Distributed scheduling scheme for video streaming over multi-channel multi-radio multi-hop wireless networks

Transcription

1 Distributed scheduing scheme for video streaming over muti-channe muti-radio muti-hop wireess networks Liang Zhou, Xinbing Wang, Wei Tu, Gabrie-Miro Muntean, Benoit Geer To cite this version: Liang Zhou, Xinbing Wang, Wei Tu, Gabrie-Miro Muntean, Benoit Geer. Distributed scheduing scheme for video streaming over muti-channe muti-radio muti-hop wireess networks. IEEE Journa on Seected Areas in Communications, Institute of Eectrica and Eectronics Engineers, 2010, 28 (3), pp < /JSAC >. <ha > HAL Id: ha Submitted on 6 Nov 2015 HAL is a muti-discipinary open access archive for the deposit and dissemination of scientific research documents, whether they are pubished or not. The documents may come from teaching and research institutions in France or abroad, or from pubic or private research centers. L archive ouverte puridiscipinaire HAL, est destinée au dépôt et à a diffusion de documents scientifiques de niveau recherche, pubiés ou non, émanant des étabissements d enseignement et de recherche français ou étrangers, des aboratoires pubics ou privés.

2 1 Distributed Scheduing Scheme for Video Streaming over Muti-Channe Muti-Radio Muti-Hop Wireess Networks Liang Zhou, Xinbing Wang, Wei Tu, Gabrie-Miro Muntean, and Benoit Geer Abstract An important issue of supporting muti-user video streaming over wireess networks is how to optimize the systematic scheduing by inteigenty utiizing the avaiabe network resources whie, at the same time, to meet each video s Quaity of Service (QoS) requirement. In this work, we study the probem of video steaming over muti-channe muti-radio muti-hop wireess networks, and deveop fuy distributed scheduing schemes with the goas of minimizing the video distortion and achieving certain fairness. We first construct a genera distortion mode according to the network s transmission mechanism, as we as video s rate-distortion characteristics. Then, we formuate the scheduing as a convex optimization probem, and propose a distributed soution by joint considering channe assignment, rate aocation, and routing. Specificay, each stream strikes a baance between the sefish motivation of minimizing video distortion and the goba performance of minimizing network congestions. Furthermore, we extend the proposed scheduing scheme by addressing the fairness probem. Unike prior works that target at bandwidth or demand fair, we propose a media-aware distortion-fairness strategy which is aware of the characteristics of video frames and ensures max-min distortion-fairness sharing among video streams. We provide extensive simuation resuts which demonstrate the effectiveness of our proposed schemes. Manuscript received March 1, 2009; revised October 20, This work is supported by NSF China (No , ), and Shanghai Innovation Key Project (No ). L. Zhou is both with the Lab. UEI, ENSTA-ParisTech, Paris, France and the Eectronic Engineering Department, Shanghai Jiao Tong University, Shanghai, China (emai: iang.zhou@ieee.org); X. Wang is with the Eectronic Engineering Department, Shanghai Jiao Tong University, Shanghai, China (emai: xwang8@sjtu.edu.cn); W. Tu is with the Nokia Siemens Networks, Shanghai, China (emai: wei.tu@nsn.com); G.-M. Muntean is with the Network Innovations Centre, Dubin City University, Dubin, Ireand (emai: munteang@eeng.dcu.ie); B. Geer is with the Lab. UEI, ENSTA-ParisTech, Paris, France (emai: benoit.geer@ensta.fr).

3 2 Index Terms muti-channe muti-radio; video transmission; distributed scheduing; QoS; fairness. I. INTRODUCTION With the motivation of improving performance of muti-hop wireess networks, in the ast few years great attention has been devoted to the networks where each node is provided with mutipe radio interfaces and can operate on mutipe channes [1] [8]. The new degree of freedom has been proved to potentiay aow for increased capacity with respect to singe-channe singeinterface networks [3], [4]. This is motivated by current WLAN standards (i.e., IEEE ) where the entire frequency band is divided into mutipe channes, and each radio can ony access one channe at a time. Therefore, if each network node has mutipe radio interfaces, it can then utiize a arger amount of bandwidth, and hence achieve high system capacity [2], [3]. Such an improved bandwidth and capacity network poses a bright appication foreground for arge data video communications. However, there are huge and different kinds of videos streaming from different users which may infuence each other and thus, it is essentia to enforce a scheduing poicy designed for suitabe video metrics and efficient network utiization, preferaby in a distributed manner. Indeed, the probem of video scheduing over muti-channe muti-radio networks is, compared to traditiona data communications in wireess muti-hop networks, further compicated by the heterogeneity in both the network conditions and the appication contents, incuding i) channe-assignment: what are the set of channes that each ink shoud be operated on? ii) rate aocation: how to aocate the appropriate rate to the given channes and inks? iii) routing: how to seect the potentia channes and inks that minimize tota video distortion? and iv) fairness: how to provide a distortion-fairness for muti-user streaming different video cips concurrenty? These four probems interact with each other, and thus form a chaenging cross-ayer contro probem across the MAC ayer and the appication ayer. In this work, our objective is to propose a distributed video scheduing scheme in muti-channe muti-radio networks so as to minimize the tota video s distortion and achieve a certain fairness. We first identify an objective function that baances the goas of the users and network operators, and then expore how to construct a stabe, distributed, dynamic and fair system that optimizes for this objective. For ease of exposition, in the rest of the paper whenever there is no source of

