Hotspot Economics: Procurement of Third-Party WiFi. Capacity for Mobile Data O oading

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1 Hotspot Economcs: Procurement of Thrd-Party WF Capacty for Moble Data O oadng Langfe Qu Unversty of Texas at Austn Huaxa Ru Unversty of Rochester Andrew Whnston Unversty of Texas at Austn September 12, 2013 Abstract The unprecedented growth of cellular tra c drven by web sur ng, vdeo streamng, and cloud-based servces s creatng challenges for cellular servce provders to ful ll the unmet demand. To mnmze congeston costs for under-served demand (e.g., dssats ed customers, or churn), the servce provder s wllng to pay WF hotspots to serve the demand that exceeds capacty. In the present study, we propose an optmal procurement mechansm wth contngent contracts for servce provders to leverage the advantages of both cellular and WF resources. As compared wth conventonal cellular communcaton technologes, WF hotspots provde data rates wth a lmted coverage. Our present work contrbutes to the exstng lterature by developng an analytcal model, whch consders ths unque challenge of ntegratng the longer range We thank Xanjun Geng at UT Dallas, Dale Stahl, Maxwell Stnchcombe, and Thomas Wseman at UT Austn, Yu Jn and Wen-Lng Hsu at AT&T Labs Research for ther helpful comments. Ths project has been led as the US Provsonal Patent

2 cellular resource and shorter range WF hotspots. We show the procedure of computng the optmal procurement mechansm wth a tght ntegraton of economcs and computng. The model s valdated usng cellular network data from a large US servce provder. The smulaton results show that the proposed procurement mechansm sgn cantly outperforms the standard Vckrey-Clarke-Groves (VCG) aucton n terms of the servce provder s expected payo. 1 Introducton We are wtnessng an exploson of moble data tra c drven by web sur ng, vdeo streamng, and onlne gamng. Global moble data tra c grew 70 percent n 2012 and wll ncrease thrteen-fold between 2012 and 2017 (Csco 2013). 1 The ncreasng popularty of smartphones has caused the surge n data usage. In 2012, the typcal smartphone generated 50 tmes more moble data tra c than the typcal non-smartphone (Csco 2013). Cloud applcatons and servces such as Net x, YouTube, Pandora, and Spotfy contrbute to the unprecedented growth of cellular tra c. 2 Busness demand s also one of the chef drvers behnd ths ncrease n data tra c as the workforce goes moble and data moves to the cloud. The huge amount of data tra c poses a challenge to the network nfrastructure: Cellular networks are overloaded and congested durng peak hours because of the nsu cent capacty. Network congeston can lead to a bad user experence and churn. 3 The network provders, such as AT&T and Verzon, need to solve the challenge of e ectvely ful llng the unmet demand from consumers for hgh network qualty. In prevous lterature, researchers proposed several solutons from both techncal and 1 Global moble data tra c reached 885 petabytes per month at the end of 2012, up from 520 petabytes per month at the end of 2011 (Csco 2013). 2 Many vdeo streamng applcatons can be categorzed as cloud applcatons. Moble vdeo streamng has much hgher bt rates than other moble content types. Globally, cloud applcatons wll account for 84 percent of total moble data tra c n 2017, compared to 74 percent at the end of 2012 (Csco 2013). 3 As reported by a New York Tmes artcle, customers were angered as Phones overloaded AT&T. Some of the customers mssed nvtatons to meet frends because ther text messages had been delayed. see 2

3 economc aspects: (1) ncreasng the number of cellular base statons or deployng the cellsplttng technology 4 ; (2) upgradng the network to fourth-generaton (4G) networks such as Long Term Evaluaton (LTE), Hgh Speed Packet Access (HSPA) and WMax; (3) expandng capacty by acqurng of the spectrum of other networks, such as the attempted purchase of T-Moble USA by AT&T; (4) adoptng tered prcng mechansms (e.g. usage based prce plans) to constran the heavest moble data users, nstead of usng at-rate prcng plans wth unlmted data 5 ; and (5) o oadng data tra c to WF networks (Bulut and Szymansk 2012). Although all these solutons help solve the problem, each of them has ts advantages and dsadvantages. The rst and second solutons requre heavy nvestments, and gettng government approval for buldng new cell towers can take two years. 6 It s extremely expensve to ncrease the number of cellular base statons just for peak tra c demands. As a result, all cellular networks augment the rst and second solutons wth other approaches to expandng capacty. The thrd soluton su ers from regulatory constrants. Cramton, Skrzypacz, and Wlson (2007) showed that an mportant market falure arses n spectrum auctons wth domnant ncumbents. They suggest that the Federal Communcatons Commsson (FCC) should place lmts on how much spectrum AT&T and Verzon are allowed to buy. Ths concern s also re ected n the acton taken by the FCC to block the recent merger between AT&T and T-Moble. Because of these techncal, economc and regulatory constrants, the fth soluton, usng WF hotspots for moble data tra c o oadng, seems to be the most promsng approach n augmentng solutons (1) and (2). WF hotspots refer to thrd-party hotspot owners, such as local restaurants, bookstores, and hotels, whch o er WF servce to ther customers. WF 4 See Balachandran et al. (2008). ("Whle cell-splttng provdes capacty bene ts, t could be qute expensve and economcally nfeasble snce n addton to the base staton hardware/deployment cost, each of the new bases needs to be provded wth backhaul connectvty ether va wrelne access or mcrowave lnks.") 5 Gupta et al. (2011) shows that the average net bene ts realzed under congeston-based prcng tend to be hgher than the average net bene ts realzed under at-rate prcng. 6 See 3

