Non-collaborative Resource Management for Wireless Multimedia Applications Using Mechanism Design

Transcription

1 Non-collaboratve Resource Management for Wreless Multmeda Applcatons Usng Mechansm Desgn Fangwen Fu and Mhaela van der Schaar Eleccal Engneerng Department, Unversty of Calforna, Los Angeles (UCLA) 1 ABSTRACT We propose to add a new dmenson to exstng wreless multmeda communcatons systems by enablng competng statons to proactvely engage n the resource management game by adaptng ther cross-layer ansmsson sateges. For ths, we model wreless statons (WSTAs) as ratonal and selfsh players competng for avalable wreless resources n a dynamc game. We focus on pollng-based wreless LAN (WLAN) networks, where developng an effcent soluton for managng the avalable ansmsson opportuntes s of paramount mportance. The resource allocaton game s coordnated by a network moderator, whch deploys a novel resource management based on the Vckrey-Clarke-Groves (VCG) mechansm to determne a) the amount of tme to be allocated to the varous users and b) the ansmsson cost assocated to the allocated resources. The ansmsson cost s referred to n the VCG mechansm as ansfer and depends not on the used resources, but rather on the nconvenence (n terms of utlty mpact) that t causes to other WSTAs. The ansfer s noduced n order to dscourage WSTAs from lyng about ther resource requrements. Importantly, ths proposed dynamc resource management approach for wreless multmeda applcatons changes the passve way statons are currently adaptng ther cross-layer sateges by enablng them to selfshly nfluence the wreless systems dynamcs by proactvely adaptng ther packet schedulng sateges, error protecton sateges etc. Hence, each wreless staton can play the resource management game by adaptng ts multmeda ansmsson sategy dependng on the experenced channel condtons, derved vdeo qualty, atttude towards rsk, wllngness to pay for resources and avalable nformaton about the wreless network. Our smulatons show that usng the VCG mechansm the WSTAs do not have any ncentves to le about ther resource requrements as otherwse they wll be severely penalzed by a hgh ansfer. We also show that deployng advanced cross-layer sateges for playng the resource management game sgnfcantly beneft the WSTAs receved vdeo qualty. The wllngness-to-pay for resources s noduced to provde WSTAs a tool to gather addtonal resources whenever they need to ansmt an mportant (part of a) vdeo sequence by agreeng to pay for resources an ncreased cost. A novel rsk-aware schedulng scheme s also proposed that provdes WSTAs the ablty to dynamcally avod network congeston and hence, reduce ther ncurred ansfer. Keywords: Wreless Multmeda Seamng, Mult-user Wreless Transmsson, Cross-layer Optmzaton, Game Theory, Mechansm Desgn, Resource Management.

2 2 I. INTRODUCTION Sgnfcant conbutons have been recently made to enhance the performance of wreless multmeda usng cross-layer mzaton (see e.g. [1][24][25]). However, the multmeda ansmsson has been often mzed n solaton, at each ndvdual staton, and does not consder ts mpact on the overall wreless system. Alternatvely, n ths paper, we propose to add a new dmenson to exstng multmeda communcaton systems by enablng WSTAs to dynamcally compete for network resources by proactvely adaptng ther mzed cross-layer ansmsson sateges, and uthfully declarng ther tme-varyng resource requrements. Hence, the conventonal passve mzaton of ansmsson sateges s now modfed to enable WSTAs to proactvely engage n the resource management game by jontly adaptng ther ansmsson, rsk atttude and wllngness-to-pay for resources 1 (.e. wllngness to accept a hgher ansfer than normally requred for a specfc derved utlty). Our focus s on autonomous WSTAs that compete for wreless resources (ansmsson tme) n order to ansmt vdeo n real-tme over a shared WLAN nfrasucture. In exstng WLANs, the avalable resources are dvded among competng statons through a pollng-based mechansm deployed by a Cenal Specum Moderator (CSM). The CSM s often mplemented at the Medum Access Conol (MAC)-layer, but t can take nto consderaton nformaton from other layers when determnng polces to dvde the avalable resources. Current sateges for wreless resource management nclude dynamc sateges such as ar-far tme [2], proportonal farness [3], longest queue hghest possble rate [26] etc. or statc admsson-conol (reservaton) based schemes (e.g. IEEE e [4]). An excellent revew of varous cross-layer wreless resource allocatons from a network, MAC and physcal layer perspectve has been presented n [26]. Statc allocaton of resources s often based on worst-case, fxed affc specfcatons [5] and hence, they are not able to scale wth the number of WSTAs or adapt to tme-varyng changes n the network condtons, content characterstcs or deployed cross-layer sateges. Exstng dynamc solutons (e.g. [2][3][26]) also do not consder the mpact on multmeda utlty such as vdeo qualty and delay consants [27]. Even more mportantly, these exstng mult-user wreless multmeda resource allocaton schemes heavly rely on the users declarng ther requrements n a uthful manner. Partcularly n a congested network, f some users exaggerate or le about ther resource requrements, the performance of the ene wreless network wll degrade. Exstng resource management solutons do not prevent WSTAs from exaggeratng ther resource needs at the expense of competng WSTAs. In a recent IEEE Specum ssue, Robert W. Lucky [6] argued the need for new, proactve resource management schemes that are able to prevent competng users from msusng common (shared) network resources and lyng about ther requrements. Importantly, he mentoned the lack of ncentves for the WSTA n current wreless networks to adhere to farness or courtesy rules: "Today we worry whether W-F wll exhbt the same meltdown. There s no ncentve, other than the ultmate survval of the system, for users to lmt ther use." Summarzng, each WSTA wll y to acqure as much of the network resources as possble (see e.g. resource 1 Subsequently, ths s referred to smply as the wllngness-to-pay.

