Queuing-Based Dynamic Channel Selection for Heterogeneous Multimedia Applications over Cognitive Radio Networks

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1 1 Queung-Based Dynamc Channel Selecton for Heterogeneous ultmeda Applcatons over Cogntve Rado Networks Hsen-Po Shang and haela van der Schaar Department of Electrcal Engneerng (EE), Unversty of Calforna Los Angeles (UCLA) Los Angeles, CA {hpshang, ABSTRACT In ths paper, we propose a dynamc channel selecton soluton for autonomous wreless users transmttng delay-senstve multmeda applcatons over cogntve rado networks. Unlke pror works that seldom consder the requrement of the applcaton layer, our soluton explctly consders varous rate requrements and delay deadlnes of heterogeneous multmeda users. Note that the users usually possess prvate utlty functons, applcaton requrements, and dstnct channel condtons n dfferent frequency channels. To effcently manage avalable spectrum resources n a decentralzed manner, nformaton exchange among users s necessary. Hence, we propose a novel prorty vrtual queue nterface that determnes the requred nformaton exchanges and evaluates the expected delays experenced by varous prorty traffcs. Such expected delays are mportant for multmeda users due to ther delay-senstvty nature. Based on the exchanged nformaton, the nterface evaluates the expected delays usng prorty queung analyss that consders the wreless envronment, traffc characterstcs, and the competng users behavors n the same frequency channel. We propose a Dynamc Strategy Learnng (DSL) algorthm deployed at each user that explots the expected delay and dynamcally adapts the channel selecton strateges to maxmze the user s utlty functon. We smulate multple vdeo users sharng the cogntve rado network and show that our proposed soluton sgnfcantly reduces the packet loss rate and outperforms the conventonal sngle-channel dynamc resource allocaton by almost 2dB n terms of vdeo qualty. Index Terms: cogntve rado networks, resource management for heterogeneous users, delay-senstve multmeda applcatons, queung analyss. The work was supported by ONR.

2 2 I. INTRODUCTION The demand for wreless spectrum has ncreased rapdly n recent years due to the emergence of a varety of applcatons, such as wreless Internet browsng, fle downloadng, streamng, etc. In the foreseeable future, the requrements for wreless spectrum wll ncrease even more wth the ntroducton of multmeda applcatons such as YouTube, peer to peer multmeda networks, and dstrbuted gamng. However, scannng through the rado spectrum reveals ts neffcent occupancy [2] n most frequency channels. Hence, the Federal Communcatons Commsson (FCC) suggested n 2002 [1] mprovements on spectrum usage to effcently allocate frequency channels to lcense-exempt users wthout mpactng the prmary lcensees. Ths forms cogntve rado networks that 1) enhance the spectrum usage of the tradtonal lcensng system, and 2) release more spectrum resources for the unlcensed allocatons n order to fulfll the requred demand. The emergence of cogntve rado networks have spurred both nnovatve research and ongong standards [3][4][6][7]. Cogntve rado networks have the capablty of achevng large spectrum effcences by enablng nteractve wreless users to sense and learn the surroundng envronment and correspondngly adapt ther transmsson strateges. Three man challenges arse n ths context. The frst problem s how to sense the spectrum and model the behavor of the prmary lcensees. The second problem s how to manage the avalable spectrum resources and share the resource to the lcense-exempt users to satsfy ther transmsson requrements whle not nterferng wth the prmary lcensees. The thrd problem s how to mantan seamless communcaton durng the transton (hand-off) of selected frequency channels. In ths paper, we focus on the second challenge and rely on the exstng lterature for the remanng two challenges [23][26]. Pror research such as [3][6] focus on centralzed solutons for the resource management problem n cogntve rado networks. However, due to the nformatonally-decentralzed nature of wreless networks, the complexty of the optmal centralzed solutons for spectrum allocaton s prohbtve [8] for delay-senstve multmeda applcatons. oreover, the centralzed soluton requres the propagaton of prvate nformaton back and forth to a common coordnator, thereby ncurrng delay that may be unacceptable for delay-senstve applcatons. Hence, t s mportant to mplement decentralzed solutons for dynamc channel selecton by relyng on the wreless multmeda users capabltes to sense and adapt ther frequency channel selectons. oreover, unlke

3 3 most of the exstng research on resource management n the cogntve rado networks [10][22] that gnores the multmeda traffc characterstcs n the applcaton layer and assumes that all competng users n the networks are of the same type (applcatons, rado capabltes), we consder heterogeneous users n ths paper, meanng that the users can have 1) dfferent types of utlty functons and delay deadlnes, 2) dfferent traffc prortes and rates, and 3) experence dstnct channel condtons n dfferent frequency channels. For example, the multmeda users can dffer n ther preferences of utlty functons, prortes of accessng the frequency channels, traffc rate requrements, capabltes of transmttng data n dfferent frequency channels. Note that n the nformatonally-decentralzed wreless network, these utlty functons, traffc characterstcs, and the channel condtons are usually consdered as prvate nformaton of the users. Hence, the man challenge here s how to coordnate the spectrum sharng among heterogeneous multmeda users n a decentralzed manner. To do ths, nformaton exchange across the multmeda users s essental. Snce the decsons of a user wll mpact and be mpacted by the other users selectng the same frequency channel, wthout explct nformaton exchange, the heterogeneous users wll consume addtonal resources and respond slower to the tme-varyng envronment [27]. The key questons are what nformaton exchanges are requred, and how autonomous users adapt ther channel selectons based on the lmted nformaton exchange to effcently maxmze ther prvate utltes. In ths paper, we propose a novel prorty vrtual queue nterface to abstract multmeda users nteractons and determne the requred nformaton exchange accordng to the prorty queung analyss. Note that such nformaton exchanges can rely on a dedcated control channel for all users, or can use a group-based scheme wthout a common control channel [19]. In ths paper, we model the traffc of the users (ncludng the lcensed users and the lcense-exempt users) and the channel condtons (e.g. Sgnal-to-Nose Rato, Bt-Error-Rate) by statonary stochastc models smlar to [22]. Our approach endows the prmary lcensees wth the prorty to preempt the transmssons of the lcense-exempt users n the same frequency channel. Based on the prorty queung analyss, each wreless user can evaluate ts utlty mpact based on the behavors of the users deployng the same frequency channel (ncludng the prmary lcensees, to whch the hghest prorty s assgned). The behavor of a user s represented by ts probablty profle for selectng dfferent frequency channels, whch s referred as the channel selecton strategy n ths paper. Based on the expected utlty evaluaton, we propose a Dynamc Strategy Learnng (DSL)