4 3 confusion, we wi use of the term scheduing to refer to the combined operation of channe assignment, rate aocation and routing. Athough some scheduing protocos can be obtained via extending the current agorithms in [1], [2], [5] that are known to achieve the maximum system capacity for muti-channe muti-radio networks. However, these works competey ignore the transmission content. In addition, these works target at eastic data transmission, where users do not have stringent deadine constraints. Therefore, due to the characteristics of video content and the deadine requirement of video appications, these soutions may not be optima for deivering muti-user, deay-constrained video appications. This point wi be vaidated by the simuation resuts presented in Section IV of this paper. Recenty, many scheduing schemes have been proposed for video streaming over wireess muti-hop networks ( [11] and [12] provide a good overview). We summarize our contributions and the differences between our work and previous reated works in the foowing. We provide a nove distributed video scheduing scheme in the context of mutichanne muti-radio muti-hop wireess networks. The support for muti-user video streams in this network requires appropriate joint channe assignment, rate contro and muti-path routing measure, ascertaining the reasonabe routes for transmitting each stream and the rate of the video to be deivered over the chosen routes. Different from previous works on video scheduing in singe-channe muti-hop wireess networks [9], [11], [13] in which channe assignment is not a concern, we consider the scheduing probem in the newy emerged networks and propose an efficient assignment agorithm. Moreover, unike conventiona works that consider routing for data traffic over wireess networks [6], [8], [9], we take into account the specific video characteristics in the routing and rate contro scheme. Network congestion is considered in the channe assignment, rate aocation and routing metric, to meet the stringent deay requirement for video transmission. In addition, each video s rate-distortion characteristic is aso incorporated in the joint routing and rate contro procedure to provide mutipe streams with various video contents. To the best of our knowedge, this work is the first one to consider the video scheduing probem in the newy muti-channe networks. We extend the scheduing scheme by proposing a strategy of media-aware distortionfairness, which is aware of the characteristics of video frames and ensures max-min distortion-fairness sharing among video streams. Every time when we tak about scheduing, fairness must be taken into consideration, as otherwise we wi end up with a serious bias on

5 4 network resource aocation, which has been shown by previous researches [14], [15]. There are existing works on max-min QoS fair sharing, such as [5], [14], [15], [24], [25]. They assume an expicit utiity function of rate and the agorithms are based on the utiity function, not reay based on the video content. The work in [5] is not specificay designed for video and it does not take into account the specia characteristics of video. In addition, the distributed agorithms in [14], [15], [24], [25] may need a ot of iterations and the rate may fuctuate dramaticay such that the video quaity fuctuates and the perceptua quaity may be poor. Different from [14], [15], we do not assume any expicit utiity function, but instead we use the importance of every frame which can be easiy and expicity cacuated [22]. In addition, our scheme is per-stream performance guaranteed. Different from IntServ [16] architecture which aso offers per-stream performance guarantees, our scheme has content awareness which is signaed over both inks and sources. Our work is aso different from DiffServ [17] which manages resources with the granuarity of traffic casses. The rest of the paper is organized as foows. Section II introduces the video distortion mode, and formuates the scheduing as a convex optimization probem. In Section III, we propose a distributed minimum distortion scheduing scheme for video streaming over mutichanne muti-radio networks. Then, some simuation resuts and comparisons are provided for the corresponding scheme in Section IV. We extend the scheduing scheme by addressing the fairness probem, and provide a media-aware distortion-fairness strategy in Section V. Section VI concudes the paper and points to future work. II. PROBLEM FORMULATION For the distortion of wireess video transmission, we empoy an additive mode to capture the tota video distortion as [10], [20], [21], and the overa distortion D a can be obtained by: D a = D comp + D oss, (1) where the distortion introduced by source compression is denoted by D comp, and the additiona distortion caused by packet oss is denoted by D oss. According to [20], D comp can be approximated by: D comp = θ R R 0 + D0, (2)

6 5 where R is the rate of the video stream, θ, R 0 and D 0 are the parameters of the distortion mode which depend on the encoded video sequence as we as on the encoding structure. Likewise, D comp can be modeed by a inear mode reated to the packet oss rate P oss : D oss = αp oss, (3) where α depends on parameters reated to the compressed video sequence [20]. In a bandwidthimited network, this combined oss rate can be further modeed based on the M/G/1 queuing mode. In this case, the deay distribution of packets over a muti-hop network is exponentia [9], [21]: P r{deay > T } = e λt, (4) where P r{ } denotes probabiity, T refects the deay constraint and λ is the arriving rate which is determined by the average deay: λ = 1 E{Deay}. (5) In what foows, we study E{Deay} in the context of a specific wireess network. Consider a muti-channe muti-radio wireess network with N = {1,...n..., N} nodes, L = {1,..., L} inks, N f non-overapping frequency channes and each node n N is equipped with N n network interfaces. The basic network mode is iustrated in Fig. 1. In order to take into account possibe channe diversity, we denote r c as the rate at ink L can transfer data on channe c, provided that there are no interfering inks transmitting on channe c at the same time. Besides, there are S = {1,...s..., S} users in the system, and each user s S is associated with a source node and a destination node. The traffic from each user may be routed over mutipe aternate paths. Let [M sj] denote the routing matrix, where M sj = 1 if path j of user s empoys ink, M sj = 0, otherwise. Let N(s) denote the number of aternate paths for user s, and F sj the fraction of traffic from user s that is routed to path j. Furthermore, et Q = [Q c ] denote the outcome matrix of the routing scheme, where Q c is the set of non-interfering inks that are chosen to transmit data in channe c. We denote Link Baance Ratio (LBR) [19] u as the fraction of ink input r in and ink output r out for ink : u = r in /r out, (6)