3 3 management for IEEE e wreless networks [5]), unless a preemptve mechansm exsts n the network. Thus, a regulatory cenal system s needed that can ensure an effcent allocaton of resources. Ths s especally mportant for multmeda users whch have multple ncentves to le about ther resource requrements. Frst, as the utlty (multmeda qualty) always ncreases wth the ansmsson rate and users are not rewarded by beng consderate to other users, WSTA always want to obtan the largest possble amount of tme for ansmsson even f the resultng qualty mprovement s mnmal. Another ncentve for lyng s that over-provsonng can enable WSTAs to cope wth sudden varatons n channel condtons or content characterstcs by provdng them addtonal opportuntes for ansmttng protecton data. Fnally, f the WSTAs are allocated suffcent resources, they have no ncentve to smartly mze ther cross-layer ansmsson sateges, as they can acheve a relatvely good vdeo qualty (e.g. through reansmttng the lost packets) even when ther ansmsson sateges are not very effcent. Prevous research has not proactvely consdered the benefts of dynamc and compettve resource management among WSTAs that reles on ther ablty to adapt ther cross-layer sateges to changng avalable resources (congeston level) and varyng channel condtons. For example, n [10], the authors proposed a dscrete resource-utlty functon amed at maxmzng the aggregate utlty by dynamcally assgnng network resources. However, ths cenalzed allocaton method passvely adjusts the allocaton based on the prevous observatons and does not take nto account the non-collaboratve user behavor. Informaton-theoretc work on mult-user wreless resource allocaton (see e.g. [26][27]) does not consder the delay-senstve nature of the multmeda data, the tme-varyng delay and mportance of the varous packets, the avalable applcaton-layer ansmsson sateges to play the resource allocaton game or the resultng mpact on multmeda utlty of the partcpatng WSTAs. Game theory has been proposed n pror research to resolve compettve resource allocaton ssues for wreless networks n a dsbuted and scalable manner [7][9][11]. In [7], a prcng mechansm s aded for resource allocaton to ensure that the sum of users' utltes s maxmzed. However, the users are assumed to be "prce takers" (.e. they do not antcpate the mpact of ther actons on the network). In [8], t has been shown that resource allocatons such as those proposed n [7] suffer from an "effcency loss", f the users explot the fact that ther actons affect the network prces. In [9], the aucton mechansm was deployed for resource allocaton. The mal aucton sateges for the resource-buyers are derved and the equlbrum s shown to exst. In [11], prcng schemes are noduced whch can be deployed by a servce provder to polce the network. However, the relatonshp between the assgned resources and the ganed utlty s not thoroughly studed n [9][11]. Furthermore, prevous research has not consdered the benefts of dynamc and non-collaboratve resource management among WSTAs that reles on ther ablty to adapt ther cross-layer sateges to tme-varyng content characterstcs, contenton-levels and channel condtons. Summarzng, even when preemptve mechansms exst n the network to force WSTAs to adhere to exstng polces for resource allocaton, the problem of determnng mal utltes and sateges for allocatng the ansmsson opportuntes among varous WSTAs seamng delay-senstve multmeda stll remans unsolved. For nstance,

4 4 defnng resource allocaton polces that capture the real beneft derved by users from the network consttutes an mportant open research area. The complexty of ths problem s further exacerbated by the fact that the cross-layer mzaton at each WSTA nvolves numerous tme-varyng parameters and nteractons among layers, makng the nteractons among WSTAs and the resultng utlty-resource adeoffs very dffcult to model. Moreover, WSTAs are consdered autonomous enttes that separately determne and mze ther deployed cross-layer sateges. Hence, another nherent property that needs to be consdered when developng wreless resource allocaton polces s to allow WSTAs to compete for resources by selfshly adaptng ther ansmsson sateges.. Last but not least, for wreless multmeda applcatons, the resource management s further complcated by the delay-senstve nature of the applcaton,.e. multmeda data that s receved after ts delay deadlne does not conbute to an mproved utlty. In ths paper, to enforce WSTAs to declare ther resource requrements uthfully and act n a socally mal way, we ad a tool from game-theoretc mechansm desgn 2 called ansfers 3 through whch the CSM can penalze WSTAs based on the nconvenence they cause to other users [14]. The nconvenence s quantfed n terms of the utlty mpact they are causng other WSTAs by consumng common resources. Each WSTA ansmts to the CSM a vector of prvate nformaton that quantfes ts utlty functon (vdeo qualty) as a functon of allocated tme. Based on ths nformaton, the CSM allocates avalable ansmsson opportuntes (TXOPs) to the WSTAs and determnes the ansfers to be pad by each staton. The ansfers are desgned n such a way by the aded game-theoretc mechansm that WSTAs have no ncentve to le about ther prvate nformaton even though they care only about ther own utltes. The focus of our paper s on desgnng proactve cross-layer sateges for WSTAs that enable them to nfluence the wreless systems dynamcs n such a way that ther own utlty s maxmzed. Each wreless staton can then play the resource management game by mally adaptng ts cross-layer ansmsson sateges and, subsequently, declarng ts prvate nformaton n order to maxmze ts own payoff. Ths payoff depends on both the expected utlty as well as the ncurred ansmsson cost (ansfer). In summary, our paper makes the followng conbutons: 1) We propose a novel scheme for non-collaboratve mult-user wreless resource management based on mechansm desgn, n whch WSTAs can compete for the avalable TXOPs. The aded mechansm desgn oblges WSTAs to proactvely choose the mal cross-layer sateges and uthfully reveal ther own prvate nformaton. Importantly, the proposed game-theoretc approach also promotes collaboraton n an ndrect way through chargng WSTAs based on the nconvenence they cause to other users rather than the used resources. In ths way, WSTAs wll naturally tend to dsbute ther requests (.e. adapt ther schedulng algorthms) over tme n an effcent manner to avod requestng resources when the network s congested and ansmttng packets s expensve. 2) To effectvely play the resource management game, WSTAs dynamcally adapt ther cross-layer sateges, based 2 For more detals on mechansm desgn, the nterested reader s referred to [14]. 3 The ansfer can be computed n terms of payments, money, computaton resources or other types of resources or ncentves, e.g. quotas [15].