4 4 algorthm for an autonomous multmeda user to adapt ts channel selecton strategy. In summary, our paper addresses the followng mportant ssues: a) Separaton of the utlty evaluaton and channel selecton usng the prorty vrtual queue nterface. We propose a novel prorty vrtual queue nterface for each autonomous user to exchange nformaton and maxmze ts prvate utlty n cogntve rado networks. Through the nterface, the user can model the strateges of the other users wth hgher prortes and evaluates the expected utlty of selectng a certan frequency channel. Importantly, the nterface provdes a smple model that facltates the user s learnng of what s the best channel selecton strategy. b) Prorty vrtual queung analyss for heterogeneous multmeda users. Unlke pror works on cogntve rado networkng, whch seldom consder multmeda traffc characterstcs and delay deadlnes n the applcaton layer, our prorty vrtual queue framework enables the autonomous multmeda users to consder 1) prortes of accessng the frequency channels, 2) dfferent traffc loads and channel condtons n dfferent frequency channels, and 3) heterogeneous preferences for varous types of utlty functons based on the deployed applcatons. Note that the prorty queung model allows the prmary lcensees to actvely share the occuped channels nstead of excludng all the other wreless users. However, by assgnng hghest preemptve prortes to the lcensees, the unlcensed users do not mpact the lcensees. c) DSL algorthm for dynamc channel selectons by wreless statons. Based on the expected utlty evaluaton from the nterface, we propose a decentralzed learnng algorthm that dynamcally adapts the channel selecton strateges to maxmze the prvate utlty functons of users. Note that a frequency channel can be shared by several users. A wreless user can also select multple frequency channels for transmsson. Our learnng algorthm addresses how multmeda users dstrbute traffc to multple avalable frequency channels to maxmze ther own utlty functons. The rest of ths paper s organzed as follows. Secton II provdes the specfcaton of cogntve rado networks and models the dynamc resource management problem as a mult-agent nteracton problem. In Secton III, we gve an overvew of our dynamc resource management for the heterogeneous multmeda users, ncludng the prorty vrtual queue nterface and the dynamc channel selecton. In Secton IV, we provde the queung analyss for the prorty vrtual queue nterface and determne the requred nformaton exchange. In Secton V,

5 5 we focus on the dynamc channel selecton and propose the DSL algorthm to adapt the channel selecton strategy for the multmeda users. Smulaton results are gven n Secton VI. Secton VII concludes the paper. II. ODELING THE COGNITIVE RADIO NETWORKS AS ULTI-AGENT INTERACTIONS A. Agents n a cogntve rado network In ths paper, we assume that the followng agents nteract n the cogntve rado network: Prmary Users are the ncumbent devces possessng transmsson lcenses for specfc frequency bands (channels). We assume that there are channels n the cogntve rado network, and that there are several prmary users n each frequency channel. These prmary users can only occupy ther assgned frequency channels. Snce the prmary users are lcensed users, they wll be provded wth an nterference-free envronment [4][23]. Secondary Users are the autonomous wreless statons that perform channel sensng and share the avalable spectrum holes [3]. We assume that there are N secondary users n the system. These secondary users are able to transmt ther traffc usng varous frequency channels. If multple users select the same frequency channel, they wll tme share the chosen frequency channel. oreover, these secondary users are lcense-exempt, and hence, they cannot nterfere wth the prmary users. In ths paper, we consder the users sharng a sngle-hop wreless ad-hoc network. Fgure 1 provdes an llustraton of the consdered network model. We assume the secondary users as transmtter-recever pars wth nformaton exchange among these pars. In order to mantan statonary property, we assume that these network agents are statc (.e. we do not consder moblty effects). Next, we model the nteracton among secondary users accessng the same frequency channel. F 1 SU 2 PU 1 ultmeda flow Sensng feedback (e.g. SINR) Informaton exchange SU 1 F 2 F 3 PU 3 PU 2 Fg. 1 An llustraton of the consdered network model.

6 6 B. odelng of the dynamc resource management problem as a mult-agent nteracton Users: As ndcated above, there are two sets of users aggregate prmary users n each channel PU = { PU1,..., PU } 1 and the secondary users SU = { SU1,..., SU N }. The prortes of users n cogntve rado networks are pre-assgned dependng on ther Qualty of Servce (QoS) requrements and ther rght to access the frequency channels. Resources: The resources are the frequency channels F = { F1,..., F }. ultple users can tme share the same frequency channel. Note that even f the same tme sharng fracton s assgned to the users choosng the same frequency channel, ther experenced channel condtons may dffer. Actons: The consdered actons of the secondary users are the selecton of the frequency channel for each packet transmsson. We denote the actons of a secondary user a = [ a, a,..., a ] A, SU usng 1 2 where a A ( A ={0,1} ). a = 1 ndcates that SU chooses the frequency channel F. Otherwse, a = 0. Let a denote the actons of the other secondary users except SU. Let T T N 1 N A = [ a,..., a ] A denote the total acton profle across all secondary users. Strateges: A strategy of a secondary user SU s a vector of probabltes s = [ s1, s2,..., s] S, where s S ( S [0,1] ) represents the probablty of the secondary user SU to take the acton a (.e. to choose the frequency channel F ). Hence, the summaton over all the frequency channels s s = 1 channel = 1. Note that s can also be vewed as the fracton of data from SU transmtted on frequency F, and hence, multple frequency channels are selected for a secondary users wth s > 0. Let T T N 1 N S = [ s,..., s ] S denote the total strategy profle across all secondary users. Utlty functons: Each secondary user has ts own utlty functon. Based on the adopted actons of the secondary users, we denote the utlty functon of SU as u. Conventonally, the utlty functon of a specfc user s often modeled solely based on ts own acton,.e. u ( a ) wthout modelng the other 1 From the secondary users pont of vew, there s no need to dfferentate dfferent prmary users n one frequency channel. Hence, we reduce the prmary users n one frequency channel nto one aggregate prmary user. A secondary user needs to back-off and wat for transmsson or select another frequency channel, once any of the prmary users starts to transmt n the same frequency channel.

