge, Mass. and New York: MIT Press and McGraw-Hi, [24] Q. Du and X. Zhang, Statistica QoS provisionings for wireess unicast/muticast of muti-ayer video streams, Networking and Information Systems Labs., Dept. Eectr. and Comput. Eng., Texas A&M Univ., Coege Station, Tech. Rep. [Onine.] Avaiabe: xizhang/papers/muti ayer video.pdf. Qinghe Du [S 09] received B.S. and M.S. from Xian Jiaotong University, and is currenty working towards to e Ph.D. degree under supervising of Prof. Xi Zhang in Networking and Information Systems Laboratory, Department of Eectrica and Computer Engineering at Texas A&M University. His research interests incude mobie wireess communications and networks wi emphasis on mobie muticast, statistica QoS provisioning, QoSdriven resource aocations, cognitive radio techniques, and cross-ayer design over wireess networks. His work co-auored wi his Ph.D. advisor Prof. Xi Zhang received e Best Paper Award in e IEEE Gobecom 2007 for e paper Cross- Layer Design Based Rate Contro for Mobie Muticast in Ceuar Networks. He has pubished mutipe papers in IEEE Transactions, IEEE J-SAC, IEEE Comm Magazine, IEEE INFOCOM, IEEE Gobecom, IEEE ICC, etc. Xi Zhang [S 89-SM 98] received e B.S. and M.S. degrees from Xidian University, Xi an, China, e M.S. degree from Lehigh University, Beehem, PA, a in eectrica engineering and computer science, and e Ph.D. degree in eectrica engineering and computer science Eectrica Engineering- Systems from The University of Michigan, Ann Arbor. He is currenty an Associate Professor and e Founding Director of e Networking and Information Systems Laboratory, Department of Eectrica and Computer Engineering, Texas A&M University, Coege Station. He was an Assistant Professor and e Founding Director of e Division of Computer Systems Engineering, Department of Eectrica Engineering and Computer Science, Beijing Information Technoogy Engineering Institute, China, from 1984 to He was a Research Feow wi e Schoo of Eectrica Engineering, University of Technoogy, Sydney, Austraia, and e Department of Eectrica and Computer Engineering, James Cook University, Austraia, under a Feowship from e Chinese Nationa Commission of Education. He worked as a Summer Intern wi e Networks and Distributed Systems Research Department, AT&T Be Laboratories, Murray His, NJ, and wi AT&T Laboratories Research, Forham Park, NJ, in He has pubished more an 170 research papers in e areas of wireess networks and communications systems, mobie computing, network protoco design and modeing, statistica communications, random signa processing, information eory, and contro eory and systems. Prof. Zhang received e U.S. Nationa Science Foundation CAREER Award in 2004 for his research in e areas of mobie wireess and muticast networking and systems. He received e Best Paper Awards in e IEEE Gobecom 2009 and e IEEE Gobecom 2007, respectivey. He aso received e TEES Seect Young Facuty Award for Exceence in Research Performance from e Dwight Look Coege of Engineering at Texas A&M University, Coege Station, in He is currenty serving as an Editor for e IEEE TRANSACTIONS ON COMMUNICATIONS, an Editor for e IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, an Associate Editor for e IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, a Guest Editor for e IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS for e specia issue on wireess video transmissions, an Associate Editor for e IEEE COMMUNICATIONS LETTERS, a Guest Editor for e IEEE WIRELESS COMMUNICATIONS MAGAZINE for e specia issue on next generation of CDMA versus OFDMA for 4G wireess appications, an Editor for e JOHN WILEY S JOURNAL ON WIRELESS COMMUNICATIONS AND MOBILE COMPUTING, an Editor for e JOURNAL OF COMPUTER SYSTEMS, NETWORKING, AND COMMUNICATIONS, an Associate Editor for e JOHN WILEY S JOURNAL ON SECURITY AND COMMUNICATIONS NETWORKS, an Area Editor for e ELSEVIER JOURNAL ON COMPUTER COMMUNICATIONS, and a Guest Editor for JOHN WILEY S JOURNAL ON WIRELESS COMMUNICATIONS AND MOBILE COMPUTING for e specia issue on next generation wireess communications and mobie computing. He has frequenty served as e Paneist on e U.S. Nationa Science Foundation Research-Proposa Review Panes. He is serving or has served as e Technica Program Committee TPC Chair for IEEE Gobecom 2011, TPC Vice-Chair for IEEE INFOCOM 2010, TPC Co-Chair for IEEE INFOCOM 2009 Mini-Conference, TPC Co-Chair for IEEE Gobecom Wireess Communications Symposium, TPC Co-Chair for e IEEE ICC Information and Network Security Symposium, Symposium Chair for IEEE/ACM Internationa Cross-Layer Optimized Wireess Networks Symposium 2006, 2007, and 2008, respectivey, e TPC Chair for IEEE/ACM IWCMC 2006, 2007, and 2008, respectivey, e Demo/Poster Chair for IEEE INFOCOM 2008, e Student Trave Grants Co-Chair for IEEE INFOCOM 2007, e Genera Chair for ACM QShine 2010, e Pane Co-Chair for IEEE ICCCN 2007, e Poster Chair for IEEE/ACM MSWiM 2007 and IEEE QShine 2006, Executive Committee Co-Chair for QShine, e Pubicity Chair for IEEE/ACM QShine 2007 and IEEE WireessCom 2005, and e Paneist on e Cross-Layer Optimized Wireess Networks and Mutimedia Communications at IEEE ICCCN 2007 and WiFi-Hotspots/WLAN and QoS Pane at IEEE QShine He has served as e TPC members for more an 70 IEEE/ACM conferences, incuding IEEE INFOCOM, IEEE Gobecom, IEEE ICC, IEEE WCNC, IEEE VTC, IEEE/ACM QShine, IEEE WoWMoM, IEEE ICCCN, etc. Prof. Zhang is a Senior Member of e IEEE and a Member of e Association for Computing Machinery ACM. Auorized icensed use imited to: Texas A M University. Downoaded on May 12,2010 at 09:25:32 UTC from IEEE Xpore. Restrictions appy.