5 5 on ther source characterstcs and channel condtons, but also rsk atttudes and wllngness-to-pay, to compete for the lmted wreless resource. In ths way, the smartness of WSTAs wll be rewarded by an mproved receved vdeo qualty. Note that even though the resource management s moderated by a cenalzed resource moderator (CSM), the varous WSTAs can actvely nfluence the CSM decson n a dsbuted manner by adaptng ther cross-layer sateges. 3) Our proposed algorthm for resource allocaton provdes the WSTAs the flexblty to cope wth the tme-varyng channel characterstcs, network congeston and/or mportance of vdeo sequences (or packets) by adaptng ther wllngness-to-pay for resources (.e. accept an ncreased ansfer) and rsk atttudes. The resource management game s played repeatedly over tme (e.g. every servce nterval [4] n e WLANs) n order to capture the tme-varyng channel and vdeo applcaton dynamcs. Ths leads to an mproved socal decson 4 for mult-user wreless resource management as opposed to exstng pre-determned schemes that are dffcult to enforce (because the users do not need to uthfully declare ther costs and utltes) farness crtera [2][3][12][13]. Note that t s not the am of ths paper to propose new jont source-channel codng or cross-layer ansmsson sateges. Rather, we llusate here the proposed approach usng only a lmted set of ansmsson sateges deployed at the varous layers. Future research wll nclude a more extensve evaluaton of how varous cross-layer sateges already avalable n the lterature can be readly used or adapted n order to enable users to play the resource management game more effectvely. For nstance, better modulaton or channel codng schemes can be used as a compettve advantage by WSTAs to derve a hgher beneft (utlty). The paper s organzed as follows. Secton II proposes a game-theoretc dynamc resource allocaton framework. Secton III descrbes the cross-layer desgn for the resource allocaton game and the correspondng types of WSTAs. Secton IV noduces the game-theoretc mechansm desgn n detal for our resource allocaton game as well as the assocated complexty. Secton V presents the smulaton results, followed by the concluson n Secton VI. The used notatons are lsted n Table 1 for the reader s convenence. 4 The term socal decson s borrowed from mechansm desgn theory, see [14] for more detals.

6 6 Table 1. Notatons Notaton Descrpton Notaton Descrpton M The number of WSTAs R The avalable wreless resource t SI The length of servce nterval SNR Sgnal to Nose Rato of WSTA 5 SNR Antcpated Sgnal to Nose Rato ξ The source characterstcs ξ The antcpated source characterstcs x Prvate nformaton x The antcpated prvate nformaton Delay( t, s, x ) The delay ncurred by ( t, s, x ) T The resource (tme) allocaton t The resource (tme) allocated to WSTA s The real-tme cross-layer sategy s The antcpated cross-layer sategy s The mal real-tme cross-layer sategy s The mal antcpated cross-layer sategy w The wllngness-to-pay vector V The set of avalable revealng sateges S The set of avalable cross-layer sateges κ Jont sategy µ The revealng sategy S V The jont sategy set µ The mal revealng sategy max Delay The maxmum delay deadlne κ The mal jont sategy θ ˆ The announced type The utlty ganed n the conventonal u( t, s, x ) ˆ The utlty ganed n the game-theoretc u (, ) cross-layer desgn t θ cross-layer desgn θ The type θ The type profle of all the WSTAs Θ The set of possble types τ The ansfers to all the WSTAs τ The ansfer (payment for allocated resources) υ The payoff Θ The set of possble type profles for all the T The resource allocaton when WSTA s WSTAs not n the network θˆ The announced type profle except WSTA H The number of prorty class per GOP L Packet length Delay gh,, The delay deadlne of class h of GOP g K gh,, The number of packets of class h of GOP g γ The modulaton mode λ h, I ghk,,, The qualty conbuton of each packet n class succ P ghk,,, h per GOP The ndcator for the k -th packet of class h of rec Q GOP g g, ( t ) η The number of packet of class h of GOP g gh,, Tme ghk,,, remanng for ansmsson ϒ The set of avalable ansmsson modes (, ) phy max( ) The probablty that the k -th packet of class h of GOP g s successfully receved The expected receved vdeo qualty of GOP g n the current SI The ansmsson tme of the k -th packet of class h of GOP g esnr γ The bt error rate R γ The maxmum achevable bt rate R ( SNR, γ, L ) The expected packet rate p max The maxmum number of ansmsson of the n ghk,,, t k -th packet of class h of GOP g packet The average ansmsson duraton of the ghk,,, k -th packet of class h of GOP g the tme pror to the maxmum delay deadlne The mal maxmum number of rsk max, t g, + 1 n GOP g that the packets n GOP g + 1 start n ghk,,, ansmsson of the k -th packet of class to be ansmtted h of GOP g P( SNR, γ, L ) The packet loss probablty γ The mal modulaton mode sys u p The expected number of packets successfully The average ansmsson tme of the k -th N,,, ansmtted Tme ghk packet of class h of GOP g ω h, The maxmum number of ansmtted The wllngness-to-pay for prorty class h H prorty classes ρ h, The utlty gan per unt tme for class h β h, Transmsson duraton for the class h ρ Announced utlty gan per unt tme for class Announced ansmsson duraton for the ˆ, h β ˆ, h h class h ( T, ˆ θ ) The aggregated system utlty t The mal resource allocaton to WSTA T The mal resource allocaton 5 In ths notaton table, the subscrpt of the symbol represents WSTA.

7 7 II. RESOURCE MANAGEMENT FOR MULTI-USER WIRELESS MULTIMEDIA COMMUNICATION A. System Descrpton We consder M autonomous WSTAs that are seamng vdeo content n real-tme over a shared one-hop WLAN nfrasucture. These WSTAs are competng for the avalable wreless resources R +, whch n our system s the amount of tme that can be allocated to the WSTAs. We assume that a pollng-based mechansm (smlar to that aded n the QoS-enabled MAC of IEEE e [4]) s deployed by the CSM to dvde the avalable resources among competng WSTAs. The resource management schemes mplemented by the CSM can be dvded n two categores. The frst category performs statc allocaton of resources, such as n IEEE e, where, based on the pre-determned negotated affc specfcaton (TSPEC) [4][5], the CSM s pollng the varous WSTAs for a fxed fracton of tme every servce nterval (SI). The length of the SI, t SI, s determned based on the channel condtons, source characterstcs and applcaton-layer delay consants [17]. The second category performs dynamc resource allocaton, where the number of TXOPs allocated to each staton changes every SI or group of SIs, based on the tme-varyng channel condton, rate or qualty requrements of users [10] etc. To enable the dynamc allocaton of resources, the WSTAs need to provde the CSM nformaton about ther status (e.g. ther channel condton, ther queue szes, the mportance of ther packets etc.) and, based on ths nformaton and avalable farness polces 6, the CSM wll n real-tme decde the TXOP allocaton. We assume that the channel condton experenced by WSTA s characterzed by the measured Sgnal to Nose Rato (SNR), SNR, whch vares over tme. The current state nformaton for WSTA s encapsulated n vector x, whch ncludes the channel condton SNR and the vdeo source characterstcs [24] ξ,.e. x =( SNR, ξ ). In the remander of ths paper, borrowng a term from game-theory, we wll refer to ths vector as the WSTA s prvate nformaton. Snce the prvate nformaton s not known precsely pror to the actual ansmsson, a WSTA wll need to determne ts sategy for playng the resource management game based on the antcpated prvate nformaton x, whch ncludes the antcpated SNR SNR and the antcpated source characterstc ξ,.e. x =( SNR, ξ ). Based on the prvate nformaton, each WSTA jontly mzes the varous ansmsson sateges avalable at the dfferent layers of the OSI stack. In ths paper, we lmt the cross-layer sateges to only nclude adaptng the modulaton mode at the physcal (PHY) layer, the number of reansmssons per packet at the MAC layer, the packet prortzaton and packet schedulng at the applcaton (APP) layer. B. Conventonal Cross-layer Desgn In the statc resource allocaton scenaros, the resource allocaton s represented by the tme allocaton vector M M T( R ) = [ t1,..., t M ] +, where t ( 0 t tsi ) denotes the allocated tme to WSTA and t. 1 t = SI Gven a statc tme allocaton, and the WSTA s specfc consants (e.g. applcaton layer delay consants), the cross-layer 6 As mentoned n the noducton, several farness polces have been already proposed n the lterature for mult-user wreless resource allocaton. See e.g. [3][12][13] for more detals.

