Reservation Policies for Revenue Maximization from Secondary Spectrum Access in Cellular Networks

Transcription

1 Reservaton Poces for Revenue Maxmzaton from Secondary Spectrum Access n Ceuar Networks Ashraf A Daoud, Murat Aanya, and Davd Starobnsk Department of Eectrca and Computer Engneerng Boston Unversty, Boston, MA Ema: {ashraf, aanya, staro}@buedu Abstract We consder the probem of provdng opportunstc spectrum access to secondary users n wreess ceuar networks From the standpont of spectrum cense hoders, achevng benefts of secondary access entas baancng the revenue from such access and ts mpact on the prmary servce of the cense hoder Whe dynamc optmzaton s a natura framework to pursue such a baance, spata constrants due to nterference and uncertan demand characterstcs render exact soutons dffcut In ths paper, we study gudng prncpes for spectrum cense hoders to accommodate secondary users va reservaton-based admsson poces Usng notons of dynamc optmzaton, we frst deveop the concept of average mped cost for estabshng a connecton n an soated ocaty The formua of the cost provdes an expct characterzaton of the vaue of spectrum access We then generaze ths concept to arbtrary topooges of nterference reatons and show that the generazaton s ustfed under an anaogue of the reduced oad approxmaton udcousy adapted from the wrene to the wreess settng An expct characterzaton of ths quantty demonstrates the ocazed nature of the reatonshp between overa network revenue and reservaton parameters Based on ths reatonshp, we deveop an onne dstrbuted agorthm for computng optma reservaton parameters The performance of the agorthm s verfed through a numerca study I INTRODUCTION The hke n the demand for wreess communcatons, aong wth reported neffcences n rado spectrum utzaton, have recenty ed to a goba effort to reform egacy spectrum reguatons [1 4] One aspect of these reforms s to grant spectrum cense hoders extended property rghts that aow tradng of spectrum n secondary markets From the standpont of spectrum reguators, such markets hep mprove spectrum utzaton From the standpont of cense hoders, secondary markets provde a nove opportunty to ncrease revenue by expandng ther subscrber poos In ths work, we focus on wreess ceuar networks and devse gudng prncpes for cense hoders to maxmze ther revenue under secondary market agreements In partcuar, we dfferentate between two types of network users The frst represents prmary, or orgna, users of the ceuar network The second type represents users who seek network access on opportunstc bass under short term agreements Whe revenue maxmzaton can be ready studed wthn the framework of dynamc programmng, t s we-known that the compexty of such approach becomes prohbtve for even smaest nontrva networks [5] In partcuar, n a wreess settng, the effect of nterference from an estabshed connecton n one ce extends beyond that ce and ndrecty affects a ces n the network For exampe, a connecton n progress eads to a tempora reducton n utzaton n ts mmedate neghborhood, whch may n turn hep accommodate more connectons n the second-ter ces around t Thus, an optma dynamc souton for the probem typcay entas makng admsson decsons based on the current state of the whoe network e, channe occupancy n each ce), and therefore ts mpementaton s rather mpractca We seek n ths work a practca and scaabe admsson pocy for accommodatng secondary users where decsons are based on oca nformaton on the base statons wthout requrng a centra authorty to carry off hghy compex computatons Whe admsson contro for ceuar networks s a we studed topc, see [6] for a recent survey, we consder the probem for genera network topooges under fu reazaton of the effect of nterference Our man contrbuton s to provde gudng prncpes for spectrum cense hoders to accommodate secondary users va reservaton-based admsson poces Under such poces, admsson of a ca request by a