4 o oadng could potentally be a wn-wn soluton: The cellular servce provder acheves sgn cant savngs by not buldng more cellular base statons just for the peak tra c demands. The WF Hotspots gan addtonal revenue from ther otherwse wasted spare capacty. Moble data o oadng wll become a key ndustry segment n the near future, and cellular servce provders show great nterests n ths approach: KDDI Corporaton, a prncpal telecommuncaton provder n Japan, has cooperated wth about 100,000 commercal WF hotspots by March 2012 (Ajaz et al. 2013). However, o oadng data tra c to thrd-party WF hotspots s not purely a technology augmentng the exstng cellular network. It s also a mechansm desgn problem, consderng the economc ncentves of thrd-party WF hotspots. Instead of focusng only on techncal aspects, we need to combne both the technology of computng and aucton theory to solve the challenge of e ectvely usng WF hotspots. The tght ntegraton of economcs and computaton technology n our system s seen as crucal to address ssues surroundng the data tra c support for cloud-based servces on moble networks, such as busness collaboraton tools, whch requre su cent download and upload speeds. As more busnesses employ moble collaboraton tools to ncrease productvty, any nterrupton to servce nconvenences users and can negatvely a ect busnesses. Moble bandwdth avalablty becomes a key ssue n marketng and operatons for servce provders. Therefore, when network congeston occurs or cell towers fal, network provders need to quckly restore servce to mnmze the mpact on customers. The objectve of the present study was to cope wth ths problem by leveragng the advantages of both cellular and WF resources for network provders. There were several challenges n the desgn of ths procurement aucton system. Frst, the longer range cellular resource ntroduces couplng between the shorter range WF hotspots. WF networks usually have a more lmted range than cellular resources. We needed to desgn an nnovatve procurement aucton consderng ths d erent spatal coverage. Second, the data tra c s uncertan and changes frequently over tme. It s crtcal to provde realtme support for computng the optmal contract. Thrd, Dong et al. (2012) proposed a 4

5 Vckrey-Clarke-Groves (VCG) type aucton for moble data o oadng. A VCG aucton s socally e cent, but t s not optmal for the cellular network (the buyer). A typcal VCG mechansm leads to an overpayment to supplers (Chen et al. 2005). The smulaton results n our study show that, as compared wth the standard VCG aucton, a procurement aucton wth contngent contracts can sgn cantly mprove the cellular network s expected payo. The man contrbuton of our study s to ntroduce and analyze a new procurement mechansm wth contngent contracts to meet these challenges n a realstc envronment. In the model, we partton the range of a cellular base staton (a cell sector) nto several regons. The cellular capacty can serve data tra c n any regon, whereas the WF resource can only serve local tra c. The aucton rule s contngent on demand uncertanty (.e. consumers moble data tra c). In the optmal desgn of such a procurement system, the economc model and the computng technology are complements. After characterzng the Bayesan-Nash equlbrum of the aucton, we need to compute the contract under each demand contngency and store the contracts. When the demand s realzed, we can nd the correspondng contngent contract. Practcal mechansm desgn requres an explct consderaton of computatonal constrants (Bchler, Gupta, and Ketter 2010). In our real-tme auctons, computng and ndng the correspondng contngent contract fast s crtcal. The number of contngent contracts we can mplement s subject to computng speeds. Recent advances n parallel computng, such as the open source cluster computng system, Spark, 7 makes t faster to nd contngent contracts n large databases. Wth extremely fast computng speeds, our aucton system can compute and mplement a huge number of contngent contracts a task that was once consdered computatonally prohbtve and sgn cantly mprove the cellular network s expected gan. In ths sense, the functon of our procurement systems s smlar to Algorthmc tradng n nancal markets (Barclay, Hendershott, and Kotz 2006; Hendershott et al. 2011). Both of them are examples of the technologcal change 7 Spark s an open source cluster computng system that ams to make data analytcs fast. It provdes prmtves for n-memory cluster computng: Data can be loaded nto memory and be quered repeatedly much more quckly than wth dsk-based systems, lke Hadoop MapReduce. 5