8 8 desgn problem has been formulated as an mzaton wth a certan objectve (e.g. maxmze goodput, mnmze consumed power) based on whch the mal jont sategy across the multple OSI layers s selected. Let s represent a cross-layer sategy avalable to WSTA, whch les n the set of feasble sateges S for that staton. The cross-layer sategy s s aded n real-tme by the WSTA. Then, gven the prvate nformaton x and the predetermned tme allocaton t, a cross-layer sategy s results n the utlty u( t, s, x ) whch, for vdeo seamng applcaton, represents here the antcpated receved vdeo qualty n terms of PSNR. Hence, the mal cross-layer sategy can be found as In the above formulaton, s = arg max u ( t, s, x ) S. (1) st.. Delay( t, s, ) s max x Delay max Delay represents the delay consant for the partcular vdeo ansmtted by WSTA and Delay( t, s, x) represents the delay ncurred by the cross-layer sategy s for the specfc prvate nformaton x and resource allocaton t. However, as mentoned before, snce the channel condtons, vdeo characterstcs, number of partcpatng WSTAs or even the user desred utlty vary over tme, the conventonal cross-layer mzaton descrbed above does not explot the network resources effcently and hence, does not provde adequate QoS support for multmeda ansmsson [1][24], especally when the network s congested. Also, mportantly, the WSTA can unuthfully declare (exaggerate) ts resource requrements durng the ntalzaton stage n order to obtan a longer ansmsson tme t. Thus, n exstng wreless networks, there s no mechansm avalable to prevent the WSTA from lyng about the requred t. C. Proposed Game-theoretc Dynamc Resource Management To elmnate the abovementoned lmtatons for mult-user wreless multmeda ansmsson, we enable WSTAs to dynamcally acqure wreless resources dependng on the desred utlty, ther avalable cross-layer sateges and prvate nformaton. We propose to model the mult-user wreless communcaton as a non-collaboratve resource management game regulated by the CSM, where the WSTAs are allowed to dynamcally compete for the avalable TXOPs by jontly adaptng ther cross-layer sateges as well as ther wllngness-to-pay and rsk atttude. In ths non-collaboratve game, the WSTAs are consdered selfsh (autonomous) users that solely am at maxmzng ther own utltes by gatherng as much resources as possble. To prevent the WSTAs from msusng the avalable resources, the CSM ads a tool from mechansm desgn, referred to as ansfer, to penalze the WSTAs from exaggeratng ther resource requrements. Specfcally, n ths paper, we use the Vckrey-Clarke-Groves (VCG) mechansm [14][18][28] to mplement and enforce the rules of the resource allocaton game. In the VCG mechansm, the resource allocaton s based on a socal decson, whch maxmzes the aggregated mult-user wreless system utlty. To encourage the WSTAs to work n ths socal mal way, the CSM charges each WSTA a ansfer correspondng to the nconvenence t causes to other WSTAs. In our

9 9 non-collaboratve wreless network, the nconvenence caused by a WSTA s quantfed as the utlty penalty (drop) that the competng WSTAs ncur to other WSTAs due to the partcpaton (resource usage) of that WSTA n the resource management game. In our formulaton, the performance of each WSTA wll depend on the prvate nformaton, the aded cross-layer sategy, but also on the WSTA wllngness-to-pay for resources. The wllngness-to-pay, denoted as w, wll affect the ablty of WSTA to ansmt more or less vdeo data durng the current SI, by acceptng to pay a larger/lower ansfer. In Secton III.D, we dscuss n detal how the wllngness-to-pay w affects the sategy wth whch the WSTA plays the resource game and ts derved utlty and ncurred ansfer. The detals of the VCG mechansm deployed at the CSM are gven n Secton IV. The mplementaton of the resource allocaton game s depcted pctorally n Fgure 1. In the resource game, a jont sategy s defned for WSTA that conssts of selectng an antcpated cross-layer sategy s S and a revealng sategy µ V, where V s the set of revealng sateges avalable to WSTA. We denote the jont sategy as κ = ( s, µ ), κ S V. The purpose of the antcpated cross-layer sategy and the revealng sategy s outlned n the subsequent paragraphs. The antcpated cross-layer sategy s s computed by WSTA pror to the ansmsson tme, n order to determne what the antcpated beneft s n terms of utlty whch t can derve by acqurng avalable resource durng the upcomng SI. Note that the antcpated cross-layer sategy s s proactvely decded at the begnnng of every SI and wll not be exactly the same as the actual real-tme sategy s aded at ansmsson tme. The reason for ths s that the sategy for playng the game also depends on the WSTA s antcpated prvate nformaton x. Unlke the real-tme cross-layer sategy whch has precse nformaton about x, the antcpated cross-layer sategy wll need to determne the modulaton mode at the PHY layer, the number of reansmssons per packet at the MAC layer, the packet prortzaton and schedulng at APP layer, etc. based on the antcpated prvate nformaton x, whch wll be descrbed n Secton III.C. To play the resource management game, each WSTA needs to announce ts type, denoted as 7 θ ( s, x, w ), whch represents the utlty that can be derved from the potentally allocated resources (TXOPs). Based on the announced types, the CSM wll determne the resources allocaton and ansfers for the partcpatng WSTAs. We refer to the set of possble types avalable to WSTA as Θ.The type s defned as a nomnal vector that encapsulates the antcpated prvate nformaton x, the antcpated cross-layer sategy s, as well as the wllngness-to-pay w for resources (ansfers). The type profle for all WSTAs s defned as θ = ( θ1,..., θ M ), wth θ Θ, Θ = Θ 1... ΘM. The type vector wll be descrbed n more detal n Secton III.D. A revealng sategy µ s aded by the WSTA to determne whch type should be declared to the CSM based on the derved real type θ. The type of WSTA revealed to the CSM (referred to as announced type) can be expressed as θ ˆ = µ ( θ). The announced type profle for all WSTAs s denoted as θˆ = ( θˆ ˆ 1,..., θ M ). In other words, the jont sategy κ aded by WSTA determnes the announced type 7 Note that to smplfy our notaton, n the subsequent part of the paper, we omt at tmes the dependences of θ on s, x, w and refer to t smply as θ.