secondary user s granted ony f the tota nterference at each ce stays beow a fxed threshod, typcay taken to be ess than the capacty of the ce Ths way, part of the capacty of each ce s reserved excusvey for prmary traffc whch has more prorty and s more rewardng as we The choce of reservaton poces s motvated by ther optmaty for the soated ce [7 9] Thus, we consder frst the soated ce for whch the average mped cost of an estabshed connecton can be expcty determned Then we extend ths concept to genera topooges and adapt the socaed reduced oad approxmaton RLA) [10], wdey used n the anayss of crcut-swtched networks, to compute certan network performance measures n the wreess settng and provde anaytca nsght The premse behnd the RLA s to assume that a decson to admt/reect a ca s based on ndependent decsons at the dfferent ces Ths aows approxmated vaues of ca bockng probabtes to be drecty cacuated

2 Our second contrbuton s to devse an adaptve mechansm for mpementng the reservaton-based admsson pocy Namey, we provde an onne agorthm that updates capacty reservaton parameters n ght of fuctuatons n traffc rates We expot the fact that senstvty of the revenue to a unt change of the reservaton parameter for a certan ce can be ocay evauated by the base staton usng measurements and ocazed message passng technques We use ths fact to propose an onne dstrbuted agorthm that computes optma reservaton parameters n the network Snce unmodaty of the revenue functon s not guaranteed n the generaty of topooges, we suggest an mpementaton akn to smuated anneang that probabstcay mproves the revenue n each step of the process Fnay, we provde a numerca study n support of the theoretca resuts The rest of ths paper s organzed as foows: In Secton II, we present an operatona mode for ceuar networks under a reservaton-based admsson pocy We suggest an anaytca framework to capture the network-wde effect of nterference and use the RLA to compute bockng probabtes In Secton III, we derve an exact expresson for the mped cost n the speca case of the soated ce and then gve formuas for genera topooges based on the RLA In Secton IV, we present the revenue-maxmzng dstrbuted agorthm We present a numerca study n Secton V and fnay concude the paper n Secton VI II ANALYTICAL FRAMEWORK A ceuar network s consdered under the foowng teetraffc condtons: At each ce, connecton requests of type m = 1, 2 arrve ndependenty as a Posson process wth rate Here, type 1 refers to requests by prmary users and type 2 to those by secondary users Once estabshed, a connecton asts for an exponentay dstrbuted tme wth unt mean, ndependenty of the hstory pror to the request arrva We mode a ceuar network as a weghted graph G = N, E) where N denotes the coecton of ces and edge weght w 0 s the nterference bandwdth requred from ce by a connecton estabshed at ce Snce a connecton may generate nterference on other connectons n the same ce, the modeed physca stuaton typcay mpes that w > 0 for each ce A connecton can be sustaned ony f t experences admssbe nterference, and that a new connecton request cannot be honored f t eads to premature termnaton of another connecton that s aready n progress To formaze ths condton, et n denote the number of connectons n progress at each ce so that N n w s the tota nterference actng on ce Gven an nterference parameter κ for, a network oad n = n : N) s feasbe f λ m) n w κ for each 1) N Furthermore, network oad evoves as a tme-homogeneous Markov process wth state space S = {n Z N + : n s feasbe} Identfyng w vaues depends on the underyng spectrum access mechansm empoyed n the network For exampe, n narrowband networks, frequency band s dvded nto nonoverappng channes and the operatona constrants under the apped frequency reuse pattern, prohbt the same channe to be assgned smutaneousy to connectons n the same ce or n any neghborng ces Thus, condton 1) dctates that w s the tota number