6 of computaton and use computer algorthms to automatcally make decsons. Our nsghts also apply more generally to optmal desgn n a class of supply chan problems. 2 Lterature Revew Three streams of lterature are related to ths study. The rst stream nvolves the study of three d erent aucton schemes: quantty auctons, mult-attrbute auctons, and auctons wth contngent contracts. Dasgupta and Spulber (1989) extended the standard xed quantty aucton and studed a quantty aucton that allows the quantty of the goods purchased to be endogenously based on the submtted bds. Our study d ered from ther approach n two crtcal ways: Frst, the unque feature of d erent spatal coverage makes a d erence for the optmal aucton desgn. The cellular resource can serve data tra c n any regon n a cell sector, whereas the WF resource can only serve local tra c. Buyng more resources from a local WF hotspot n one regon frees up more cellular resources. Second, our aucton rules were determned by the contngency terms. The terms of a contngent contract are not nalzed untl the uncertan demand s realzed. In many procurement stuatons, the buyer cares about other attrbutes n addton to prce when evaluatng the submtted bds. In a mult-attrbute scorng aucton, supplers submt multdmensonal bds, and the contract s awarded to the suppler who submtted the bd wth the hghest score accordng to a scorng rule. Che (1993) developed a scorng procurement aucton n whch supplers bd on two dmensons of the good. Ths scorng aucton allows only sole sourcng. However, o oadng data tra c to multple WF hotspots s naturally done n our procurement settng. In a keyword advertsng market, Lu et al. (2010) studed a weghted unt-prce rule that s d erent from prevous scorng auctons. Adomavcus et al. (2012) examned the mpact of feedback on the outcomes and dynamcs of the mult-attrbute auctons usng a laboratory experment. Contngent contracts have been wdely studed n economcs lterature (Wlson 1989). 8 8 A contngent contract s a type of forward contract that depends on the realzatons of some uncertan 6

7 Hansen (1985) studed an aucton wth contngent payments. DeMarzo et al. (2005) proposed securty-bd auctons n whch bdders compete for an asset by bddng wth securtes whose payments are contngent on the asset s realzed value. Chen et al. (2009) showed that the procurement auctons wth contngent contracts can manage the project falure rsk of supplers and sgn cantly mprove both socal welfare and the buyer s payo. The model n our study d ers from such auctons n the applcaton settng and aucton formats. The second stream of lterature related to ours s the study of supply chan management. Conceptually, the key problem n the procurement of thrd party WF capacty s the supply chan management. The outsourcng decsons become complcated when supplers have d erent characterstcs. Cachon and Larvere (2005) demonstrated that revenue-sharng contracts can mprove the supply chan performance. Tomln (2006) studed the optmal dsrupton management strategy when a buyer can source from two supplers: one that s unrelable and another that s relable but more expensve. Allon and Meghem (2010) consdered the case when a buyer faces supplers of multdmensonal types: a responsve nearshore source wth hgher cost (e.g., Mexco) and a low-cost o shore source (e.g., Chna). They analyzed a talored base-surge sourcng to capture the classc trade-o between cost and responsveness. Yang et al. (2012) appled the revelaton prncple to derve the buyer s optmal procurement contract when supplers possess prvate nformaton about ther dsrupton lkelhood. In our context, the coverages of WF hotspots (supplers) mght be d erent. The procurement mechansm thus needs to consder how to optmally ntegrate the cellular capacty of servce provders and the thrd-party WF capacty. Besdes that, demand and supply uncertantes tend to a ect the supply chan desgn. Mendelson and Tunca (2007) showed that a combnaton of xed-prce contracts and open market tradng can mprove supply chan e cency. In the wreless ndustry, cellular tra c s hghly dynamc and unpredctable, and we propose a contngent mechansm to handle ths tra c uncertanty. Our research s also related to the computer scence lterature on moble data o oadng. events. For example, a contract can be contngent on the uncertan demand or the future spot market prce. 7

8 Balasubramanan et al. (2010) desgned a WF o oadng system to augment moble 3G capacty. They found that for a realstc workload, WF o oadng can reduce 3G usage by almost half for a delay tolerance of one mnute. 9 Dong et al. (2012) propose a VCG procurement aucton for moble o oadng to ncentvze WF hotspot owners to be truthful n the bddng process. Ios ds et al. (2013) desgned a double aucton mechansm talored to the wreless o oadng problem. The ntegraton of economcs and computaton technology allows us to mprove the cellular network s expected payo n two mportant ways: (1) The approprate mechansm desgn avods overpayment n the VCG aucton (economcs); and (2) the parallel computng technology mproves the performance of the procurement aucton by ndng the optmal contract under each contngency on demand uncertanty (computaton technology). 3 A Benchmark Model: Sngle WF Regon A cellular network provdes servce to ts customers who demand bandwdth. Congeston results when network capacty cannot satsfy nstantaneous user demand. When the user demand for moble data s below a certan threshold X B, the cellular servce provder faces no addtonal cost except the sunk cost of buyng the spectrum and keepng the system runnng. However, when the demand X ~ exceeds the threshold, the cellular servce provder ncurs a cost of C 0 ( ~ X X B ). The threshold X B s the cellular capacty 10 owned by the servce provder. The standard metrcs used n the telecommuncatons ndustry to measure qualty of servce (QoS), such as Erlang B formula and Klenrock delay formula, depend on the d erence between user demand and capacty or ther rato (Pnto and Sbley 2013). In our problem settng, ~ X XB s the d erence between user demand and capacty. Note 9 Lee et al. (2010) show that a WF network o oads about 65% of the total moble data tra c and saves 55% of battery power wthout usng any delayed transmsson. 10 X B s nterpreted as the channel capacty stated by the Shannon Hartley theorem (Kennngton et al. 2011). The theorem shows that when the nformaton transmtted rate s less than X B, the probablty of error at the recever can be made arbtrary small. When the nformaton transmtted rate s greater than X B, the probablty of error ncreases as the nformaton transmtted rate s ncreased. 8