7 7 secondary users [8][28]. However, the utlty functon for multmeda users relates to the effectve delay and throughput that a secondary user can derve from the selected frequency channel, whch s coupled wth the actons of other secondary users. Hence, the utlty functon u s also nfluenced by the acton of other secondary users that select the same frequency channel. In other words, the utlty functon can be regarded as u ( a, a ). We wll dscuss ths utlty functon n detal n Secton III.C. Expected utlty functon wth dynamc adaptaton: In an nformatonally-decentralzed cogntve wreless network that conssts of heterogeneous secondary users, the secondary user SU may not know the exact actons of other secondary users a. oreover, even f all the actons are known, t s unrealstc to assume that the exact acton nformaton can be collected tmely to compute and maxmze the actual utlty functon u ( a, a ). Hence, a more practcal soluton s to dynamcally model the other secondary users behavor by updatng ther probablstc strategy profle of actons s based on the observed nformaton, and then compute the optmal channel selecton strategy s that maxmzes the expected utlty functon of SU,.e. U ( s, s ) E [ u ( a, a )], (1) = ( s, s ) where E( s, s )[ u ( a, a )] s the expected utlty functon, gven a fxed strategy profle S = ( s, s ). In the next secton, we dscuss how secondary users perform dynamc resource management that maxmzes the expected utlty functon U( s, s ) by modelng the strategy (behavor) s of the other users n cogntve rado networks. III. DYNAIC RESOURCE ANAGEENT FOR HETEROGENEOUS SECONDARY USERS USING PRIORITY QUEUING In ths secton, we provde our dynamc resource management soluton usng the mult-agent nteracton settngs n the prevous secton. We frst emphasze the heterogenety of the secondary users n cogntve rado networks and then ntroduce our soluton wth the prorty queung nterface and adaptve channel selecton strateges.

8 8 A. Prortzaton of the users We assume that there are K prorty classes of users n the system. The hghest prorty class C 1 s always reserved for the prmary users PU n each frequency channel. The heterogeneous secondary users SU can be categorzed nto the rest of K 1 prorty classes ( C2,..., C K ) to access the frequency channels 2. We assume that the users n hgher prorty classes can preempt the transmsson of the lower prorty classes to ensure an nterference-free envronment for the prmary users [14]. The prorty of a user affects ts ablty of accessng the channel. Prmary users n the hghest prorty class C 1 can always access ther correspondng channels at any tme. Secondary users, on the other hand, need to sense the channel and wat for transmsson opportuntes for transmsson (when there s no hgher prorty users usng the channel) based on ther prortes. We assume that there are N k users n each of the class C k. Hence, N 1 = (number of aggregate prmary users) and K k = 2 N k = N (number of secondary users). Varous multple access control schemes can be adopted for the secondary users to share the spectrum resource. For smplcty, n ths paper, we consder a AC protocol smlar to IEEE e HCF [12] 3 to assgn transmsson opportuntes (.e. TXOP) and ensure that a secondary users n the lower prorty class wll stop accessng the channel and wat n the queue or change ts acton (channel selecton) f a hgher prorty user s usng the frequency channel. Note that for secondary users, they not only can have dfferent prortes to access the frequency channels, but they can also have dfferent channel condtons and possess ther own preferences for a certan type of utlty functon, whch s dscussed n the followng subsectons. B. Channel condtons of the heterogeneous secondary users For a certan frequency channel F, the secondary users can experence varous channel condtons for the same frequency channel. We denote T and p as the resultng physcal transmsson rate and packet error rate for the secondary user SU transmttng through a certan frequency channel F. Let R = [ T, p ] R 2 The prortzaton of the secondary users can be determned based on ther applcatons, prces pad for spectrum access, or other mechansm desgn based rules. In ths paper, we wll assume that the prortzaton was already performed. 3 Ether the pollng-based HCCA or contenton-based EDCA protocols can be appled, as long as the prorty property of the users s provded. However, a more sophstcated AC protocols can also be consdered to deal wth the spectrum heterogenety (such as HD-AC n [19]). Dfferent AC protocols wll have dfferent overheads ncludng the tme of watng for the AC acknowledgement, contenton perod, etc. that affect the servce tme dstrbuton of the /G/1 queung model.

9 9 be the channel condtons of the channel F for the secondary user SU. We denote the channel condton N matrx as R = [ R ] R. The expected physcal transmsson rate and packet error rate can be approxmated as sgmod functons of measured Sgnal-to-Interference-Nose-Rato (SINR) and the adopted modulaton and codng scheme as n [17]. Note that the expected can be dfferent for varous secondary users. T and p of the same frequency channel C. Goals of the heterogeneous secondary users In general, the utlty functon u s a non-decreasng functon of the avalable transmsson rates. Several types of obectves for the secondary users can be consdered n practce, such as mnmzng the end-to-end delay, loss probablty, or maxmzng the receved qualty, etc. For smplcty, we assume only two types of utlty functons 4 n ths paper. The delay-based utlty for delay-senstve multmeda applcatons. Let D ( a, a ) represent the end-to-end packet delay (transmsson delay plus the queung delay) for the secondary user SU. Let d represent the delay deadlne of the applcaton of secondary user SU. We consder ths type of utlty functon as (as n [20]): u (1) ( a, a ) = Prob( D ( a, a ) d ), (2) whch depends on the end-to-end delay D( a, a ) and the delay deadlne d mposed by the applcaton. The throughput-based utlty for delay-nsenstve applcatons. Let eff T represent the effectve avalable throughput for the secondary user SU. The second type of utlty functon s assumed to be drectly related to the throughput (as n [18]). In ths paper, we defne t as: where u (2) eff T ( a, a ) max, f eff (, ) (, ) T a a a a T = eff 1, f T ( a, a ) > max T max T max T s the physcal throughput requred by the secondary user SU., (3) We assume that a secondary user can possess multple applcatons that can be ether delay-senstve 4 Ths model can be easly extended to more types of utlty functons. oreover, our utlty functon can also be easly modfed to a qualty-type utlty functon usng dfferent prortes. For smplcty, we do not consder the qualty mpact of dfferent multmeda packets n our utlty functon.