of channes a connecton estabshed at ce woud ock at ce In wdeband networks, connectons share the whoe frequency band and w can be characterzed by the strength of eectromagnetc coupng between connectons at the dfferent ces One approach to compute such vaues s va provdng guarantees on the sgna to nterference ratos at the ces See for exampe [12] and [13] for an ndepth dscusson on dentfyng such vaues n wdeband networks Now consder a reservaton-based admsson poces Each such pocy w be represented by a vector R = R : N) where 0 R κ refers to a reservaton parameter at ce Under such poces, a type 1 connecton s admtted f ts ncuson preserves condton 1), whe a type 2 connecton s admtted at a ce ony f ts ncuson preserves the tota nterference, from type 1 and type 2 connectons, at each ce beow R Ths way, the pocy guarantees prorty for type 1 connectons by reservng κ R ) of the nterference capacty of each ce excusvey for type 1 connectons Assume that the cense hoder charges an admtted type 1 connecton r 1) unts currency and charges an admtted type 2 connecton r 2) unts Gven a reservaton pocy R, et B m) denote the bockng probabty of type m connectons at ce The ong-term revenue rate under pocy R can be expressed as WR) = N m=1,2 r m) λ m) 1 B m) ) 2) Note that W) depends aso on λ 1), λ 2) ) Ths dependence s suppressed n the seque for notatona convenence A maor dffcuty n computng the equbrum dstrbuton of ce occupances and hence bockng probabtes arses due to the need to compute arge normazng constants However, even n cases where such computaton s possbe, the resuts gve tte nsght on the reatonshp between the overa revenue and ndvdua reservaton parameters Such a reatonshp can be aternatvey pursued by adaptng the RLA to the stuaton n hand [11] Our startng pont s to consder an soated ce wth capacty κ, reservaton parameter R, and arrva rate vector λ = λ 1), λ 2) ) Assume that an estabshed connecton requres one unt capacty from the ce Aso et n denote the tota number of connectons n progress n the ce The state dagram of the ce occupancy process s shown n Fgure 1 The steady state probabty of havng a tota of n connectons n progress can be drecty obtaned by sovng the detaed baance equatons Hence π λ n) = { λ 1) +λ 2) ) n n! Z f 0 n < R λ 1) +λ 2) ) R λ 1) ) n R n! Z f R n κ,

3 0 λ 1) +λ 2) λ 1) +λ 2) λ 1) +λ 2) λ 1) λ 1) 1 R-1 R R+1 κ 1 R-1 R R+1 κ Fg 1 State transton dagram of the occupancy process for the soated ce under a reservaton pocy wth parameter R where Z s a normazng constant such that κ n=0 π λn) = 1 Furthermore, bockng probabtes for type 1 and 2 are gven respectvey by B 1) λ, κ, R) = π λ κ) 3) B 2) λ, κ, R) N = κ π λ n) 4) n=r For genera topooges, we approxmate the bockng probabty for type m n ce, B m), by the quantty ˆB m) = 1 1 b m) ) w, 5) where {b m) wth ρ = ρ 1), ρ 2) ) and ρ m) : N} satsfy the fxed pont reaton b m) = B m) ρ, κ, R ), 6) = 1 b m) ) 1 N w λ m) N 1 b m) ) w 7) The ratona behnd ths anaogous formua of the RLA s that any connecton request s subect to ndependent admsson/reecton decson for each unt of nterference that t generates at each ce Namey, a connecton request s admtted f a unts nterference sub-requests are admtted ndependenty at a ces Under the reservaton pocy, a unt nterference by a type 2 connecton s admtted at ce f the tota nterference at the ce s beow R Equaty 5) gves the bockng probabty of a fu) type m connecton request at ce, provded that each ce admts a unt nterference wth probabty 1 b m) In vew of the exact anayss of the soated ce, equates 6) and 7) are consstency condtons that shoud be satsfed by the probabtes {b m) : N} III IMPLIED COST Subectng a gven ce to an addtona unt of nterference affects bockng at a the ces n the network, at varous extents For exampe, durng the hodng tme of a connecton, the nterference generated by that connecton can cause reecton of new connectons arrvng at neghborng ces, whch may n