9 that capacty should not be nterpreted as a strct output lmt, but rather as a factor n mantanng QoS. The cost functon C 0 () s strctly ncreasng and strctly convex, whch captures the rapdly rsng cost of congeston (e.g., dssats ed customers, or churn). A smlar convex cost functon has been wdely used n modelng the congeston cost of the Internet (Dong et al. 2012). Apparently, we have C 0 (x) = 0 for any x 0. Denote c 0 (x) = C0(x) 0 as the margnal cost of congeston. We model the demand for bandwdth as a random varable X ~ wth a cumulatve dstrbuton functon G( X) ~ n the support [0; 1] 11. Gven the unprecedented growth rate of moble data demand and the hgh cost assocated wth congeston, the cellular network s nterested n procurng spare resources from thrd-party WF hotspots. Fgure 1: Tmelne for a Sngle Regon Aucton In ths benchmark model, we assume: (1) A sngle wnnng hotspot obtans the procurement contract. (2) The range of a cellular base staton (a cell sector) s the same as the range of a hotspot (a WF regon), for smplcty. Thus, we only have a sngle WF regon n a cell sector. We relax these two assumptons n Secton 4. The tmelne for ths benchmark model s shown n Fgure 1. If the cellular network purchases Y 1 unts of bandwdth from the hotspot, then the expected reducton of congeston 11 Note that the assumpton of the support s essentally sayng that demand s bounded, whch s wthout loss of generalty for any realstc stuaton. Of course, the nterpretaton of 1 wll be d erent for d erent scenaros. For example, 1 could be nterpreted as 1 terabyte per second or 10 terabytes per second. 9

10 cost for the cellular network s Z 1 V (Y 1 ) = C 0 ( X ~ X B )dg( X) ~ 0 {z } congeston cost wthout WF Z 1 C 0 ( X ~ X B Y 1 )dg( X) ~ ; (3.1) X B +Y 1 {z } congeston cost wth WF whch s the valuaton that the cellular network attaches to the addtonal bandwdth Y 1. The rst part R 1 0 C 0( ~ X X B )dg( ~ X) s the expected congeston cost wthout procurng from WF hotspots, and the second part, R 1 X B +Y 1 C 0 ( ~ X X B Y 1 )dg( ~ X) s the expected congeston cost when the purchase quantty s Y 1. Because V 0 (Y 1 ) = Z 1 X B +Y 1 C 0 0( ~ X X B Y 1 )dg( ~ X) > 0 (3.2) and V 00 (Y 1 ) = Z 1 X B +Y 1 C 00 0 ( ~ X X B Y 1 )dg( ~ X) C 0 0(0)g(X B + Y 1 ) < 0; where g() s the densty functon of ~ X. V (Y1 ) s strctly ncreasng and strctly concave, whch s not surprsng gven that the cost of congeston s convex. We assume that the cost functon for hotspot to provde capacty Q to the cellular network s C(Q; ) Z Q 0 c(q; )dq; = 1; 2; :::; n: where c(q; ) 0 s the margnal cost functon for hotspot, and where represents each hotspot s prvate nformaton about the cost of capacty provson. The cost of provdng bandwdth for a hotspot s based on ts nstantaneous user demand and many other consderatons that may not be revealed to the cellular network. For example, congeston encourages customers of hotspots to balk and cause a negatve mpact on hotspots pro ts. Ths mpact mght d er among d erent hotspots, and only hotspots know the actual mpact. We assume c q (q; ) 0 to capture the fact that the margnal cost of provdng capacty for each hotspot ncreases as more capacty s provded to the cellular network. Margnal costs are ncreasng 10