10 10 θ,.e. θ ˆ = κ ( x, w ) = µ ( θ ( s, x, w )). ˆ For the dynamc resource allocaton game, the outcome s denoted as M T(, θ ˆ R ), where T : Θ s a + + functon mappng both the announced type profle ˆθ and the avalable resource R to the resource allocatons. Thus, M T( θ ˆ, R ) = [ t1,..., t M ], where t denotes the allocated tme to WSTA wthn the current SI and t. 1 t = SI Based on the dynamc resource allocaton t and ts derved type θ, WSTA can derve utlty u( t, θ ). However, the utlty computed at the CSM sde for WSTA s u (, ˆ t θ ), as ths s determned based on the announced type θ ˆ. Note thatt s decded by the CSM whch s a functon of the announce type profle ˆθ and the avalable resource R. Hence, note that the real utlty derved by a WSTA and the utlty that a CSM beleves that the WSTA s obtanng can dffer, snce the CSM solely reles on the nformaton announced by the WSTA. In our resource management game, the utlty s computed not only based on the antcpated receved vdeo qualty lke n the conventonal cross-layer desgn, but also on the wllngness-to-pay for resources of a WSTA, w. The ansfer computed by the CSM s represented by M τ(, θˆ R ), where τ : Θ + s a functon of both the announced type profle ˆθ and the avalable resource R, and τ( θ ˆ, R) = [ τ1,..., τ M ], where τ denotes the ansfer that WSTA needs to pay durng the current SI. By partcpatng n the resource allocaton game, WSTA gans the payoff υ (, θˆ θ, R ) = u ( t, θ ) + τ, whch s always non-negatve n the VCG mechansm [14]. In summary, we propose to mplement the followng dynamc, game-theoretc resource allocaton at the CSM sde durng each SI. 1. Socal decson: After recevng the announced type profle θˆ = ( θˆ ˆ 1,..., θ M ) from the WSTAs, the CSM decdes the resource allocaton T(, θ ˆ R ) such that the mult-user wreless system utlty (.e. the sum of utltes of all WSTAs) s maxmzed. 2. Transfer Computaton: Next, t computes the ansfers τ(, θ ˆ R ) assocated wth ths resource allocaton to enforce the WSTA to reveal ther real type uthfully. 3. Pollng WSTAs: The CSM polls the WSTAs for packet ansmsson accordng to the allocated tme. At the WSTAs sde, the subsequent steps are performed by WSTA n order to play the resource management game. 1. Prvate nformaton estmaton: Each WSTA estmates the antcpated prvate nformaton x, whch ncludes the antcpated vdeo source characterstcs ξ and channel condtons n terms of SNR. 2. Selecton of mal jont sategy and correspondng type : Based on the prvate nformaton, WSTA determnes the mal jont sategy to play the resource allocaton game,.e. κ = ( s, µ ) = argmax υ ( θˆ, θ, R) κ = ( s, µ ) S V = arg max { u ( t, θ ) + τ }. (2) κ = ( s, µ ) S V max θ Delay s.. t Delay( t, ) Note that the WSTA cannot explctly solve the above mzaton problem, snce both the resource allocaton

11 11 t and the ansfer τ depend on the announced types of the other WSTAs, whch are not known by ths staton. However, n Secton IV, we prove that whenever the VCG mechansm s used, the mal jont sategy can be smply determned by frst proactvely selectng the antcpated mal cross-layer sategy s that maxmzes the antcpated receved vdeo qualty wthout consderng the mpact of the other WSTAs. Then, based on ths, the mal revealng sategy µ through whch the real (uthful) type (ncludng wllngness-to-pay atttude) s revealed s determned,.e. ˆ θ = µ ( θ ) = θ. The detals of the antcpated cross-layer sategy, revealng sategy and type computaton are presented n Secton III. 3. Reveal the type to CSM: The determned type θ ˆ s declared by each WSTA to the CSM. 4. Transmt vdeo packets: When polled by the CSM, each WSTA determnes and deploys the mal real-tme cross-layer sategy s for vdeo ansmsson that maxmzes the antcpated receved vdeo qualty. Ths cross-layer sategy s determned as dscussed n Secton III.B. Note that whle the ansfers are computed for each WSTA durng every SI, the CSM can communcate and charge the WSTA the ncurred (cumulatve) ansfer every couple of SIs. The precse detals of the chargng mechansm and the protocol used for ths are beyond the scope of ths paper. For nstance, a mechansm that can be used for chargng WSTAs can be found n [16]. Summarzng, to play the resource management game, WSTAs deploy three dfferent types of sateges at dfferent stages of the ansmsson: the antcpated mal cross-layer sateges and the revealng sateges (pror to the actual ansmsson, n order to determne the announced type) and the mal real-tme cross-layer sategy (n real-tme, durng the actual ansmsson). These varous sateges wll be descrbed n detal n the next secton. Fgure 1. Mechansm desgn framework for the mult-user wreless vdeo resource allocaton game.