7 6 Link Interface Channe Interface Interface Channe Interface Node Node Fig. 1. Basic network mode. where and r in = N(s) S MsjF sj R s, (7) s=1 r out R s in (7) represents the video rate of user s. j=1 = c: Q c r c, (8) Considering the interference reationship, for each ink, it is assumed that there is a set I of inks that interfere with. That is, if ink and another ink in I are transmitting on the same channe at the same time, neither of the inks can transfer data, which is simiar to the CSMA/CA mechanism used in networks [19], [28]. We assume that each radio can ony tune to one channe at any given time and switch channes dynamicay as in [2], [6]. Therefore, for ink to successfuy communicate on channe c, both the sending and receiving nodes must tune one radio to channe c. In this case, the tota LBR in I can be defined as: u I = I u. (9) Congestion over each wireess ink is measured as the average deay for a packets traversing that ink. Foowing the cassic M/G/1 queuing mode, the average packet deay over a ink is inversey proportiona to the Potentia Transmission Abiity (PTA) [23]. Motivated by [18], we can set PTA of ink as: P T A = r out /(u I γ), (10)

8 7 where γ > 1 is an over-provisioning factor. Therefore, we can mode the average packet deay for path j of user s 1 : E{Deay} = L =1 where ω is the average packet size. Therefore, P r{deay > T } = e λt = exp { (u I γ) r out ω M sj, (11) { T } = exp E{deay} L =1 T (u I γ) ω M sj r out }. (12) Taking into account the average packet oss rate P B due to transmission errors, the tota packet oss rate for path j of user s is then: P oss = P B + (1 P B )P r{deay > T } (13) The tota distortion for path j of user s from packet oss can be expressed as ( D oss = αp oss = α P B + (1 P B ) exp { T } ). (14) L =1 (u I γ) ω M sj r out Based on the previous discussions, we seek a joint optima scheduing outcome M to achieve the overa minimum video distortion: { min D a = M subject to r out = N(s) S θ s ( R s Rs 0 s=1 c: Q c r c j=1 s=1 j=1 } + Ds 0 + D oss ) (15) N(s) S MsjF sj R s = r in, (16) N(s) N(s) 1, F sj 0, F sj = 1, (17) j=1 R s 0, n 1, r c 0, (18) where θ s, R 0 s and D 0 s in (15) are the corresponding parameters for user s S. Intuitivey, the reconstructed video quaity is affected by the user s source rate R s, the channe rate r c, and the routing information [M sj]. As mentioned before, this scheduing probem is impicity couped 1 In practice, congestion may be a more compicated function of rate as predicted by M/G/1 mode. However, this expression can be viewed as an approximation of the average ink deay, capturing the non-inear increase of deay with tota channe time utiization.

9 8 Channe Assignment Congestion Weight Update Avaiabe Channes Joint Rate & Routing Network Congestion Trade-Off Coding Distortion Scheduing Output Interference Network Conditions Rate-Distortion Optima Criterion Fig. 2. Bock diagram of distributed scheduing scheme. with a channe assignment, a rate aocation probem and a muti-path routing probem. In the next section, we propose a distributed agorithm where each source, each ink and each channe jointy sove this scheduing probem through efficient cooperation. III. DISTRIBUTED MINIMUM-DISTORTION SCHEDULING SCHEME The optimization probem defined in (15)-(18) invoves severa network ayers, and we propose a 3-step method to resove this probem. First, we propose a channe assignment agorithm by using convex programming formuation to simpify the goa function, and the constraints paced by nodes, inks, and channes to fix the rate aocation and routing. Our aim is to construct the mapping reationship between the channe assignment and video distortion. Second, we propose a joint rate aocation and muti-path routing agorithm to achieve the trade-off between the coding distortion and network congestion. Third, we propose exact operation steps to provide a distributed minimum-distortion scheduing (DMDS) soution based on channe assignment, rate aocation and muti-path routing computed in the previous two steps. The system diagram of the distributed scheduing scheme is dispayed in Fig. 2. A. Channe Assignment In the processing of channe assignment, we focus on every node to seect optima channes to achieve minimum video distortion. However, it is difficut to define the minimum video distortion in the process of channe assignment. Hence, we map the index of minimum video distortion to optima network congestion 2. Specificay, we present a inear programming (19) 2 As stated previousy, the stream rate is fixed in the process of channe assignment, so D comp is not changed in this process.