11 and convex n the cost parameter, c 0, c 0. Also, we assume c q 0. Hotspots cost parameters are ndependently and dentcally dstrbuted wth a contnuously d erentable cumulatve dstrbuton functon F () de ned on [; ] whch s common knowledge. De ne H() F ()=F 0 (), and let H() be an ncreasng functon of. Ths assumpton of monotone hazard rate s sats ed by commonly used dstrbuton functons such as the unform dstrbuton. It follows from Dasgupta and Spulber (1989) that the optmal allocaton can be mplemented va a quantty aucton (sealed bd) where The cellular servce provder announces a payment-bandwdth schedule B = B(Q); Each hotspot chooses the bandwdth they want to sell gven B(Q); and The hotspot choosng to provde the hghest capacty, Q, wns the aucton and sells the chosen capacty to the cellular servce provder. Ths quantty aucton s optmal for the cellular servce provder f we assume that a sngle wnner emerges. Gven the payment-bandwdth schedule B(Q), the hotspots bdng strategy s denoted by Q (): A hotspot wth prvate cost parameter, 2 [; ], bds Q (). Let be a threshold cost parameter: Hotspots for whch the cost parameter exceeds do not bd, whle those wth < bd accordng to Q (). Ths represents the ndvdual ratonalty constrant. Proposton 1 (Sngle Regon) In the optmal quantty aucton, the payment-bandwdth schedule B (Q) and the optmal bddng strategy Q () are gven by the followng equatons: B (Q) = C Q; Q 1 (Q) + R Q 1 (Q) (1 F (x))n 1 C (Q (x) ; x) dx (1 F (Q 1 (Q))) n 1 ; (3.3) V 0 (Q ()) = C Q (Q () ; ) + C Q (Q () ; ) H () ; (3.4) 11

12 where Q 1 () denotes the nverse functon of Q (). The cellular servce provder s expected gan s Z n (1 F ()) n 1 F 0 () [V (Q) C (Q; ) C (Q; ) H ()] d: (3.5) Under asymmetrc nformaton, ths s the hghest expected pro t for the cellular servce provder when t must procure from a sngle wnnng hotspot. Proof. See Appendx. Note that the hotspot wth the lowest always wns the aucton, because t has the lowest margnal cost of provdng bandwdth and provdes the hghest Q under the paymentbandwdth schedule B(Q). In equaton 3.5, n (1 F ()) n 1 F 0 () s the densty of the lowest. The cellular servce provder s bene t s the expected reducton of the congeston cost, whch s gven by equaton 3.1. C (Q; ) + C (Q; ) H () s the "vrtual cost" the cellular servce provder pays to the wnnng hotspot. Under complete nformaton, the payment to the wnnng hotspot s the cost C (Q; ). The nformaton asymmetry s re ected n the term C (Q; ) H (), whch s the nformaton rent of the wnnng hotspot. 4 Multple WF Regons 4.1 A Non-Contngent Procurement Aucton In the benchmark model, we assume that only a sngle hotspot wns the aucton. However, the WF capacty for one hotspot s lmted, and relyng on multple hotspots s optmal because of the convexty of the congeston cost functons. The benchmark model also assumes that the range of a cellular base staton s the same as the range of a hotspot. However, cellular resources and WF resources actually have d erent spatal coverages. In suburban areas, a typcal cellular base staton covers 1-2 mles (2-3 km) and n dense urban areas, t may cover one-fourth to one-half mle ( m). A typcal WF network has a range of 12

13 Fgure 2: Multple WF Regons 120 feet (32 m) ndoors and 300 feet (95 m) outdoors. 12 Therefore, we need to partton a cell sector nto several regons. In Fgure 2, a red crcle s a WF regon. Usually, a WF regon has several WF hotspots that are close together. Now suppose there are M WF regons n a cell sector, 1; 2; ; M, and the demand for regon m s X ~ m. The demand vector ( X ~ 1 ; X ~ 2 ; ; X ~ M ) has a jont dstrbuton functon G( X ~ 1 ; X ~ 2 ; ; X ~ M ). We assume the same congeston cost functon of the cellular servce provder for all regons. Cellular resources can serve tra c n any regon m, whereas WF hotspots n regon m can only serve local tra c. 13 A unque challenge n the procurement aucton s that the longer range cellular resource ntroduces couplng between the shorter range WF hotspots. In ths secton, we derve the optmal aucton rule under d erent spatal coverages. The tmelne for a multple regon aucton s shown n Fgure 3. The cellular servce provder follows a two-step decson procedure: In the rst stage, t purchases WF capacty 12 See and 13 A WF hotspot mght be on the boundary of two regons. In Secton 6, we generate regons by clusterng the WF hotspots usng k-means method. Note that for smplcty, we assume that cellular capacty can be reallocated seamlessly from one WF regon to another. In practce, some cellular capacty can be redrected (e.g., core processng for the base staton), and some capacty cannot be redrected (e.g., rado capacty for drectonal antennas these cover only a certan drecton and angular range). 13