12 12 III. PROACTIVE CROSS-LAYER STRATEGIES FOR PLAYING THE RESOURCE MANAGEMENT GAME To decde the mal jont sateges for playng the dynamc resource allocaton game, the WSTAs need to frst determne the antcpated mal cross-layer sategy by consderng the antcpated prvate nformaton. Subsequently, based on the antcpated mal cross-layer sategy and wllngness-to-pay for resources, each WSTA determnes ts own type and the utlty for varous tme allocatons. In current wreless vdeo ansmsson systems, the real-tme cross-layer sategy s aded on-the-fly to mze the antcpated receved vdeo qualty, as shown n Equaton (1). However, n our resource allocaton game, each WSTA has to determne the antcpated mal cross-layer sategy that maxmzes ts receved antcpated vdeo qualty at the begnnng of every SI. The antcpated mal cross-layer sategy s computed before ansmsson, n order to decde the sategy (type) for playng the game. Note that the antcpated cross-layer sategy may dffer from the real-tme cross-layer sategy that the WSTA wll actually deploy at ansmsson tme, when t s polled by the CSM. However, the antcpated cross-layer sategy and real-tme cross-layer sategy wll appertan to the same sategy set S. The secton s organzed as follows. In Subsecton A, we present a sategy for prortzng the vdeo packets nto multple classes. In Subsecton B, we dscuss how WSTAs can mze ther cross-layer sateges at ansmsson tme. In Subsecton C, we determne how WSTAs can antcpate ths mal cross-layer sategy that wll be used at ansmsson tme. Fnally, n Subsecton D, the type for each WSTA and the correspondng utlty are derved based on the antcpated cross-layer sategy. A. Vdeo Prorty Classes In [19][20], t has been shown that parttonng the packets nto dfferent prorty classes and correspondngly adjustng the ansmsson sateges for each class can sgnfcantly mprove the overall receved qualty and provde graceful degradaton as congeston levels and channel condtons are changng. In ths paper, we assume that each WSTA ansmts a pre-encoded vdeo seam n real-tme to another WSTA over a one-hop wreless nfrasucture. Based on ther mpact on the overall dstorton and ther delay consants, we dvde the packets of each encoded vdeo seam nto several prorty classes. For compressng the vdeo, we ad a 3D wavelet codec that uses a spato-temporal wavelet ansform followed by embedded codng [21]. However, note that ths coder s smply used for llusaton purposes and the proposed framework can be appled usng any alternatve vdeo codng scheme (e.g. a hybrd vdeo coder such as MPEG-2, MPEG-4 or H.264). As n [20], we determne the prorty classes by jontly consderng the conbuton of the packets to the reconsucted vdeo qualty and ther delay deadlnes. We assume that all the packets correspondng to a specfc Group Of Pctures (GOP) that are n a certan class have the same qualty conbuton and delay deadlne. For smplcty, we also assume that the packet length L (whch ncludes the varous packet headers etc.) stays the same for a specfc WSTA. The number of prorty classes for WSTA equals the number of packets n class h (1 h H ) for GOP g equals K gh,,. H and Summarzng, each packet k ( 1 k Kgh,, ) of class h n GOP g s assocated wth the followng parameters: the

13 packet length L (n bts), the delay deadlne Delay gh,, and the qualty conbuton λ h, (see [20] for more detals). The qualty conbuton λ h, depends on the underlyng vdeo characterstcs, encodng parameters, etc. and typcally ncreases wth the mportance or dstorton mpact of the packet. We assume that the classes are prortzed n decreasng order of ther qualty conbuton,.e. λ,1 > λ,2 >... > λ, H. Due to the herarchcal temporal sucture deployed n 3D wavelet vdeo coders, as shown n [20][21], the packets wth the largest qualty conbuton are scheduled frst for ansmsson. Hence, n ths paper, we also assume Delayg,,1... DelaygH,,. B. Cross-layer Desgn for Real-tme Transmsson The real-tme cross-layer sategy s chosen on-the-fly such that the receved vdeo qualty s mzed. Let I ghk,,, be an ndcator functon whch s equal to 1, when the k -th packet n class h of GOP g of WSTA s receved succ successfully, and 0 otherwse. The probablty that Ighk,,, equals to 1 s denoted as P ghk,,,. Let η gh,, ( 0 ηgh,, Kgh,, ) be the number of packets of class h of GOP g remanng n the ansmsson queue at the begnnng of the current SI. The antcpated receved vdeo qualty 8 of WSTA durng the current SI 9, assumng a certan tme allocatont, can 13 be computed as H Kgh,, rec succ g, ( ) ghk,,, λh, h= 1 k= K η + 1 Q t P =. (3) gh,, gh,, Then, the mal real-tme cross-layer sategy can be determned n real-tme to maxmze the receved vdeo qualty as rec g, s = arg max Q ( t) s S, (4) st.. I Tme Delay,forall h, k ghk,,, ghk,,, gh,, where 1 h H, Kgh,, ηgh,, + 1 k Kgh,, and Tmeghk,,, s the current ansmsson tme for the k -th packet n class h of GOP g of WSTA. In the followng, we llusate how the mal real-tme cross-layer sategy s determned. Modulaton mode at PHY layer and reansmsson lmt at MAC layer Let γ ϒ denote the PHY layer modulaton mode aded by WSTA, and modes for WSTA. Gven the experenced channel condton rate esnr (, γ ) [22]. Then, the packet loss probablty s gven by ϒ be the set of avalable PHY SNR, the modulaton mode γ determne the bt-error L P( SNR, γ, L ) = 1 (1 e( SNR, γ )). (5) phy The maxmum achevable bt rate R max ( γ ) can be determned by the specfc modulaton mode γ [22]. At the MAC layer, gven the packet loss rate n Eq.(5), the ansmtted packet rate can be computed as p phy Rmax( γ ) γ γ L R ( SNR,, L ) = (1 P( SNR,, L )). (6) 8 As before, we use a bar above the vdeo qualty mec to ndcate that ths s the expected receved qualty and not the actual qualty derved by the WSTA at ansmsson tme. 9 Ths mzaton assumes that, durng the current SI, only the packets n GOP g are ansmtted. When the length of SI s small, ths assumpton s reasonable.