10 9 method to obtain approximate soutions of the optima channe assignment. In this formuation, we define (r in r out ) as the factor of network congestion, and the corresponding constraints remain identica to (17) and (18). min L (r in r out ) (19) The sketch of the proposed Channe Assignment Agorithm (CAA) is provided in Tabe I. The optima channe assignment soution A is computed by soving the inear programming equation (19). During the execution of CAA, if there is a ink from node n to node m, then N c records the number of the common channes in nodes n and m, whie N n and N m record the number of avaiabe network interfaces of node n and m, respectivey. N fc represents the number of the required channes which is determined by the corresponding aocated rate in the seected ink and the number of avaiabe network interfaces. Note that the congestion weight of channe c in ink is u c, which can be defined as: When assigning a channe c to ink, r c during the execution of the CAA 3. u c = u /r c. (20) amount of stream is aocated, and can be updated Remark: The purpose of choosing a channe with the smaest congestion weight is to make the channes assigned to spatiay cose nodes as different as possibe [5]. Note that in the repacement procedure of ChanneAssignment (pease see the steps 12, 17, 21, and 35 in Tabe I), we aways use the seected channe to repace the channe with the argest congestion weight. In the worst case, the agorithm wi eventuay stop after passing through a N nodes. B. Joint Rate Aocation and Muti-Path Routing Here, we empoy muti-path routing with the goa of finding mutipe potentia paths to minimize the tota system congestion induced by each video user. Motivated by [21], we consider dividing the tota rate increment of each video stream R s into K (K 1) sma increments (corresponding to N(s) paths described in Section II) such that R s = K k=1 Rk s. Assuming that (k 1) of the K paths and their increments are aready known, path P k s and its increment can 3 r c is initiaized with the capacity of channe c.

11 10 TABLE I CHANNEL ASSIGNMENT ALGORITHM (CAA) 01: Input: 02: A(n) =, n N; 03: Seect the inks one by one in the descending order of their potentia rate aocation vaues; 04: Update A(n) and A(m), n, m N, L; 05: Output: 06: Optima Channe Assignment A = [A(1),...A(n)..., A(N)]; 07: Procedure ChanneAssignment 08: N c = A(n) A(m) ; N fc = N f N c; 09: N n = N f A(n) ; N m = N f A(m) ; 10: if (N fc > 0 and N n > 0 and N m > 0) 11: N min = min{n fc, N n, N m}; 12: Add N min channes with the smaest congestion weight to A(n) and A(m); 13: N fc = N fc N min; 14: end if 15: if (N fc > 0 and N n > 0 and N m = 0) 16: N min = min{n fc, N n, A(m)\A(n) }; 17: Add N min channes with the smaest congestion weight to A(n); 18: N fc = N fc N min; 19: ese if (N fc > 0 and N n = 0 and N m > 0) 20: N min = min{n fc, N n, A(n)\A(m) }; 21: Add N min channes with the smaest congestion weight to A(m); 22: N fc = N fc N min; 23: end if 24: if (N fc > 0 and N n = 0 and N m = 0) 25: whie(n fc > 0) 26: for (n = 1, n N, n + +) 27: Let i be the channe with the smaest interference among channes in A(n) A(m); 28: Let i be the channe with the argest interference in A(n); 29: Repace i by i; 30: N fc = N fc 1; 31: endfor 32: endwhie 33: endif 34: whie(n fc > 0) 35: Assign nodes having unassigned network interface with the channes having the smaest congestion weight among channes assigned to their neighboring nodes; 36: endwhie

12 11 be determined to achieve the minima congestion. The average deay on each ink is proportiona to 1/P T A where r out using the M/G/1 queuing mode: = r out P T A = r out /(u I γ), (21) + k 1 k =1 Rk s denotes the existing current traffic of ink in P k s pus the potentia contributions from the other k 1 path rate increments. Therefore, we can choose another appropriate P k s for the next increment R k s, such that min Rs k L r out + Rs k P T A. (22) Rk s Actuay, this is aso equa to optimizing the increase congestion in the tota network: ( ) r out + Rs k min Rs k P T A L rout Rs k min. (23) Rk s P T A Rs k P T A L The approximation hods when R k s is sma, which aso restricts the traffic assignment for R k s to be assigned to other paths other than P k s. This resuts in a sub-optima soution to (22), but since the increment is sma, the degradation in performance is expected to be insignificant. Therefore, the optima aocation of increment R k s can be reaized by finding a path P k s source to destination minimizing the increase congestion in the overa network. Since ony inks in P k s experience a change, the optimization now becomes: min P k s P k s from Rs k. (24) P T A We now jointy consider routing and rate aocation probem by optimay aocating rate to each video stream among mutipe paths. The necessary and sufficient conditions for the optima soution to (15) are the aocated rate to each stream shoud either meet the boundary condition exacty, or correspond to zero partia derivative: dd comp dr s + dd oss dr s = 0, (25) where dd comp /dr s is derived from the video distortion mode (15) as: dd comp dr s θ s = (R s Rs). (26) 0 2 Therefore, the distortion reduction caused by increasing encoding rate by R k s is: D k comp θ s (R s R 0 s) 2 Rk s. (27)

13 12 On the other hand, the sope of packet oss distortion increment dd oss /dr s can be expressed as: r out dd oss dr s α(1 P B ) L α(1 P B ) L u I γ α(1 P r out B ) (u γ) I r out L 1. (28) P T A is aso the cross-traffic which incudes contributions from current traffic r out streams. Then, the resuting packet oss distortion increment D k oss and other video can be approximated as: D k oss α(1 P B ) L R k s. (29) P T A Note that (29) is amost the same as the optimization formuation in (24), and can be accumuated over the chosen inks on one path. Remark: Given the packet oss distortion increment Doss k in (29) and the video compression distortion reduction D k comp in (27), the source node can make the rate aocation decision by comparing these two quantities. The aocated rate wi be increased by R s k unti Dk comp > Doss k, i.e., when the benefit of distortion reduction is no onger worthwhie the consequentia network congestion. Therefore, the rate contro agorithm can continue unti it reaches the optima rate that strikes a baance between the two trade-off sopes [18]. C. Distributed Scheduing Scheme Based on the given channe assignment, the joint rate aocation and routing agorithms, DMDS scheme is provided to present an optima scheduing scheme for video transmission over mutichanne muti-radio muti-hop wireess networks. The key chaenges in designing DMDS are how to seect optima channes, paths as we as aocated rates to ensure the resuting system is both stabe and optima. We iustrate the interpay between the source, ink and channe in Tabe II. For DMDS, each channe computes the congestion weight to make the channes assigned to spatiay cose nodes as different as possibe, each ink cacuates the rates to strike a baance between the rate increment and network congestion, and each source determines the optima path distribution to achieve minimum video distortion. Specificay, congestion weight message is fed back from the channes to the inks to avoid network congestion, queue ength message is from the inks to the sources to prevent the source rates from exceeding the transmission abiity,