14 Fgure 3: Tmelne for a Multple Regon Aucton from hotspots n d erent regons. In the second stage, the cellular servce provder adjusts the allocaton of cellular resources across regons. We rst focus on the optmzaton problem n the second stage. If the cellular servce provder purchases Y m unts of bandwdth from hotspots n regon m, then the expected congeston cost s Mn y1 ;y 2 ; ;y M Z 1 s:t: 0 Z 1 0 Z 1 0 MX C 0 ( X ~ m Y m y m )dg( X ~ 1 ; X ~ 2 ; ; X ~ M ) m=1 MX y m = X B ; y m 0; for m = 1; 2; :::M; (4.1) m=1 where y m s the amount of cellular capacty allocated to regon m. The cellular servce provder can adjust the allocaton of cellular resources across regons through varyng y m. Purchasng more capacty from a local WF hotspot frees up more cellular resources, whch can be allocated to other regons. Note that the value of ths mnmzaton problem s the expected congeston cost when the servce provder can ntegrate both cellular resources and WF resources. 14

15 Smlarly, wthout hotspots, the expected congeston cost s Mn y1 ;y 2 ; ;y M Z 1 s:t: 0 Z 1 0 Z 1 0 MX C 0 ( X ~ m y m )dg( X ~ 1 ; X ~ 2 ; ; X ~ M ) m=1 MX y m = X B ; y m 0; for m = 1; 2; :::M: m=1 The value of ths mnmzaton problem s the expected congeston cost when the servce provder reles solely on cellular resources. where Because C 0 () s convex, usng Jensen s nequalty, we have MX m=1 MX m=1 C 0 ( ~ X m y m ) M C 0 1 M C 0 ( ~ X m Y m y m ) M C 0 1 M! MX ( X ~ m y m ) = M C 0 X m=1! MX ( X ~ m Y m y m ) = M C 0 X Y ; m=1 (4.2) X X = ~ 1 + X ~ X ~ M M X B ; and Y = Y 1 + Y Y M M : If we de ne X = ~ X 1 + ~ X ~ X M X B as the total excess demand of the sector, X = X=M can be nterpreted as the average excess demand across regons. The optmal allocaton of cellular resources should be y m = ( ~ X m X) (Ym Y ) wth usng WF hotspots and y m = ~ X m X wthout usng hotspots. For such allocatons of cellular resources across regons to be feasble, we need y m 0, or equvalently, X B M Y m 1 M! MX Y =1 ~X m 1 M MX =1 ~X! ; (4.3) for m = 1; 2; :::; M, and for all possble pro les of prvate cost parameters ( ; ). The condton s more lkely to be sats ed f bandwdth demand and hotspots supply are relatvely homogeneous across regons or f X B s relatvely large. Alternatvely, the condton s more 15

16 lkely to be sats ed f more hotspot bandwdth supply s avalable n regons wth more bandwdth demand (.e., Xm ~ and Y m are postvely correlated). Apparently, the second condton s a reasonable assumpton because the economc ncentve to supply bandwdth s larger n regons wth hgh demand. In ths secton, we assume nequalty 4.3 s always sats ed. We relax ths assumpton n Secton 5. The expected reducton of congeston cost for the cellular servce provder after the procurement of hotspot bandwdth s V (Y 1 ; Y 2 ; ; Y M ) Z 1 Z 1 Z 1 = M C 0 ( X)dG( X ~ 1 ; X ~ 2 ; ; X ~ M ) {z } congeston cost wthout WF Z 1 Z 1 Z 1 M C 0 ( X Y )dg( X ~ 1 ; X ~ 2 ; ; X ~ M ): {z } congeston cost wth WF Because the valuaton functon s only a functon of ~ X1 ; ; ~ X M through X, we denote the dstrbuton of X as G and rewrte the valuaton as V (Y 1 ; Y 2 ; ; Y M ) = V Y = M Z 1 0 C 0 ( X)d G( X) M Z 1 Y C 0 ( X Y )d G( X) (4.4) Note the smlarty between the valuaton functon for the case of a sngle regon (equaton 3.1) and the valuaton functon for the case of multple regons (equaton 4.4), whch mmedately mples that V Y s also ncreasng and concave n Y. Indeed, the sngle regon case can be vewed as the same as a multple-regon case n whch M = 1. Because the valuaton functon s only a functon of Y 1 ; ; Y M through Y, the task of undertakng multple procurements n multple regons s essentally the same task as undertakng a sngle procurement n one sector n whch the bandwdth capacty s procured from several hotspots n d erent regons. In other words, we are dealng wth a varable quantty procurement aucton wth multple wnners. In the rst stage, the cellular servce provder s optmzaton problem s characterzed as a drect revelaton game n whch hotspots announce ther types and truthful revelaton s a Bayes-Nash equlbrum. We adopt the 16