10 10 multmeda traffc or delay-nsenstve data traffc. Hence, we defne the utlty functon of a secondary user as a mult-crteron obectve functon (as n [6][21]) of these two types of utlty functons. Dfferent secondary users can have dfferent preferences θ 5 (0 θ 1). Specfcally, the goal of a secondary user SU s to maxmze the followng utlty functon: Note that, n ths settng, 0 u ( a, a ) 1. (1) (2) θ + θ u ( a, a ) = u ( a, a ) (1 ) u ( a, a ). (4) D. Example of three prorty classes wth dfferent utlty functons Let A k be the acton set of the secondary users n the classes C2,..., C k,.e. Ak = { a SU Cl, l = 2,..., k}. Note that Ak 1 Ak A. Due to the prorty queung structure, the actons of the secondary users wth lower prorty wll not affect the users n the hgher prorty class [11]. Hence, the decentralzed optmzatons are performed startng from the hgher prorty classes to the lower prorty classes. In other words, the decentralzed optmzaton of a secondary user n a lower prorty class also needs to consder the actons of the users n hgher prorty classes. For example, three classes can be assumed ( K = 3 ) the frst prorty class s composed by the prmary users whose actons are fxed (no channel selecton capablty). The second prorty class C 2 s composed by the secondary users transmttng delay-senstve multmeda applcatons, and the thrd prorty class C 3 s composed by the secondary users transmttng regular data traffc, whch requres throughput maxmzaton. The obectve functon for each of the secondary users n prorty class C 2 s ( 1, for SU C2 θ = ): (1) maxmze U ( s, s ). (5) maxmze E [Prob( D ( A ) d ))] ( s, s ) 2 Then, the obectve functon for the secondary users n the class C 3 s ( θ = 0, for SU C3 ): (2) maxmze U ( s, s ), (6) eff maxmze E [ T ( A)] ( s, s ) wth the constrant that A2 A are predetermned by (5). The effectve transmsson rate of each secondary 5 In ths paper, we assume that the preferences θ are predetermned by the secondary users. The preferences can be determned based on the applcatons. See e.g. [15]. θ of the mult-crteron optmzaton

11 11 user can be expressed as: eff E s s [ T ( A )] = s T (1 p ). (7) (, ) = 1 From the above three classes example, note that delay analyss s essental for the heterogeneous secondary users wth delay-senstve applcatons n a cogntve rado network. To maxmze the expected utlty functon as stated n equaton (1), a secondary user needs to consder the mpact of the other secondary users. In order to effcently regulate the nformaton exchange among heterogeneous users and effcently provde expected utlty evaluaton, a coordnaton nterface must be developed. Based on ths nterface, the secondary users can nteract wth each other n a decentralzed manner. In the next subsecton, we propose a novel dynamc resource management wth such an nterface for a secondary user SU to adapt ts frequency selecton strategy s. E. Dynamc resource management wth prorty vrtual queue nterface The resource management for delay-senstve multmeda applcatons over cogntve rado networks needs to consder the heterogeneous wreless users havng varous utlty functons, prortes of accessng the channel, traffc rates, and channel condtons. Specfcally, the man challenge s how to coordnate the spectrum sharng among competng users and select the frequency channel to maxmze the utlty functons n a decentralzed manner. For ths, we propose a novel prorty vrtual queue nterface. Unlke pror research assumng that secondary users apply 2-state spectrum holes (on-off model [22]) for spectrum access [4] n our prorty vrtual queue nterface, we allow secondary users to obtan transmsson opportuntes once the prmary user n a specfc channel stops transmttng. The prmary users have the hghest prorty, thereby beng able to preempt the transmsson of the secondary users transmsson. The prorty vrtual queue nterface has two man tasks 1) determnes the requred nformaton exchange and 2) evaluates the utlty mpact from the wreless envronment as well as the competng users behavors n the same frequency channel. In the prorty vrtual queue nterface of a user, the vrtual queues are preemptve prorty queues [14] for each of the frequency channels. They are emulated by each multmeda user to estmate the delay of selectng a specfc frequency channel for transmsson. Fgure 2 llustrates the archtecture of the proposed dynamc resource management wth prorty vrtual queue nterface that exchanges nformaton and

12 12 emulates the expected delay. Note that these vrtual queues are n fact dstrbuted (physcally located) at the secondary users. Cogntve Rado Network SU 1... SU... SU N Informaton exchange SU 1 Prorty queung performance Prorty vrtual analyss queue nterface s 1 U 1 Dynamc Dynamc channel channel Dynamc selecton strategy selecton adaptaton Heterogeneous traffc PU 1 PU PU Transmsson opportunty from the AC protocol F 1 F F Prorty vrtual queues for each of the wreless channels Fg. 2 The archtecture of the proposed dynamc resource management wth prorty vrtual queue nterface. The mplementaton of the dynamc resource management wth prorty vrtual queue nterface of the secondary users s presented below: 1. Informaton exchange collecton: The secondary user SU collect the requred nformaton from other secondary users through the prorty vrtual queue nterface. The requred nformaton exchange wll be dscussed n Secton IV.D based on the queung analyss. 2. Prorty queung analyss: The nterface estmates s and performs prorty queung analyss based on the observed nformaton to evaluate the expected utlty U ( s, s ). The prorty queung analyss wll be dscussed n detals n Secton IV. 3. Dynamc strategy adaptaton: Based on the expected utlty U ( s, s ), the secondary user adapts ts channel selecton strategy s. We propose a dynamc strategy learnng algorthm, whch wll be dscussed n detal n Secton V. 4. Assgn actons for each packet based on the strategy: Based on current channel selecton strategy s, SU can assgn to each packet an acton (select frequency channel accordng to the probablty profle). As the channel selecton strategy adapts to the network changes, the behavor of a secondary user selectng the frequency channels for ts packets wll also change. 5. Wat for the transmsson opportunty and transmt the packets: The packets wat n queues to be