14 13 and rate aocation and routing message is from the sources to the inks to achieve the optima performance. TABLE II THE DMDS SCHEME At each time sot t: Source s: determine the optima path distribution for each source max F s P (F sj) 2 P j j P F sj Msjq (t) where F s = [F s1..., F sj,...f sns], F sj 0, and q (t) denotes the queue ength for ink at time sot t; Queue Length Update: q (t + 1) = [q (t) + λ q(t)` P s Pj M sjf sjrs(t) j P c rc (t) ] + where [x] + = max(x, 0), and λ q(t) is the step size. Link : determine the optima traffic in each ink min P k s P P k s R k s (t) P T A Rate Increment Update: Rs k (t + 1) = [ Rs k (t) + λ R(t)` P k Dk oss Dcomp k ]+ where λ R(t) is the step size. Channe c: determine the minimum congestion in each channe min P (r in r out ) Congestion Weight Update: u c (t + 1) = u (t + 1)/r c (t + 1). Specificay, the sources send a outgoing inks with path discovery messages, which are forwarded by the intermediate nodes on the contro channe. At each intermediate node, the

15 14 path discovery messages contain the information of congestion weight and queue ength reated to every possibe stream between the source and intermediate node. This intermediate node then extends the path as the source does. Upon reception of path discovery messages from the destinations, the sources determine the possibe paths between the sources and destinations based on expicit feedback from the inks, in form of queue ength, rate increment and congestion weight. In particuar, the source minimizes the tota distortion whie baancing the congestion of channes and inks. In fact, it is simiar to the standard TCP dua agorithm except that the maximization probem is conducted over a vector not a scaar, to refect the muti-path nature of DMDS. Remark: From Tabe II, it can be found that the computations at the sources are inear with the number of sources, whie the computations at the inks and channes do not grow with the number of sources. Specificay, determining the minimum congestion channe takes a constant time O(N f ). The compexity of finding optima traffic in each ink is O(N n N), since each node n N is equipped with N n interfaces. The compexity caused by a the inks is O(L N f +L N n N). In addition, the compexity of mutipe-path routing for each source s S is a constant O(N(s)). Therefore, for each source s S, the computation compexity of a the users is O(S N(s)). Therefore, the tota computation compexity is O(L N f +L N n N+S N(s)). Proposition 1: DMDS scheme converges to the joint goba optimum M of (15) for sufficienty sma queue ength step size λ q and rate increment step size λ R. Outine of the Proof: The idea of DMDS scheme is to decoupe the couped objective function in (15) by introducing auxiiary variabes and additiona constraints, and then use Lagrange dua decomposition to decoupe a the constraints. There are two exact steps: i) introduce new variabes to enabe decouping; ii) empoy dua decomposition and gradient descent method to derive the DMDS sheme. See Appendix for the detaied proof. IV. SIMULATION OF THE DMDS SCHEME In this section, we conduct extensive simuations to study the performance of the proposed DMDS scheme in muti-channe muti-radio muti-hop wireess networks. Concerning the unreiabe contro channes, we use retransmission mechanism to ensure that the information exchange between each node is avaiabe. In addition, we empoy the mechanism introduced in [26] and [27] to impement reiabe contro channe and node synchronization, respectivey. To simuate the

16 15 Y-PSNR per User (db) User-1(Tennis) User-2(City) User-3(City) User-4(Tennis) Iteration Fig. 3. Pots of PSNR versus time for the 1st frame of each video (step sizes: λ q = , λ R = ). video appications, two HD (High-Definition) sequences (City and Tennis) are used to represent video with dramaticay different eves of motion activities. In terms of HD video, the sequence has spatia resoution of pixes, and the frame rate of 60 frames per second. Video stream is encoded using a fast impementation of H.264/AVC codec at various quantization step sizes, with GOP (Group Of Pictures) ength of 25 and IBBP... structure simiar to that often used in MPEG-2 bitstreams. Encoded video frames are segmented into packets with maximum size of 1500 bytes, and the transmission intervas of each packet in the entire GOP are spread out eveny, so as to avoid unnecessary queuing deay due to the arge sizes of intra coded frames. In the foowing, we set T = 300ms, P B = 1%, and α = 350 uness otherwise specified. To study the characteristics of the proposed DMDS scheme, we experiment with the setting of S = 4, N = 10, L = 15, N f = 2, N n = 2. The simuation resuts are presented in Fig. 3. It can be observed from Fig. 3 that the curves foow an increasing concave trajectory, converging cose to the optimum in ess than 15 iterations. Whie the graphs in Fig. 3 are for one particuar initia condition, we have done simuations for a variety of initia conditions to verify that the convergence time is independent of the initia conditions. In addition, it shoud be noted that, in a experiments, we start with an initia routing configuration (i.e. the eariest path known by the source) that spits the traffic eveny among the paths for each source-destination pair.