17 notatonal conventon of wrtng = ( 1 ; :::; 1 ; +1 ; :::; n ). The optmal allocaton for the cellular servce provder can be mplemented va a drect revelaton mechansm where The cellular servce provder announces a payment-bandwdth schedule P ( ; ), and a bandwdth allocaton schedule q = Q ( ; ); Hotspot reports the prvate cost parameter gven P ( ; ) and Q ( ; ); Hotspot provdes bandwdth q = Q ( ; ) to the cellular servce provder and ts payment s P = P ( ; ). The optmal mechansm (P ( ; ); Q ( ; )) for the cellular servce provder s gven by the followng proposton: Proposton 2 (Multple Regons) In the optmal drect revelaton mechansm, all hotspots truthfully announce ther cost parameters. The optmal bandwdth allocaton schedule q = Q ( ; ), for = 1; 2; :::n s gven by: bv 0! nx q = c(q ; ) + c (q ; )H( ): =1 where V Y = V b ( P n =1 q ) = M R 1 C 0 0( X)d G( X) M R 1 1 P C n 0( P X 1 n M =1 q M =1 q )dg( X). The optmal payment schedule P = P ( ; ), for = 1; 2; :::n s gven by: Z P ( ; ) = C(Q ( ; ) ; ) + C (Q (; ) ; )d: The cellular servce provder s expected gan s E " bv! nx Q ( ; ) nx C(Q ( ; ) ; ) # nx C (Q ( ; ) ; )H( ) : =1 =1 =1 Under asymmetrc nformaton, ths s the hghest expected pro t for the cellular servce provder when t can procure capacty from multple hotspots n d erent regons (second best). 17

18 Proof. See Appendx. In the drect revelaton game, hotspot announces ts cost parameter. The capacty t needs to provde s q = Q ( ; ), and ts payment s P = P ( ; ). Ths optmal mechansm s a global aucton ncludng all hotspots from d erent regons. Note that launchng separate auctons wthn each regon s not optmal because the cellular resource can serve tra c n any regon. The ntuton s that procurng more WF resources n one regon frees up more cellular resources, and the cellular servce provder can allocate the cellular resources to other regons. In equlbrum, the vrtual margnal costs c(q ; ) + c (q ; )H( ) are equalzed across hotspots n d erent regons, and the margnal bene ts of procurng WF capacty should be equalzed across regons as well. In addton, the number of hotspots mght be small n some spec c regons. The global aucton e ectvely creates the nter-regon competton among the hotspots when the ntra-regon competton s lmted. Under our procurement mechansm, the network becomes more reslent because the peak data tra c can be seamlessly o oaded to some nearby hotspots wth mnmal servce dsrupton. The procedure of computng the optmal procurement aucton s ncluded n Appendx. 4.2 A Contngent Procurement Aucton In the prevous secton, the procurement mechansm s mplemented before the demand s realzed. In ths sense, there s an ex-post ne cency: The cellular servce provder mght purchase ether too much or too lttle bandwdth. Contngent contracts can be useful n mtgatng ths problem. In ths secton, the aucton rule s contngent on demand uncertanty. A prerequste for a contngent contract s that the uncertan demand should be contractable, whch means the realzed demand must be one that both cellular servce provder and hostpots can observe and measure and that nether sde can covertly manpulate. An ncreasngly mportant response to cost pressure n supply chans s the nformaton sharng between retalers and supplers (Avv 2001). Emergng technologes, such as Electronc Data Interchange (EDI) and Rado Frequency Ident caton (RFID), facltate sales data-sharng 18

19 and make the desgn of contngent contracts more practcal and relable. In our problem settngs, the cellular servce provder can drectly observe the demand nformaton, but the hotspots cannot observe t. In ths secton, we show that the cellular servce provder does not have ncentve to msreport the prvate demand nformaton. Therefore, the desgn of a procurement aucton wth contngent contracts s practcal. 14 Now we present a theory on how to desgn the optmal mult-regon procurement aucton wth contngent contracts. Followng from equaton 4.4, the expected reducton of congeston cost for the cellular servce provder after the procurement of hotspot bandwdth gven the realzaton of the demand ( X ~ 1 ; X ~ 2 ; ; X ~ M ) s U(Y 1 ; Y 2 ; ; Y M ) = U Y = M C 0 ( X) M C 0 ( X Y ); where X = ~ X 1 + ~ X 2 ++ ~ X M M X B. U Y s also ncreasng and concave n Y. When the demand s realzed, the cellular servce provder can observe a vector of demand, ( X ~ 1 ; X ~ 2 ; ; X ~ M ), and then announces a vector, X a, to the hotspots. The optmal allocaton for the cellular servce provder can be mplemented va a drect revelaton mechansm where The cellular servce provder announces a payment-bandwdth schedule P ( ; ; X ~ 1 ; X ~ 2 ; ; X ~ M ), and a bandwdth allocaton schedule q = Q ; ; X ~ 1 ; X ~ 2 ; ; X ~ M ; Hotspot reports the prvate cost parameter gven P ( ; ; X ~ 1 ; X ~ 2 ; ; X ~ M ) and Q ; ; X ~ 1 ; X ~ 2 ; ; X ~ M ; After the demand s realzed, the cellular servce provder announces the demand nformaton, X a. Hotspot provdes bandwdth q = Q ( ; ; X a ) to the cellular servce provder and 14 Sharng demand nformaton wth hotspots s a type of open book polcy for a cellular servce provder. The contnung nteracton between a cellular servce provder and hotspots makes contngent contracts more reasonable and attractve. 19