13 13 transmtted. Based on the prortes of the users, the hgher prorty secondary users wll have a better chance to access the channel and transmt ther packets. Note that the prmary users wll transmt whenever needed n ther correspondng frequency channels. Next, we present the prorty queung analyss for delay-senstve multmeda users to evaluate U ( s, s ). IV. PRIORITY QUEUING ANALYSIS FOR DELAY-SENSITIVE ULTIEDIA USERS In ths secton, we dscuss the prorty queung analyss for delay-senstve multmeda applcatons. It s mportant to note that the packets of the competng wreless users are physcally watng at dfferent locatons. Fgure 3 gves an example of the physcal queues for the case of frequency channels and N secondary users. Each secondary user mantans physcal queues for the varous frequency channels, whch allows users to avod the well-known head-of-lne blockng effect [24]. The channel selecton decsons are based on the queung analyss, whch wll be dscussed n detal n Secton V. In ths secton, we focus on the prorty queung analyss from the perspectve of each secondary user to evaluate U ( s, s ). PU 1 PU 2 Physcal queues at the secondary users SU 1 to F 1 V 1 to F 2 s 1 to F SU 2 to F 1 V 2 to F 2 s 2 to F Cogntve Rado a 11 a 12 Network a 21 a 22 a = a = 1 0 PU a a 1 2 V N SU N s N to F 1 to F 2 a N 1 a N 2 a N to F F 1 F 2 F Fg. 3 Actons of the secondary users Vrtual queues for dfferent frequency channels a and ther physcal queues for each frequency channel A. Traffc models of the users Traffc model for prmary users We assume that the statonary statstcs of the traffc patterns of prmary users can be modeled by all secondary users. The packet arrval process of a prmary user s modeled as a Posson process wth average

14 14 packet arrval rate PU λ for the prmary user PU usng the frequency channel F. Note that the aggregaton of Posson processes of prmary users n the same frequency channel s stll Posson. We denote the m th moments of the servce tme dstrbuton of the prmary user PU n frequency channel PU m F as E[( X ) ]. We adopt an /G/1 model for the traffc descrptons. Note that ths traffc model descrpton s more general than a arkov on-off model [22], whch s a sub-set of our queung model wth an exponental dle perod and an exponental busy perod. Traffc model for secondary users We assume that the average rate requrement for the secondary user SU s B (bt/s). Let λ denote the average packet arrval rate of the secondary user SU usng the frequency channel F. Snce the strategy s represents the probablty of the secondary user SU takng acton a (transmttng usng the frequency channel F ), we have B λ = s, (8) L where L denotes the average packet length of the secondary user SU. If a certan secondary user SU can never use the frequency channel F, we fx ts strategy to s = 0, and hence, λ = 0. For smplcty, we also model the packet arrval process of the secondary users usng a Posson process. Note that the average arrval rate s the only suffcent statstcs requred to descrbe a Posson process. Snce packet errors are unavodable n a wreless channel, we assume that packets wll be retransmtted, f they are not correctly receved. Ths can be regarded as a protecton scheme smlar to the Automatc Repeat Request protocol n IEEE networks [12]. Hence, the servce tme of the users can be modeled as a 2 geometrc dstrbuton [13]. Let EX [ ] and EX [ ] denote the frst two moments of the servce tme of the secondary user SU usng the frequency channel F. We have: L + Lo EX [ ] =, (9) T (1 p ) o T (1 p ) ( L L ) (1 p ) EX [ ] =, (10)

15 15 where L s the average packet length of the secondary user SU and L o represents the effectve control overhead ncludng the tme for protocol acknowledgement 6, nformaton exchange, and channel sensng delay, etc. (see [12] for detals). Let us denote X = [ EX [ ] = 1,..., ] and X 2 = [ EX [ 2 ] = 1,..., ]. To descrbe the traffc model, we defne the traffc specfcaton 7 for the secondary user SU as 2 = [ Ck, B, L,, ], f SU Ck TS X X. Ths nformaton needs to be exchanged among the secondary users, whch wll be dscussed n detal n Secton IV.D. B. Prorty vrtual queung analyss In order to evaluate the expected utlty U ( s, s ) for delay-senstve multmeda applcatons, we need to calculate the dstrbuton of the end-to-end delay D( a, a ) for the secondary user SU to transmt ts packets. The expected end-to-end delay 8 ED [ ] of the secondary user SU can be expressed as: ED [ ( a, a )] = s ED [ ( R ( A ))], (11) = 1 where ED [ ( R ( A ))] s the average end-to-end delay f the secondary user SU chooses the frequency channel F. Note that s s the strategy of the acton a n A. Usng the queung model n Fgure 3, each arrvng packet of SU wll select a physcal queue to on (acton a ) accordng to the strategy s. Note that there are N physcal queues from N secondary users for a frequency channel F. Only one of them can transmt ts packets at any tme. Hence, we form a vrtual queue for the same frequency channel as llustrated n Fgure 3. In a vrtual queue, the packets of the dfferent secondary users wat to be transmtted. Importantly, the total soourn tme (queue watng tme plus the transmsson servce tme) of ths vrtual queue now becomes the actual servce tme at each of the physcal queues. The concept s smlar to the servce on vacaton [11] n queung theory, and the watng tme of the vrtual queue can be regarded as the vacaton tme. 6 Here we only consder retransmsson due to channel errors. We consder the protocol overhead n the AC layer ncludng possble contenton perod, tme for acknowledgement, etc. n the effectve control overhead. 7 The traffc specfcaton s smlar to the TSPEC n current IEEE e [12] for multmeda transmsson. 8 In order to smplfy the notaton, we use smple expectaton notaton E[] nstead of the expectaton over the acton strateges E( s, s )[] hereafter n ths paper.