14 max Gven the delay deadlne Delay gh,, of the packet, the maxmum number of ansmssons n ghk,,, (.e. the maxmum reansmsson lmt plus one) for a packet can be determned as t wll be shown later n ths secton. Then, the probablty that ths packet s successfully receved,.e. I ghk,,, = 1, becomes succ n max,,, Pghk,,, = 1 ( P ( SNR, γ, L)) ghk (7) 14 and the average ansmsson duraton for the packet s gven by packet ghk,,, t = R phy max max nghk,,, L 1 ( P ( SNR, γ, L)) ( γ ) 1 P ( SNR, γ, L ). (8) Followng a smlar approxmaton as n [5][20], the above average duraton becomes: packet ghk,,, t = R L 1. (9) ( γ )1 P ( SNR, γ, L ) phy max The mal PHY sategy s selected to mnmze the average ansmsson duraton per packet, such that a larger number of packets can be ansmtted and the receved vdeo qualty (based on Eq.(3)) s maxmzed. Thus, choosng the mal PHY mode can smply be done by maxmzng the effectve packet rate, snce γ packet ghk,,, = arg mn { t } γ ϒ phy max R ( γ ) = arg max{ (1 P( SNR, γ, L))} γ ϒ L = arg max{ R ( SNR, γ, L )} γ ϒ p (10) As shown n [20], wthn one GOP, the mal real-tme cross-layer sategy reansmts the most mportant packets untl ther delay deadlne expres. Wth the prortzaton n the APP layer descrbed n Secton III.A, the mal maxmum number of ansmssons for a specfc packet (gven the current ansmsson tme Tme ghk,,, ) can be computed n real-tme as n max, ghk,,, phy Rmax ( γ )( Delaygh,, Tmeghk,,, ) =. (11) L Delay-based and rsk-aware packet schedulng sateges at APP layer Besdes determnng the mal PHY mode selecton and MAC reansmsson lmt, the WSTA needs to determne the schedulng of the vdeo packets n the dfferent prorty classes. For ths, besdes the conventonal delay-based packet schedulng, we noduce a rsk-aware packet schedulng scheme whch enables WSTAs to reduce ther rsk of loosng the hgher prorty packets by ansmttng them pror to other packets that have an earler deadlne but have lower prorty. The delay-based packet schedulng ansmts the packets startng wth the most mportant class n a Frst-In-Frst-Output (FIFO) fashon. When the WSTA s polled, the packet at the head of the hghest prorty ansmsson queue s selected for the delay deadlne check. If the packet s deadlne s not expred, the packet s ansmtted; otherwse, the packet s dropped. As proven n [20], the mal delay-based schedulng s to ansmt the

15 15 packet untl t s receved or expred. However, ths schedulng does not consder possble future changes n the channel condton. For example, when the tme allocated to the WSTA s lmted (e.g. because the network s congested) or when the experenced channel condtons are bad, the mportant packets from subsequent GOPs should be ansmtted earler, even f the packets wth a low prorty (.e. wth lmted dstorton conbutons) n the current GOP are not expred. We refer to ths new packet schedulng as rsk-aware schedulng, whch adaptvely and proactvely determnes the schedulng tme for the packets across dfferent GOPs. For the packets wthn one GOP, the rsk-aware schedulng also ads the FIFO polcy. However, the mportant packets n the next GOP can be ansmtted pror to the lower prorty packets n the current GOP, even f these are not expred. Whenever the channel s congested, the rsk-aware scheme wll schedule for ansmsson the hgher prorty packets n subsequent GOPs ahead of tme, to ensure that at least the mnmum vdeo qualty s guaranteed for the WSTA. Formally, we defne t g rsk, + 1as the tme pror to the maxmum delay deadlne n GOP g that the packets n GOP g + 1 start to be ansmtted. When the current tme t cur s greater than the threshold ( Delaygh,, t g, + 1 remanng packets n GOP g are dscarded and the packets n GOP g + 1 are scheduled to be ansmtted. Otherwse, the remanng packets n GOP g are ansmtted n a FIFO fashon. Note that the delay-based schedulng s a partcular rsk case of rsk-aware schedulng wth, 1 = 0. The rsk-aware packet schedulng algorthm s presented n Table 2. t g+ The tme t g rsk, + 1 can be computed based on the vdeo rate requrement, the prvate nformaton as well as the rsk atttude of the WSTA for playng the game. It s worth to note that t g rsk, + 1 can be dynamcally determned by WSTAs. However, determnng the mpact of varous values of t g rsk, + 1 on the vdeo qualty performance of the WSTA as well as on ts ansfer s not consdered n ths paper and forms an mportant area of our future research. γ Summarzng, the mal real-tme cross-layer sategy s rsk ), the conssts of the PHY modulaton mode selecton computed n Eq.(10), the mal maxmum number of MAC ansmssons max, n computed n Eq.(11), the rsk-aware APP packet schedulng outlned n Table 2 and the APP packet prortzaton descrbed n III.A. C. Antcpated Cross-layer Sategy In the prevous subsecton, we have dscussed how the mal real-tme cross-layer sategy s s selected n real-tme. To play the resource allocaton game, the WSTAs need to determne what the antcpated beneft s n terms of utlty that they can derve durng the current SI. For that, they cannot determne the mal real-tme cross-layer sategy because ths depends on the nstantaneous prvate nformaton and the actual successful ansmsson of packets, whch are not known pror to the ansmsson tme. Instead, they wll determne what s the antcpated mal cross-layer sategy s. To compute the antcpated mal cross-layer sategy, the WSTA frst estmates the antcpated prvate nformaton x based on nformaton avalable for prevous SIs and avalable channel and source models. Hence, for the antcpated cross-layer sategy, the mal PHY mode s determned as n Eq.(10) by replacng SNR wth SNR. The delay-based or rsk-aware packet schedulng polcy can also be performed, wth the ghk,,,

16 only dfference that now the current ansmsson tme Tme ghk,,, s replaced by the expected ansmsson tme ghk,,, Tme. Table 2. Rsk-aware packet schedulng 10 for WSTA Intalzaton: Set the current tme t cur,determne the frst packet to be ansmtted,.e. specfy khg.,, Repeat: rsk If tcur Delay,, g H t, g + 1, g g + 1, h 1, k 1 else Tmeghk,,, tcur; f Tmeghk,,, Delaygh,,, k k + 1; // go to next packet f k > K gh,,, k 1, h h + 1 ; // go to next class f h > H, h 1, g g + 1 ; // go to next GOP end end end end max, Determne the reansmsson lmt n and the PHY mode ; ansmt the packet. ghk,,, Update the current tme t cur. Untl: WSTA s not polled or the ansmsson queue s empty. If we assume that the k0 -th packet n class h 0 of GOP g s stuated at the begnnng of the ansmsson queue, then the expected ansmsson tme for the k -th packet n class h ( h h0 ) s computed as γ Kgh,, 0 h 1 Kgm,, k 1 packet packet packet ghk,,, = gh,, 0, l + gml,,, + ghl,,, l= k0 m= h0+ 1 l= 1 l= 1. (12) Tme t t t In the above equaton, the frst term s the average tme needed to ansmt the remanng packets of class h 0, the second term s the average ansmsson tme for the packets of class h to h 1, and the thrd term s the average ansmsson tme for the packets of class h pror to the k -th packet. The prortzaton n the APP layer s also based on the prorty class llusated n Secton III.A. In the antcpated cross-layer sategy, we do not need to explctly determne the maxmum number of reansmsson for each packet. Instead, we only have to calculate the expected number of packets successfully ansmtted, gven a certan TXOP t n the current SI, as Hence, the maxmum number of prorty classes, be determned as H N p p = R t. (13), n whch all packets have been ansmtted n the current SI can H p = η,, g h h = 1 The number of packets ansmtted n classes h = 1,, H s η,, H max{ H N, 0 H H }. (14) gh. After ansmttng the packets n class h ( 1 h H ), the remanng ansmsson opportuntes are assgned to class H + 1 f H < H. Hence, the p H number of packets ansmtted n the class H + 1 s ( N η 1 gh,, ). Thus, the antcpated receved vdeo qualty h = durng one SI becomes The packet schedulng s performed when the ansmsson opportuntes are assgned to WSTA.