17 16 Average Y-PSNR (db) MTS PEMS DMDS Frame Number Average Y-PSNR (db) MTS PEMS DMDS Frame Number (a) Tennis (User-1 and User-4) (b) City (User-2 and User-3) Fig. 4. Pots of average PSNR versus time for two different videos. For background stream, it is generated according to an on/off source mode with exponentia distribution of staying time, and average rates between 0 and 0.2 r in for each ink. To demonstrate the effectiveness of our proposed scheme, DMDS is benchmarked against other two popuar scheduing schemes for muti-channe muti-radio wireess networks : i) Maximum Throughput Scheduing (MTS) introduced in [5], in which this scheme seeks for a feasibe end-toend rate aocation vector aong with feasibe channe assignment to achieve optima throughput; ii) Provaby-Efficient Maxima Scheduing (PEMS) introduced in [2], in which a distributed onine agorithm is provided to achieve a provabe fraction of the maximum system capacity. Fig. 4 shows the first 200 frames achieved by four users requesting two different video cips under the given network reaization. From Fig. 4, we can see that compared to MTS and PEMS schemes, our proposed DMDS scheme has a considerabe performance advantages. That is because the above competing schemes ony consider the rate maximization or throughput optimum, whie our scheme aims at minimum video distortion by jointy considering the characteristics of network and video. Note that some of the frame s PSNR vaues of MTS and PEMS may be higher than that of our proposed DMDS scheme, however without any significant performance improvement compared to the video quaity of our proposa. Then, we test the proposed DMDS scheme in a dynamic environment where users can join or eave the given network randomy. We start with 4 users (two are City and two are Tennis).

18 17 Y-PSNR per User (db) Add 4 Users User-1(Tennis) User-2(City) User-3(City) User-4(Tennis) Remove 2 Users Time (s) Fig. 5. Average performance per user in case users join/eave the network. At time t = 2s, we add 4 new users (two are City and two are Tennis), and at time t = 8s, we randomy remove 2 users (one is City and one is Tennis). Fig. 5 presents the average PSNR for origina 4 users obtained by proposed DMDS scheme. From Fig. 5, an interesting observation can be found that our proposed DMDS scheme can achieve a satisfying average performance in this dynamic environment, however, the performance differences between each frame and each video vary dramaticay. Meaning that the distortion-fairness property of DMDS is not so good. For exampe, the standard derivation of each frame for user-1 is 1.29 db, and the average performance difference between user-3 and user-4 is 1.20 db. In some cases, distortion-fairness is aso an important issue for video transmission, especiay for muti-user wireess environments. Given the above simuation resuts, a natura question arises: can we deveop a distributed distortionfairness scheduing agorithm that can take into account different video contents based on the proposed DMDS scheme? In the next section, we wi study this probem. V. EXTENSION: MEDIA-AWARE DISTORTION-FAIRNESS DISTRIBUTED SCHEDULING SCHEME Nowadays, there exists ots of fairness strategies in terms of bandwidth sharing and demand satisfaction [5], [14]. However, users care about QoS rather than the bandwidth or demand, and

19 18 the same QoS may need different bandwidth or demand according to different video contents. In this section, we propose a media-aware distortion-fairness strategy which is aware of the characteristics of video frames and ensures max-min distortion fair sharing among video steams based on the proposed DMDS scheme. A. Media-Aware Distortion-Fairness Strategy The basic idea of Media-Aware Distortion-Fairness (MADF) strategy is as foows. Sources send side information indicating the importance of each frame to the inks, then the sources and inks cooperativey decide the optima threshod of dropping frames for each user, where the frames with ess importance than the threshod wi be dropped [24]. The scheduing shaping aong with distortion metrics in the appication ayer is the same as the proposed DMDS scheme. The resuting media-aware distortion-fairness strategy, in which the sources and inks can distributed cooperate with others such that the end-to-end distortion fairness as we as good video quaity are achieved among users. Here we define the importance of each frame based on the inter-frame motion as [22], whie taking into account of the prediction structures of the frames. For the case of mutipe users sharing inks, each shared ink decides a common distortion threshod of dropping frames for a users, such that each user can satisfy the distortion caused by the congestion. The same threshod of dropping frames makes each user experiences a max-min fairness distortion. Fig. 6 iustrates the architecture of the MADF with dropping frame strategy that exchanges information between the sources and inks. The key point of MADF strategy is to find the optima threshod of dropping frames for each user. In this strategy, each ink finds an equa distortion eve to its users not marked with Fag ; each user sets its frame dropping eve as the most stringent one over a the inks on its path; afterwards, if the ink is bottenecked based on its users updated dropping eve, the ink marks itsef and the users mark it Fag, and other inks drop corresponding frames of the users marked Fag ; then the iteration goes to another round. In this way, each user gets distortion as ow as possibe and fairy, and the distortion of the user who experiences most stringent botteneck is minimized, achieving the max-min distortion fairness share. The detai operation of MADF is presented in Tabe III. The agorithm iterates among the inks and then the sources, unti the threshods can not be changed any further. Remark: The work in [24] is simiar to our media-aware distortion-fairness strategy; however,