16 16 Snce the number of the secondary users n a regular cogntve rado network s usually large, we can approxmate the vrtual queue usng prortzed /G/1 queung model (.e. when N, the nput traffc of the vrtual queue can be modeled as a Posson process). The average arrval rate of the vrtual queue of the frequency channel F s N λ = 1. Let us denote the frst two moments of the servce tme for the vrtual queue of the frequency channel F as EX [ 2 ] and EX [ ]. For a packet n the vrtual queue of frequency channel F, we determne the probablty of the packet comng from the secondary user SU as: f λ =. (12) N λ k = 1 k Hence, N EX [ ] = f EX [ ], EX [ 2 ] = f EX [ 2 ]. (13) = 1 N = 1 Snce there are K prorty classes among users ( K > 2, PU C1, SU { C2,..., C K }), we assume that μ k represents the normalzed traffc loadng of all the class C k secondary users usng the frequency channel F. By the defnton of the normalzed traffc loadng [11], we have: μ = λ EX [ 2 2 ], and μk = λ EX [ ]. (14) k SU C k SU C k Assume that ED [ k ] and EW [ k ] represent the average vrtual queung delay and average vrtual queue watng tme experenced by the secondary users n class applyng the ean Value Analyss (VA) [14], we have: C k n the vrtual queue of the frequency channel F. By k 2 2 ρ + μl k = k + = l = 2 k 1 k + ED [ ] EW [ ] EX [ ] EX [ ], (15) 2(1 ρ μ )(1 ρ μ ) l l l= 2 l= 2 where ρ represents the normalzed loadng of the prmary user PU for the frequency channel F, and ρ PU PU 2 PU PU 2 = λ EX [ ], ρ = λ E[( X ) ]. (16) Recall that the average nput rate of the prmary user PU s λ PU, and the frst two moments of the servce PU 2 tme s EX [ ] and EX [ PU ].

17 17 Snce the average vrtual queung delay ED [ k ] s the average servce tme of the physcal queue, the average end-to-end delay of the secondary user SU sendng packets through frequency channel F s approxmately: ED [ k ] ED [ ] =, for λ ED [ ] < 1, SU C 1 λ ED [ ] k k k. (17) Strateges ( s, s ) such that λ ED [ ] 1 wll result n an unbounded delay ED [ ], whch s undesrable for k delay-senstve applcatons. The advantage of ths approxmaton s that once the average delay of the vrtual queue ED [ k ] s known by the secondary user SU, the secondary user can mmedately calculate the expected end-to-end delay ED [ ] of a packet transmttng usng the frequency channel F. Note that n equaton (17), we assume that once a packet selects a physcal queue, t cannot swtch to another queue (change poston to the other queues). However, by consderng current physcal queue sze q for user SU usng the frequency channel F, a packet can change ts channel selecton after t s put n the physcal queue. The swtchng probablty from a longer queue q a to a shorter queue q b n a tme nterval t can be defned as 1 exp( t ( q q )). To evaluate such expected end-to-end delay ED [ ], a more sophstcated queung a b model wth ockey mpatent customers [30] needs to be consdered. Let P ( s, s ) represent the probablty of packet loss for the secondary user SU sendng packets through frequency channel F. By applyng G/G/1 approxmaton based on the work of [16], we have: λed [ k ] d λ ED [ ]exp( ), for λ ED [ ] < 1, SU C P (, ) ED [ ] s s = 1, for λed [ k ] 1 k k k. (18) For a delay-senstve secondary user SU, the obectve functon n (5) becomes: (1) maxmze U ( s, s ) s maxmze s (1 P ( s, s )) s = 1 λed [ k ] d mnmze s λ E[ D ]exp( ), for SU C s ED [ ] k k = 1. (19)

18 18 C. The overhead of requred nformaton exchange and the aggregate vrtual queue effects In the prevous subsecton, we calculate P ( s, s ), the packet loss probablty for a packet of the secondary user SU transmttng usng the frequency channel F. In a general case, we can calculate the expected utlty functon of equaton (4) as: (1) (2) a a θ + θ Eu [ (, )] = U (1 ) U max s (1 (, )) (1 ) (1 )/ 1 P s s θ s 1 T p T = = = θ + = 1 = s EV [ ( a, a )], (20) where max = θ + θ EV [ ( a, a )] (1 P ( s, s )) (1 ) T (1 p )/ T. EV [ ( a, a )] represents the aggregate vrtual queue effect for the secondary user SU of class C k transmttng usng the frequency channel F. Note that EV [ ( a, a )] 1. The aggregate vrtual queue effect EV [ ( a, a )] can be regarded as a metrc of the dynamc wreless envronment and the competng wreless users behavors [4][5], whch reflects the mpact of the tme-varyng envronment and the mpact of the other users (ncludng the prmary user and the other secondary users) on the secondary user SU n the specfc frequency channels F. To evaluate EV [ ( a, a )], modelng other secondary users s necessary 9. Our prorty vrtual queue nterface requres the followng nformaton to compute μ l and μ 2 l n (15): 1. Prorty: the secondary users prortes. 2. Normalzed loadng: the secondary users normalzed loadng parameters λ EX [ ], whch not only nclude the nformaton of s, but also reflects the nput traffc loadng and the expected transmsson tme usng a specfc frequency channel Varance statstcs: the secondary users varance statstcs wth the normalzed parameter λ EX [ ]. To determne the above nformaton, two knds of nformaton need to be exchanged: Informaton exchange of other secondary users traffc specfcaton TS (see Secton IV.A). 9 Although we apply /G/1 prorty queung analyss, more sophstcated queung models can be appled for evaluatng the aggregate vrtual queue effects, f usng dfferent traffc model descrpton.

19 19 Informaton exchange of the acton of the other secondary users a (to model the strateges s ). Snce the traffc specfcaton TS only vares when the frequency channels change dramatcally (we do not consder moblty effects and ths nformaton exchange s assumed to be truthfully revealed), the traffc specfcaton can be exchanged only when a secondary user ons the network to reduce the overhead. On the other hand, the acton nformaton can be observed (sensed) more frequently (once per packet/servce nterval [12]). Note that snce the users n the hgher prorty classes wll not be affected by the users n the lower prorty classes, they do not need the nformaton from the users n a lower prorty class. Hence, hgher prorty secondary users wll have small nformaton exchange overhead and computatonal complexty. In concluson, the nformaton overheads for hgher mportance secondary users are lmted. Based on the acton nformaton observaton, the nterface updates the strateges ( s, s ) and compute all the requred nformaton to evaluate the aggregate vrtual queue effect EV [ ( a, a )]. Next, we dscuss how to make use of EV [ ( a, a )] to determne the frequency channel selecton. V. DYNAIC CHANNEL SELECTION WITH STRATEGY LEARNING From Secton III, we know that the goals of the secondary users are to maxmze ther utlty functons. We defne the best response strategy for the decentralzed optmzaton by consderng the strategy that yelds the hghest utlty U of the secondary user users n one class 10. The decentralzed optmzaton s: SU. To smplfy the descrpton, we now consder all the secondary arg max [ (, )]. (21) * = E ( s, s ) u a a s S s From equaton (20), the decentralzed optmzaton problem n equaton (21) can be wrtten as: * = s s S = 1 EV a a s arg max [ (, )]. (22) Based on the strategy s *, a secondary user can choose ts acton (frequency channel), and then the secondary user models s based on the acton nformaton exchange revealed by the other secondary users (.e. a ) n 10 For multple prorty classes case, the same algorthm can be appled consecutvely from hgher prorty classes to lower prorty classes wthout losng generalty.