turn open up room for admttng new connectons n other ces Here the concept of mped cost that captures such effects of acceptance/reecton decsons s dscussed A Isoated Ce Consder the soated ce exampe and et σ R n) denote the reducton n the ong-term revenue rate f the system s started wth n+1 nstead of n connectons Hence, σ R n) can be nterpreted as the mped cost of admttng a connecton when the ce occupancy s n A reservaton parameter R s optma f t dctates admsson of a type m connecton when r m) > σ R n), e, when the mmedate reward exceeds the mped cost of admsson The quantty σ R n) s expcty dentfed n [14] for the soated ce where for 0 n < R: σ R n) = r1) λ 1) B 1) λ, κ, R) + r 2) λ 2) B 2) λ, κ, R) λ 1) + λ 2) )B 1) λ, n, n) and for R n κ: σ R n) = r1) λ 1) B 1) λ, κ, R) λ 1) B 1) λ, n, R) + r2) λ 2) B 2) λ, κ, R) B 2) λ, n, R) ) 9) λ 1) B 1) λ, n, R) Now et π 1) o n) = { π λ n) κ 1 =0 π λ) f 0 n κ 1 0 otherwse 8) 10) denote the system occupancy dstrbuton seen by an admtted type 1 connecton Aso et { π λ n) π o 2) R 1 f 0 n R 1 n) = π λ) =0 11) 0 otherwse be the same dstrbuton seen by an admtted type 2 connecton The average mped cost c m) of admttng a connecton of type m can be obtaned by averagng σ R n) over the system occupancy dstrbuton; e, κ 1 c m) = π o m) n)σ R n), m = 1, 2 12) n=0 In the foowng theorem, we compute the average mped cost n an soated ce based on formua 12) In partcuar, Theorem III1 Average Imped Cost n an Isoated Ce): For m = 1, 2 ) 1 c m) = 1 B m) λ, κ, R) r k) λ k) Bk) λ, κ, R) λ m) k=1,2 13) Proof: The proof of the theorem foows from usng the expressons 8,9,10,11) n formua 12) In vew of Theorem III1, the average mped cost n an soated ce can be exacty and drecty computed However, t w be mportant n the subsequent dscusson of genera topooges to consder an nsghtfu form of 13) Namey, assocate wth each type m a fow of fcttous connecton requests wth rate ˆλ m) and reward per connecton ˆr m) such that ˆλ m) = ˆr m) = 0 Thus, the ong-term revenue rate as gven by 2) remans unchanged Furthermore, the average mped cost n an soated ce can be ready wrtten n the

4 equvaent form ) 1 d c m) = 1 B m) λ, κ, R) WR) 14) dˆλ m) B Genera Topooges An extenson of Theorem III1 to genera topooges can be pursued under the RLA Namey, each bockng probabty B m) m) s approxmated by the quantty ˆB as gven n expressons 5,6,7) In ths case, the ong-term revenue rate 2) can be approxmated by ŴR) = r m) λ m) 1 ˆB m) ), 15) N m=1,2 by repacng B m) m) wth ˆB The defnton of fcttous fows can be extended to the present context so that for any ce, m) ˆλ the fcttous fow of type m s such that = ˆr m) = 0, w = 1, and w = 0 for Expresson 15) can be used as a proxy to WR) and, by mmckng 14), the average mped cost of type m connectons at ce s defned as c m) = 1 ˆB m) ) 1 d dˆλ m) ŴR) Proofs of Theorem III2 and Theorem III3 beow foow the broad nes of [11, Theorem 22 and Theorem 23], respectvey, yet the theorems here amount to a nontrva extenson of the anayss of [11] to those cases where the parameters w s are not restrcted to vaues taken from the set {0, 1} Theorem III2 : For m = 1, 2 and N c m) where = 1 b m) ) 1 ρ k) N ρ k) = 1 b k) k=1,2 B k) ρ, κ, R ) ρ m) r k) w 1)c k) ) 1 w λ k) N N w c k), 16) 1 b k) ) w 17) In Theorem III2, ρ k) represents the ntensty of type k nterference from ce to ce, after beng thnned at other ces n the network The tota arrva rate of nterference to ce n 7) can be verfed to satsfy ρ k) = N ρk) Note that the reaton 16) s near n the mped costs; hence {c k) : k = 1, 2, N} can be computed va matrx nverson methods Now for each ce and a gven functon HR), et H denote the eft dervatve of HR) n the th entry That s, HR) s the amount by whch HR) ncreases when the R s decreased by 1 H = H R H R 1 18) Aso et + H denote the rght dervatve + H = H R +1 H R 19) The foowng theorem dentfes the senstvty of ŴR) to ndvdua reservaton parameter vaues