20 19 Information Exchange ink Fairness Strategy Heterogeneous traffic ink source Dropping Frame Threshod Scheduing Scheme ink Information Exchange Dropping Frame Fina frame output for each of the inks Fig. 6. Architecture of the MADF scheduing scheme with dropping frame strategy. the main focus of [24] is how to optimize the utiity function, whereas our work aims at reducing the distortion unfairness in wireess setting. The authors of [5] deveop a proportiona fair end-toend rate aocation for muti-radio wireess mesh networks by introducing Demand Satisfaction Factor (DSF). The DSF of a session is defined as the ratio between the rate actuay aocated to that session and its traffic demand. In fact, the agorithm in [5] just considers the demand-fair for each user, and does not consider the characteristics of video streaming. We refer the readers to the discussions in the Introduction part regarding the difference between our work and [5], [24] and the potentia impications. Proposition 2: The additiona number of iterations induced by MADF is at most the number of bottenecks, where the botteneck is counted in the same network where a the streams are fuy eastic without any upper bound. Proof: In each iteration, there wi be at east a ink whose current threshod wi not change in the next iteration, and such ink is a ink which woud be fuy utiized if the streams on it are fuy eastic without any upper bound. Next we consider the cost (penaty) function D(z, z ) when MADF is empoyed. (14) can be rewritten as D oss = αp oss + Q c D(z, z ). (30)

21 20 From (30), each ink wi keep updating its state information, uness the performance difference of empoying the proposed dropping frame agorithm becomes sma. Hence, in the proposed MADF strategy, assume the difference between the current strategy z s and the previous strategy z s for user s is e s, i.e., e s = z s z s. Let U diff s = e s max[z Msjq ] (31) be the distortion difference between the current strategy and the previous strategy. Note that, according to the proposed dropping frame agorithm, we choose the max operation in the j TABLE III MADF STRATEGY 01: Input: 02: A inks are set Fag=FALSE, and z = maxi; 03: A users are set Fag=FALSE, and z s = maxi; where maxi is a given upper bound of the frame importance; 04: Output: 05: Optima Media-Awareness Distortion-Fairness Scheduing; 06: Procedure FrameDrop 07: if (ink Fag=FALSE ) 08: The frame queuing in ink whose importance eve beow the threshod z is dropped; 09: Recacuates the threshod z for the update queue; 10: if (z z ) 11: Link is set Fag=TRUE ; 12: User reevant to is set Fag=TRUE and z s =max {z, z }; 13: endif 14: endif 15: if (user s Fag=FALSE ) 16: The frame dropping eve is set z s =max z over a the inks on its path; 17: User s is set Fag=TRUE ; 18: ese 19: User s drops the frames whose importance is ess than z s; 20: endif 21: Procedure DistributedScheduing 22: The same to the DMDS scheduing presented in Tabe II;

22 21 TABLE IV PERFORMANCE COMPARISON FOR DIFFERENT SCHEMES IN DIFFERENT SCENARIOS DMDS MMGMT PFEE MADF Scenario-1 Average Y-PSNR Average Y-PSNR Average Y-PSNR Average Y-PSNR Y-PSNR Standard Y-PSNR Standard Y-PSNR Standard Y-PSNR Standard (db) Deviation (db) Deviation (db) Deviation (db) Deviation user user user user user DMDS MMGMT PFEE MADF Scenario-2 Average Y-PSNR Average Y-PSNR Average Y-PSNR Average Y-PSNR Y-PSNR Standard Y-PSNR Standard Y-PSNR Standard Y-PSNR Standard (db) Deviation (db) Deviation (db) Deviation (db) Deviation user user user user user distortion expression. Caim 1: If e s satisfies the foowing condition: U diff s Q c D(z, z ) (32) for a users s S, the proposed scheduing scheme converges to a stabe state.

23 22 Proof: Equation (32) can be derived as: { D(z, z ) (z z ) max[z Msjq ] } Q c Q c j z max[z Msjq ] j z max[z Msjq ] D(z, z ) j z s max[z Msjq ] D(z s, z s) j U diff s. (33) The remaining proof foows [2, Proposition 2], so the strategy converges to a stabe state. Caim 2: If the penaty function D(z, z ) is a convex function of z, when the proposed dropping frame agorithm converges to a stabe state, the distortion difference between the proposed MADF strategy and the DMDS scheme is not arger than Q c D(z, z ). Proof: As ong as the penaty function D(z, z ) is a convex function of z, the additiona video distortion function is a convex function, since for each iteration, max[z j M sjq ] in (31) does not change with z. Hence, when the proposed scheduing scheme converges to a stabe state, the worst distortion reduction is Q c D(z, z ). B. Numerica Resuts In order to provide a meaningfu comparison between our proposed MADF approach and other aternative approaches, we consider the use of the recent Max-Min Guaranteed Maximum Throughput (MMGMT) and Proportiona Fair End-to-End (PFEE) schemes introduced in [5], and the proposed DMDS scheme in Section III as comparison systems. For each simuation, we generate end-to-end communication streams with random source and destination nodes. 5 users transmit different videos concurrenty: user-1 sends video cip City; user-2 sends Mobie; user-3 sends Mother; user-4 sends View; user-5 sends Tennis. The traffic demand for each communication stream for a the schemes is given by a random number uniformy distributed in [0.2r in, 0.6r in ]. We evauate the performance of the above four schemes in terms of PSNR vaue under different scenarios. Specificay, Scenario-1 denotes N = 10, L = 15, N f = 2, N n = 2, and Scenario-2 corresponds to N = 15, L = 30, N f = 3, N n = 3. The simuation resuts are presented in