20 20 order to evaluate a new EV [ ( a, a )]. The concept s smlar to the fcttous play [25] n mult-agent learnng n game theory. The dfference s that a user not only models the strateges of the other users, but also explctly calculates the aggregate vrtual queue effect EV [ ( a, a )] that drectly mpacts the utlty functon. Based on the prorty queung analyss n Secton IV, the aggregate vrtual queue effect EV [ ( a, a )] can be evaluated usng equaton (20) by each of the secondary users. The teratve learnng algorthm based on EV [ ( a, a )] can be wrtten as: * s s s S s ( n) = arg max U (, ( n 1)), (23) = arg max s EV [ ( a ( n 1), a ( n 1))] s S = 1 where the ntal stage s s (0). We show the system dagram of a secondary user n Fgure 4. The optmal strategy * s can be determned by the secondary user SU for a gven EV [ ( a, a )] from the nterface. Then, based on the best response strategy s * ( n), a packet of the secondary user SU selects an acton a ( n). Let the frequency channel wth the largest EV [ ( A ( n 1))] be F * ( n ),.e. F * ( n) = arg max{ EV [ ( A ( n 1))]}. Recall that A( n 1) = [ a ( n 1), a ( n 1)]. The soluton of (23) s: F F * s 1, f ( ) * = F = F n s ( n) =. (24) s = 0, otherwse For a specfc frequency channel F, even though the correspondng prmary user s traffc s statonary, t s not guaranteed that the secondary users strateges wll converge to a steady state, snce the secondary users mutually mpact each other. Hence, our soluton adopts a mult-agent learnng whch resembles the gradent play [25] n game theory. Our approach does not employ a best response strategy, but rather adusts a strategy n the drecton of the perceved better response. In addton, due to the cost of frequency hoppng and the hardware lmtatons, only a lmted set of selectable frequency channels can be selected by a secondary user for transmsson. Hence, we assume that the selectable frequency channels for the secondary user SU are n a set F F. Let us denote H = { F s > 0} F as the set of frequency channels wth s > 0. The maxmum number of selected frequency channel s H,.e. H F.

21 21 a Acton nformaton observaton a Secondary user SU C k Prorty vrtual queue Interface Dynamc Strategy Learnng Strategy modelng ( s, s ) a a Frequency selecton Channel based on strategy Prmary user estmaton R modelng s Packet Prorty vrtual transmsson queung analyss Strategy Learnng EV [ ( a, a )] SINR TS, TS Channel sensng Traffc specfcaton exchange Transmsson opportunty Fg 4. The block dagram of the prorty vrtual queue nterface and dynamc strategy learnng of a secondary user. Note that changng the selected frequency channels requres channel sensng, control sgnalng, and also addtonal ncurred delays, etc. for the spectrum handoff [23]. In Appendx, we dscuss the convergence propertes of the proposed algorthm consderng the cost of changng the frequency selecton strategy. We refer to ths cost for the secondary user SU as χ ( s ( n), s ( n 1) ), whch s a functon of the dfference between the selected strategy and the prevous strategy (see Appendx for more detal). The utlty functon of SU now = 1 becomes U ( s ( n), s ( n 1)) = s ( n) EV [ ( A( n 1))] χ ( s ( n), s ( n 1) ). The steps n our DSL algorthm are summarzed below: Step 1. odel the strategy matrx from the acton nformaton exchange: The prorty vrtual queue nterface collects the acton nformaton from the other users and accordngly updates the strategy matrx. Step 2. Calculate vrtual queue effects: Gven the strategy matrx of the prevous stage, S( n 1) = [ s ( n 1), s ( n 1)] and the channel loadng specfcaton, we calculate the aggregate vrtual queue effects EV [ ( A ( n 1))] based on equaton (18) and (20). Step 3. Determne the set of selected frequency channels: Determne the set H of selected frequency channels from F : ( H ) F F H ( n) = arg max { EV [ ( A ( n 1))]}, (25) ( N ) where we denote the operaton max (X) as the largest N choces from a set X. Recall that the frequency

22 22 channel wth the largest EV [ ( A ( n 1))] be F * ( n ). Step 4. Determne the channel selecton strateges: Based on H ( n), we determne the strategy s ( n) usng the followng polcy: * max(0, s ( n 1) σ), f F H( n), F F ( n) * s ( n) = 1 * max(0, s ( 1) ), f ( ), ( ) F F ( n) n σ F n F = F n H, (26) 0, f F H( n) where σ s a constant step sze of changng the strateges such that the polcy favors a frequency channel leadng to a larger V (( S n 1)). Specfcally, the polcy concentrates the traffc dstrbuton to the frequency channel F * ( n ) from the other frequency channels n H, whle learnng from the prevous strategy s ( n 1). Step 5. Update the new strategy: Update the new strategy s ( n ) f the strategy s ( n) leads to an mproved utlty. s ( n), f U ( s ( n), s ( n 1)) > U ( s( n 1), s ( n 1)) s ( n) =. (27) s ( n - 1), otherwse Step 6. Determne a frequency channel for packet transmssons based on the strategy. The proposed dynamc channel selecton algorthm has the followng advantages: 1. Decentralzed decson makng allows heterogeneous secondary users (n terms of ther prortes, utltes, source traffc and channel condtons) to optmze ther own utlty functons based on the nformaton exchanges. 2. Vrtual queung analyss provdes the expected utlty mpacted by other users usng the same frequency channel and hence, smplfes the requred nformaton exchange. 3. The teratve algorthm provdes real-tme adaptaton to the changng network condtons and source traffc varatons of the prmary users or other secondary users. VI. SIULATION RESULTS Frst, we smulate a smple network wth two secondary users and three frequency channels (.e. N = 2, = 3 ) n order to show the results of our soluton usng a smple example such that the behavor of the