n terms of the average mped costs The theorem forms the bass of the adaptve admsson contro agorthms studed n the next secton Theorem III3 : For N, ± ŴR) = ± Bk) ρ, κ, R ) k=1,2 N r k) w 1)c k) N ρ k) w c k) IV REVENUE MAXIMIZATION VIA ADAPTIVE RESERVATION 20) A gudng prncpe for revenue maxmzaton nvoves updatng the reservaton parameters to mprove ŴR) based on the ncrements/decrements ± ŴR) A straghtforward mpementaton of ths prncpe may have two ptfas: 1) Unmodaty of ŴR) cannot be guaranteed n ght of the generaty of consdered topooges; hence cassca technques based on steepest ascent may ead to oca maxma of ŴR) 2) Computaton of ± ŴR) needs to be oca for the maxmzaton procedure to scae gracefuy to arge networks In ths secton, the frst ssue s addressed by resortng to agorthms based on smuated anneang; a generc method for goba optmzaton and wdey used n probems that nvove dscrete state spaces [15] The second ssue s addressed by expotng expressons 16) and 20) whch are of partcuar nterest from the standpont of dstrbuted mpementaton Note the oca propertes of both expressons: Apart from the numbers b m) s and c m) s, the rest of the quanttes can be ether measured or computed ocay at the base statons Note that quanttes such as the ntensty of nterference ρ m), practcay, cannot be measured by the base staton of ce However, f each ce passes the quantty λ m) N 1 ) w to ts neghborng ces; e, ces that are affected by nterference from that ce, then ce w be abe to compute ρ m) based on formua 17) Now gven that nterference s practcay effectve around a oca neghborhood of the ce, any suggested message passng technque w be ocazed around the ce, perhaps across the frst and second ters of b m) neghborng ces St, computng the quanttes ± ŴR) by each ce requres obtanng frst b m) by sovng the system of fxed pont equatons 6), and second the correspondng mped cost vaues c m) that sove the system 16) Thus, gven a vector x = x m) : m = 1, 2; N), defne frst the foowng

5 near mappng usng formua 6) f m) : R 2 N R N, f m) = f m) 1, f m) 2,, f m) ), 21) where f m) x) = B m) ρ x), κ, R ), N Here ρ x) = ρ 1) x), ρ 2) x)) s defned as n 7) so that ρ m) x) = 1 x m) ) 1 w λ m) 1 x m) ) w N N Defne aso the mappng g m) : R 2 N R N, g m) = g m) 1, g m) 2,, g m) ), 22) based on formua 16) Namey, for a gven vector y = y m) : m = 1, 2; N), g m) y) =1 b m) ) 1 B k) ρ, κ, R ) N Note that {b m) ρ k) k=1,2 ρ m) r k) w 1)y k) N N N w y k) : m = 1, 2; N} and {c m) : m = 1, 2; N} are fxed ponts of the mappngs f 1), f 2) ), and g 1), g 2) ), respectvey Repeated substtuton can be empoyed here to compute the fxed ponts, startng wth arbtrary nta vaues Each ce can terate based on oca measurements and passed messages We suggest the teratons to be performed on dfferent tme scaes so that the mappng 21) terates faster and hence the numbers {b m) : m = 1, 2; N} can be obtaned before an teraton s trggered for the mappng 22) Note that the mappng 21) requres aso the knowedge of the mped costs, c k), estmated on the neghborng ces Ths can be acheved by ettng each ce perodcay broadcast ts mped cost vaue to ts neghborng ces Ths way, each ce can therefore estmate the quanttes ± ŴR) Dstrbuted Smuated Anneang: Now et each ce update ts reservaton parameter R at rate γ In partcuar, for a gven R defne the set of neghborng states {R 1, R + 1 : 0 R ± 1 κ } When an nterna cock tcks, the ce chooses a neghborng state R accordng to a certan probabty dstrbuton The ce then computes the correspondng vaue ± ŴR) based on the conventons n 18) and 19); that s, t computes ŴR) f R = R 1 case 1) + ŴR) f R = R + 1 case 2) The ce adopts R as a new reservaton parameter f ŴR) < 0 n case 1) or f + ŴR) > 0 n case 2) If nether of these condtons hods, then R s adopted wth probabty exp ŴR) s ), or exp + ŴR) t s ), based on t Dstrbuted Smuated Anneang Agorthm 1 Intaze R start 2 R R start 3 Wth rate γ 31 Choose a neghborng state R {R 1, R + 1} wth probabty p 32 If R = R If mn {1, exp WR) s t )} > random[0, 1) R R 33 If R = R If mn {1, exp R R 34 t t WR) s t )} > random[0, 1) the case Here, s t represents a tme decreasng temperature schedue at the ce such that s t goes to 0 as tme t Ths way agorthm avods oca maxma of the functon Ŵ) A pseudo-code for the dstrbuted agorthm s gven as foows: The agorthm can be seen as a dstrbuted verson of the smuated anneang agorthm It can adapt to traffc fuctuatons due to the tme-of-day use of the network In partcuar, when traffc rate changes at a certan ce, t trggers new vaues for the mappngs 21) and 22), and then ces update ther reservaton parameters accordng to the agorthm Thus, n effect, there are three separated tme scaes that govern network computatons, sted as foows from smaer to arger: 1) Tme scae 1: Ces compute {b m) : m = 1, 2; N} 2) Tme scae 2: Ces compute {c m) : m = 1, 2; N} 3) Tme scae 3: Ces update ther reservaton parameters {R : N} V NUMERICAL EXAMPLE In ths secton, we gve a numerca exampe for appyng the proposed agorthm and show ts adaptvty to fuctuatons n traffc rates In partcuar, consder a 7-ce attce topoogy wth a graph representaton shown n Fgure 2 Assume that an estabshed connecton at a gven ce generates nterference n that ce and every other ce that t shares a boundary wth Thus, nterference between ces that share no boundary w be negected The exampe s based on a wdeband system wth the foowng parameters: channe bandwdth = 125 MHz, data rate = 644 kbps, actvty factor = 04, and path oss exponent = 40 We compute w and κ usng the approach detaed n [13] wth mobe termnas taken to be unformy

6 at most two dstnct reservaton parameter vaues; one for ce 1 and one for ces 2 7 In ths context, we mt our search to a sub-doman that covers a reservaton parameter vectors R whch have at most two dstnct entry vaues For each set of parameters, we compute revenue rate under the RLA The maxmum rate s found to be 811, acheved at the same set of parameters obtaned by the agorthm In the same manner, the resuts of the second part of the experment have been verfed 6 5 Fg 2 Network graph of a 7-ce hexagona attce topoogy used for the numerca exampe of secton V dstrbuted n the ces Namey, we obtan: { w = 150 w = 10 f and are neghbors, and κ = 540 for a Now assume that the cense hoder opens ce 1 for type 2 traffc; e, λ 2) = 0 for = 2,, 7 Let r 1) and r 2) be 10 and 075, respectvey Assume aso that each ce updates ts reservaton parameter usng a Posson cock wth rate γ = 10 Once the cock tcks, the ce chooses a neghborng state R = R ± 1 wth probabty 05 The ce then computes + Ŵ R), or Ŵ R), and updates ts reservaton parameter f necessary To obtan vaues of ± Ŵ R), we frst sove equatons 6) and 16) teratvey va repeated substtuton In ths experment, we do not use a temperature schedue at the ces as t s not the purpose of the exampe to verfy oca maxma avodance technques Fgure 3a) shows the traectores of updatng the reservaton parameters at the dfferent ces For the frst 1000 steps, λ 1) for = 1,, 7 are taken to be 10 and λ 2) 1 s 50 The agorthm starts wth each ce havng a reservaton parameter R = 25 As each ce updates ts parameter accordng to ts own Posson cock rate, the ces converge to the vaue R = 52 for a In the second part of the experment, we change the traffc rates so that for the rest of the experment λ 1) = 15 for a and λ 2) 1 = 40 The resut shows that a the ces adapt ther reservaton parameters and converge fast to the vaues R1 = 51 and R = 50 for = 2,, 7 Fgure 3b) shows the rate of revenue from the network at the dfferent tme steps of mpementng the agorthm For the frst 1000 steps and whe λ 2) 1 = 10, the revenue rate ncreases gracefuy to the vaue 811 When traffc rates change, the agorthm adapts and the revenue mproves and converges to the new vaue 1099 Verfyng optmaty of agorthm performance requres an exhaustve search over a the possbe