17 Note that we enforce λ, + 1 = 0 f H H H H rec p g, ( ) = ηgh,, λh, + (,, ) ηgh λ,( H + 1) h= 1 h= 1. (15) Q t N = H. In ths equaton, the frst term corresponds to the qualty gan obtaned from the vdeo classes n whch all packets have been ansmtted. The last term s the qualty gan from the last class p (.e the vdeo class H + 1 ) from whch ( N ηgh,, ) packets have been ansmtted. H h = 1 Summarzng, the antcpated mal cross-layer sategy s selecton as n Eq.(10) usng 17 determnes the mal PHY modulaton mode SNR, computes the expected number of successfully ansmtted packets as n Eq.(13) and ads the delay-based or rsk-aware packet schedulng polcy as dscussed n Secton III.B. Based on s, the antcpated receved vdeo qualty s derved as n Eq.(15). D. Determnng the True and Announced Type To play the resource allocaton game, the WSTAs not only have to proactvely determne the antcpated mal cross-layer sategy, but also they need to specfy the WSTAs wllngness-to-pay w for a certan vdeo qualty level,.e. acceptng to pay hgher/lower ansfer. In other words, the wllngness-to-pay w can be adapted based on the H mportance of the vdeo sequence. Specfcally, we denote the wllngness-to-pay as w = [ w,1,..., w, H ] +, where w h, (1 h H ) represents the mportance of the packets n the prorty class h (hence the utlty of the packet n the class h becomes wh, λ h, ). For example, w h, < 1 means that the packets n class h are less mportant for WSTA and ths WSTA s less wllng to pay for resources n order to ansmt them (.e. wants to pay for them only at a dscounted cost). On the other hand, w h, > 1 means that the packets n class h are more mportant to WSTA and ths WSTA s wllng to pay more for resources to ensure that they are ansmtted. Based on the dstorton conbuton of the packets n dfferent classes ( λ,1 > λ,2 >... > λ, H ), we can assume that w,1... w, H. Then, based on Eq.(15), the resultng utlty u( t, θ ) gven t becomes H H p (, θ) = η,, g h, hλ, h + (,, ) η g h,( H + 1) λ,( H + 1) h= 1 h= 1 u t w N w. (16) Note that the utlty functon u( t, θ ) depends on the GOP ndex g. However, to smplfy the notaton, we gnore the subscrpt g n the utlty functon u( t, θ ). Snce the packets wth dfferent prortes have already been ordered n descendng order of ther qualty conbuton, gven the allocated tme t, only the frst p N packets are successfully ansmtted. As shown n Secton IV.A, the socal decson wll depend on the form of the utlty functon (e.g. whether the utlty functon s concave). Thus, to smplfy the computaton of the socal decson, we allow the expected number of packets 11 p p to be a postve real number,.e. N = R t nstead of Eq.(13). Hence, the utlty functon u( t, θ ) n Eq.(16) can be rewrtten as 11 To smplfy the notaton, we use ue for the utlty u( t, θ ). p N for both the dscrete and the contnuous verson of expected number of successfully ansmtted packet. The same holds

18 H H ηgh,, p ηgh,, p θ =,, p hλ h + p,( H + 1) λ,( H + 1) h= 1 R h= 1 R u ( t, ) ( R w ) ( t )( R w ). (17) p For each class h, we defne the utlty gan per unt tme ρ h, as ρh, = Rwh, λh, and ansmsson duraton βh, as 12 p βh, ηgh,, R =. Then, the antcpated receved vdeo qualty n Eq.(17) becomes u ( t, θ ) = β ρ + ( t β ) ρ, h, h, h H, h= 1 h= 1 H H. (18) From the computaton of utlty n Eq.(18), t s suffcent for WSTA to report to the CSM the followng parameters: the utlty gan per unt tme for all the classes ρ, (1 h H ) and ansmsson duraton for all the classes h βh, (1 h H), snce they characterze the utlty functon over varous possble resource allocatons. Recall that, gven a certan tme allocaton t, the type of WSTA, θ, should fully determne the ganed utlty. Hence, the type of WSTA, θ, ncludes: the ansmsson duraton for each class: β h, (1 h H ); the utlty gan per unt tme for each class: ρ h, (1 h H ). To play the resource allocaton game, each WSTA ads ts revealng sategy µ to announce ts type to CSM. The revealng sategy µ can be used to exaggerate, understate or uly report the values of the ansmsson duraton β h, and utlty gan per unt tme h, ρ. The announced values are denoted as, Correspondngly, the announced type θ ˆ = µ ( θ ) becomes the ansmsson duraton for each class: β ˆ, h (1 h H ); the utlty gan per unt tme for each class: ρ ˆ, h (1 h H ). β ˆ h + and, ρ ˆ h + 18, respectvely. In ths paper, we smply assume that ρˆ,1... ρˆ, h such that the utlty functon derved at CSM sde stll has the concavty property. Hence, the announced utlty functon whch CSM beleves s computed as Note that ρ ˆ, + 1 = 0 f H H A. VCG Mechansm Desgn = H. H H. (19) u ( t, θˆ) = βˆ ρˆ + ( t βˆ ) ρˆ, h, h, h H, h= 1 h= 1 IV. MECHANISM DESIGN FOR RESOURCE ALLOCATION As mentoned n the noducton, the key challenges for effcent mult-user wreless resource management are two-fold. Frst, an effcent and far mechansm for allocatng the TXOPs among WSTAs needs to be developed. Second, snce the effcency of the resource management algorthms heavly depend on the uthful declaraton of the resource requrements by the selfsh WSTAs, a mechansm needs to be mplemented n the CSM to prevent the WSTAs from exaggeratng ther resource requrement and msusng the avalable resources. To address the above two challenges, n the proposed resource allocaton, the VCG mechansm renders two tasks: 1) t makes a socal decson 12 Note that we gnore the subscrpt g here.