24 23 Tabe IV. It shoud be noted that a the simuation resuts in this subsection have been obtained using 300 runs in order to obtain statisticay meaningfu average vaues. Based on the given objective simuation resuts, there are two main observations: With regards to the average PSNR vaue, MADF achieves a satisfying performance. Its performance is comparabe to that of DMDS, and much better than those of MMGMT and PFEE schemes. For exampe, the average performance differences between MADF and DMDS for 5 users in two scenarios are ony 0.2 db and 0.1 db, respectivey. However, compared to MMGMT and PFEE schemes, the proposed MADF scheme can achieve 1.7 db and 1.7 db performance improvement for scenario-1, and 1.9 db and 1.8 db for scenario-2. That is to say, MADF is derived from DMDS, and hods the basic characteristics of DMDS. With regards to the PSNR derivation vaue, MADF has the best constant performance. We can observe that athough DMDS scheme gobay achieves the best PSNR performance, it resuts in a severe unfairness on performance. In addition, MMGMT and PFEE schemes aso consider the fairness probems in scheduing, and they can achieve certain performance improvement compared to DMDS scheme. However, MMGMT and PFEE schemes do not consider the content of video, as expected, their performances are worse than the proposed MADF scheme. VI. CONCLUSIONS In this paper, we have deveoped fuy distributed scheduing schemes that jointy sove the channe-assignment, rate aocation, routing and fairness probems for video streaming over muti-channe muti-radio networks. Importanty, unike conventiona scheduing schemes focus on optima system throughput or scheduing efficiency, our work aims at achieving minima video distortion and certain fairness by jointy considering media-aware distribution and network resource aocation. Extensive simuation resuts are provided which demonstrate the effectiveness of our proposed schemes. The resuts in this paper have some interesting impications on the practica use of muti-radio muti-channe muti-hop wireess networks, i.e., mutimedia sensor network is a good exampe. As we know, current sensor networks due to their imit transmit capacities can hardy transmit arge amount of mutimedia data concurrenty. Muti-channe muti-radio technique is a direction to provide a satisfying mutimedia service in wireess sensor networks. In addition, 3GPP LTE (Long Term Evoution) system using reay is aso an exampe. As we know, LTE uses OFDM

25 24 (Orthogona Frequency Division Mutipexing) for the downink, in which the transmitter sends information over a arge number of sub-carriers [2]. So it can be viewed as a specia type of mutichanne muti-radio muti-hop wireess system. Therefore, our proposed video scheduing scheme for muti-channe muti-radio muti-hop wireess networks is eager to have arge appication ground. For future work, we pan to study some practica issues for impementing the proposed schemes. Note that in rea video transmission over muti-channe muti-radio systems, additiona works need to be deveoped in order to: i) reduce the dependence of the video content for scheduing scheme can automaticay adapt; ii) simpify the scheduing scheme, especiay the channe and ink information exchange and feedback; iii) extend the resuts to more practica systems (e.g., OFDM) and channe modes (e.g., heterogeneous channes). In our ongoing work, we pan to carefuy address these open probems and study their impacts on the actua mutichanne muti-radio systems. APPENDIX Proof of Proposition 1: Since (15) is a convex optimization probem satisfying Sater s condition, the duaity gap is zero. Therefore, a distributed agorithm for (15) can be derived through the Lagrange dua probem. First we form the foowing Lagrangian: L(D a, M, φ ) = s D a j φ (t)(r in r out ). (34) However, (34) can not be decouped yet because φ refers to many variabes. Therefore, we keep on introducing a new variabe κ s and additiona constraints P T A and Rk s. Note that P k s corresponds to the path j of user s, so L(D a, M, φ, κ s ) = s κ s (t)d a φ (t)(r in r out ) + Ps k So far, (35) can be decouped with three sub-probems as foows: κ s (t) Rk s(t). P T A Each source s: max F s j κ s (t)(f sj ) 2 j F sj φ (t)msjq (t) (35) where q (t) is the queue ength of ink at time sot t.

26 25 Each ink : min P k s P k s κ s (t) Rk s(t). (36) P T A Each channe c: min φ (t)(r in r out ). (37) The Lagrangian dua function L d (φ, κ) is defined as the maximized L(D a, M, φ, κ) over D a and M for given φ and κ. Each source can compute an optimizer D a and each ink and channe c can compute an optimizer M (φ, κ). The Lagrange dua probem of (15) is: min L d (φ, κ s ) = L(D a, M (φ, κ s ), φ, κ s ), (38) where (φ, κ s ) are the dua variabes. Note that (38) is a convex minimization. In addition, we can define the iteration method for u c (t) as: u c (t + 1) = u (t + 1)/r c (t + 1). (39) Since L d (φ, κ s ) may be non-differentiabe, an iterative subgradient method can be used to update the dua variabes to sove (38). Queue Length Update: q (t + 1) = [q (t) + λ q (t) ( MsjF sj Rs(t) j s c j r c (t) ) ] +, (40) where λ q (t) represents the queue ength step size. Rate Increment Update: Rs(t k + 1) = [ Rs(t) k + λ R (t) ( Doss k Dcomp) k ] +, (41) where λ R (t) represents the rate increment step size. (40) and (41) are exacty the DMDS scheme steps described in Tabe II. Certain choices of step sizes, such as λ q (t) = λ 1 /t, λ R (t) = λ 2 /t where λ 1 > 0, λ 2 > 0, guarantee that this agorithm wi converge to the joint optimum. In this case, the convergent point is a gobay optima M to the probem (15) since we have shown that the probem can be written as convex k optimization.

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