reservaton parameters Ths task s computatonay ntense However, the prevous resuts show that the acheved poces are symmetrc and have 4 VI CONCLUSION In ths paper, we have consdered an admsson contro probem for wreess ceuar networks under the obectve of revenue maxmzaton The probem nvoved servce measures whch favor prmary users by reservng part of the capacty of each ce for ther excusve use We have deveoped an anaytca framework that captures the average mped cost of estabshng a connecton n the network An mportant vaue of ths work es n the fact that t deveops concepts from wrene to wreess teephony and proves ther usefuness We have used smpfed reasonng n expanng these concepts and makng them appea to readers who are more nterested n the practca sde of the probem In ths respect, and startng wth an soated ce, we have exacty and expcty characterzed the average mped cost of estabshng a connecton by usng notons from dynamc programmng An extenson of ths resut to genera topooges has been pursued under the reduced oad approxmaton and ed to gudng prncpes for updatng reservaton parameters at the ces Gven the compexty of mpementng a reservaton-based pocy n a centrazed fashon, we have suggested a dstrbuted onne agorthm that can be empoyed at the base statons and can adapt to fuctuatons n traffc rates ACKNOWLEDGEMENT Ths work was supported n part by the US Natona Scence Foundaton NSF) under grant CNS REFERENCES [1] Federa Communcatons Commsson, In the Matter of Uncensed Operaton n the TV Broadcast Bands, Second Report and Order and Memorandum Opnon and Order, FCC , November, 2008 [2] M BH Wess, Secondary Use of Spectrum: A Survey of the Issues, Info, vo 8, no 2, pp 74 82, 2006 [3] M Cave, C Doye, and W Webb, Essentas of Modern Spectrum Management, Cambrdge Unversty Presss, 2007 [4] P J Weser and D Hatfed, Spectrum Pocy Reform and the Next Fronter of Property Rghts, George Mason Law revew, vo 15, no 3, pp , 2008 [5] D P Bertsekas, Dynamc Programmng and Optma Contro, Athena Scentfc, Bemont, 1984 [6] M Ahmed, Ca Admsson Contro n Wreess Networks: A Comprehensve Survey, IEEE Communcatons Surveys, vo 7, no 1, pp 50 69, 2005 [7] S A Lppman, Appyng a New Devce n the Optmzaton of Exponenta Qeueng Systems, Operatons Research, vo 23, no 4, pp , 1975 [8] R Ramee, R Nagaraan, and D F Towsey, On Optma Ca Admsson Contro n Ceuar Networks, Infocom, pp 43 50, 1996 [9] H Mutu, M Aanya, and D Starobnsk, Spot Prcng of Secondary Spectrum Access n Wreess Ceuar Networks, IEEE/ACM Transactons on Networkng, vo 17, no 6, pp , 2009

7 Reservaton Parameter R) Ce 1 Ce 2 Ce 3 Ce 4 Ce 5 Ce 6 Ce Step t) a) Revenue Ŵ) Step t) Fg 3 a) Traectores for updatng the reservaton parameters n a 7-ce attce topoogy In the frst 1000 steps, the reservaton parameters converge to the vaues R = 52 for = 1, 7 When traffc rates change, the agorthm adapts and the reservaton parameters converge fast to the new vaues R 1 = 51 and R = 50 for = 2, 7 b) Rate of revenue at dfferent tme steps of the mpementaton In the frst 1000 steps, the revenue rate mproves to the vaue 811 After the change n traffc rates, the agorthm adapts the reservaton parameters and the rate mproves to the new vaue 1099 b) [10] F P Key, Loss networks, Annas of Apped Probabty, vo 1, pp , 1991 [11] F P Key, Routng and Capacty Aocaton n Networks wth Trunk Reservaton, Math of Oper Res, vo 15, pp , 1990 [12] J S Evans and D Evertt, On the Teetraffc Capacty of CDMA Ceuar Networks, IEEE Trans on Vehcuar Tech, vo 48, no 1, pp , 1999 [13] J S Evans and D Evertt, Effectve Bandwdth-Based Admsson Contro for Mutservce CDMA Ceuar Networks, IEEE Trans on Vehcuar Tech, vo 48, no 1, pp 36 46, 1999 [14] P B Key, Optma Contro and Trunk Reservaton n Loss Networks, Probabty n the Engneerng and Informatona Scences, vo 4, pp , 1990 [15] B Haek, A Tutora Survey of Theory and Appcatons of Smuated Anneang, IEEE Conference on Decson and Contro CDC, 1985