23 23 proposed cogntve rado model can be clearly understood. We assume that each secondary user can choose all the frequency channels,.e. H = 3. The two secondary users are n the same prorty class. The smulaton parameters of the secondary users are presented n Table I ncludng the channel condtons R = [ T, p ], and ntal strateges s (0), etc. The normalzed traffc statstcs of the prmary users are n Table II. Gven these statstcs, Fgure 5 provdes the analytcal experenced delays ED [ ] (usng equaton (17)) that are bounded by the delay deadlnes for the two secondary users usng dfferent strategy pars ( s1, s 2 ) n the three frequency channels. Importantly, a strategy par ( s 1, s 2 ) that results n an unbounded ED [ ] wll make the utlty functon drop abruptly for delay-senstve applcatons (see equaton (2)), whch s undesrable for these secondary users. Hence, equaton (17) provdes the analytcal operaton ponts for the strategy pars. In the followng subsecton, each secondary user apples the proposed DSL algorthm from a unform traffc dstrbuton over the three channels to fnd the channel selecton strateges. Secondary users Physcal transmsson rate T (bps) TABLE I SIULATION PARAETERS OF THE SECONDARY USERS Physcal packet error rate p Intal strategy s (0) Satsfacton rate max T = 3B F 1 F 2 F 3 F 1 F 2 F 3 F 1 F 2 F 3 (bps) (bytes) (sec) SU /3 1/3 1/ Rate requrement B (bps) Packet length L Delay deadlne d SU /3 1/3 1/ TABLE II SIULATION PARAETERS OF THE PRIARY USERS Prmary users Normalzed loadng ρ Second moment normalzed loadng 2 ρ PU PU PU A. Impact of the delay senstvty preference of the applcatons In ths smulaton, we show that the delay senstvty preferences of the secondary users affect the stablty of utlty and also the resultng channel selecton strateges. Fgure 6 gves the strateges and the resultng utltes of the two secondary users wth two dfferent θ (applcatons that care less about delay wth θ = 0.2, = 1, 2 n Fgure 6(a) and applcatons that care more about delay wth θ = 0.8, = 1, 2 n Fgure 6(b)).

24 24 Fg. 5 Analytcal expected delay of the secondary users wth varous strateges n dfferent frequency channels, shadow part represents a bounded delay below the delay deadlne (stable regon). Strategy of SU 1 (a) s 11 s 12 s 13 Strategy of SU 1 (b) s 11 s 12 s Strategy of SU s 21 s 22 s 23 Strategy of SU s 21 s 22 s 23 Utltes SU 1 SU Iteraton n Utltes SU 1 SU Iteraton n Fg. 6 (a) Smulaton results of the DSL algorthm strateges of the secondary users and the utlty functons of less delay-senstve applcatons ( θ = 0.2, σ = 0.05, χ = 0 ). (b) Smulaton results of the DSL algorthm strateges of the secondary users and the utlty functons of delay-senstve applcatons ( θ = 0.8, σ = 0.05, χ = 0 ). The delay-senstve applcatons n Fgure 6(b) do not acheve a steady state, snce the small changes n the channel selecton strateges can push the experenced delay over the delay deadlne and hence, mpact the utlty functon dramatcally. oreover, compared wth the resultng strateges of the applcatons n Fgure 6(a), Fgure 6(b) shows that the delay-senstve applcatons prefer a channel wthout other secondary users to transmt the

25 25 data SU 1 transmts most of ts data through channel F 1, whle SU 2 transmts through F 2 and F 3 (.e. s11 1, s21 0 ). Ths s because for a secondary user wth delay senstve applcatons, the utlty functon s more senstve to the traffc n a frequency channel. The data traffc from other secondary users can ncrease the uncertanty of the channel, whch makes such channel undesrable for the delay senstve applcatons. oreover, the resultng utlty s more unstable for the applcatons wth a larger θ. The resultng strategy ( s 11,0), (0, s 22), and (0, s 23) of Fgure 6(b) are closer to the regon wth unbounded delay for ED [ 11], ED [ 22 ], and ED [ 23 ], respectvely (see Fgure 5). B. Impact of the prmary users n dfferent channels Next, we smulate the mpact of the hghest prorty users the prmary users n Fgure 7. We change the normalzed traffc loadng of PU 1 n the frequency channel F 1 from 0 to 1 and fx the normalzed loadng of the other two prmary users as n Table II. Due to the prorty queung, we know that once ρ 1 reaches 1, frequency channel F 1 s not accessble for the secondary users. For dfferent normalzed loadng of PU 1, Fgure 7 shows the resultng strateges and the utltes of the two secondary users after convergence. Both s 11 and the utlty value U 1 decreases when the avalable resource from F 1 decreases ( ρ 1 > 0.6 ). Interestngly, even though SU 2 does not utlze channel F 1 ( s 21 0 ) and the resultng strateges do not change wth ρ 1, U 2 also decreases. Ths s because more traffc from SU 1 wll now be dstrbuted to F 2 and F 3. Ths smple example llustrates that the traffc of a hgher prorty class user can stll affect the utltes of the secondary users n lower prorty classes even when these secondary users avod selectng the same channels as the hgher prorty class user. C. Comparson wth other cogntve rado resource management solutons In ths subsecton, we smulate a larger number of secondary users and a larger number of frequency channels. Frst, we look at the case wth 6 secondary users wth vdeo streamng applcatons ( Coastguard, frame rate of 30Hz, CIF format, delay deadlne 500ms) sharng 10 frequency channels ( N = 6, = 10, θ = 1). We compare our DSL algorthm wth other two resource allocaton algorthms the Statc Assgnment [10] and the Dynamc Least Interference [9]. In the Statc Assgnment algorthm, a secondary user wll statcally select a

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