20 ts payment s P = P ( ; ; X a ). Note that X a can be some value other than ( ~ X 1 ; ~ X 2 ; ; ~ X M ). However, we show that X a = ( ~ X 1 ; ~ X 2 ; ; ~ X M ) n equlbrum n the followng proposton. Proposton 3 In the equlbrum of a mult-regon procurement aucton wth contngent contracts, the cellular servce provder truthfully announces the demand nformaton: X a = ( ~ X 1 ; ~ X 2 ; ; ~ X M ). Proof. See Appendx. Ths proposton shows that n equlbrum the cellular servce provder wll truthfully report the demand nformaton. The ntuton s that f the cellular servce provder msreports the demand nformaton, t dstorts the bandwdth provson of WF hotspots and reduces the expected payo of the cellular servce provder. The optmal mechansm P ( ; ; X ~ 1 ; X ~ 2 ; ; X ~ M ); Q ; ; X ~ 1 ; X ~ 2 ; ; X ~ M for the cellular servce provder s gven by the followng proposton: Proposton 4 In a mult-regon procurement aucton wth contngent contracts, the optmal bandwdth allocaton schedule q = Q ; ; ~ X 1 ; ~ X 2 ; ; ~ X M, for = 1; 2; :::n s gven by: bu 0! nx q = c(q ; ) + c (q ; )H( ): (4.5) =1 where U Y = b U ( P n =1 q ) = M C 0 ( X) M C 0 ( X 1 M P n =1 q ). The optmal payment schedule P = P ( ; ; ~ X 1 ; ~ X 2 ; ; ~ X M ), for = 1; 2; :::n s gven by: P ( ; ; X ~ 1 ; X ~ 2 ; ; X ~ M ) = C Q ; ; X ~ 1 ; X ~ 2 ; ; X ~ M ; Z + Q ; ; X ~ 1 ; X ~ 2 ; ; X ~ M ; d: C 20

21 The cellular servce provder s expected payment s E P n =1 C(Q ; ; ~ X 1 ; ~ X 2 ; ; ~ X M ; ) + P n =1 C (Q ; ; ~ X 1 ; ~ X 2 ; ; ~ X M ; )H( ) : (4.6) Proof. See Appendx. Ths proposton s smlar to Proposton 2, but the optmal mechansm depends on the contngent demand. Therefore, ths contngent procurement mechansm can mprove the ex-post e cency. 5 Extenson In Secton 4, we assume that y m 0 for all m, or equvalently, the cellular capacty X B s su cently large such that for all m and all possble pro les of cost parameters ( ; ) drawn from the dstrbuton F (), condton 4.3 s always sats ed: X B M Y m 1 M! MX Y =1 ~X m 1 M We call t the feasblty condton. Note that condton 4.3 may hold for some pro les of cost parameters ( ; ) but not for some others. Our feasblty condton requres that condton 4.3 holds for every pro le of cost parameters ( ; ). In ths secton, we ntroduce a mod ed contngent procurement mechansm to dscuss the optmal procurement mechansm when the feasblty assumpton s relaxed. We start wth a smple toy model wth two WF regons, that s, M = 2. To gan some ntutons about the feasblty condton, we depct two llustratng examples n Fgure 4. We assume that there are two WF regons (M = 2), and that each regon has four hotspots (n = 8). The congeston cost functons for the servce provder and WF hotspots are smple: C 0 (x) = 2x 2, and C (x; ) = x 2, where the prvate cost parameters for hotspots,, s drawn from a unform dstrbuton U[0; 1] for 1,000 tmes. 21 MX =1 ~X! :

22 Fgure 4: Illustratng Examples of the Feasblty Condton ~ m, m = 1; 2, s drawn from ndependent standard unthe data tra c for each regon, X form dstrbutons U [0; 1] for 1,000 tmes. In the gure, The blue "X"s ndcate that the ~1; X ~ 2, the red dots ndcate feasblty condton s always sats ed when the demand s X that condton 4.3 s volated for some pro les of cost parameters ( ; ) drawn from the dstrbuton F ( ), and the black stars ndcate that condton 4.3 s volated for all possble pro les of cost parameters ( ; ) drawn from the dstrbuton F ( ). When the feasblty condton s always sats ed (the blue "X"s), the optmal procurement mechansm s the global aucton we dscussed n Secton 4.2. When the feasblty condton s always volated (the black stars), the margnal bene ts of procurng WF capacty for the cellular servce provder cannot be equalzed across d erent regons. In ths case, a separate local aucton for each regon s optmal. Our mod ed mechansm manly focuses on the thrd scenaro: the condton 4.3 s volated for some pro les of cost parameters ( ; ) (the red dots). The cellular capacty, XB, s set to be 0:4 n the left panel and 0:2 n the rght panel. Fgure 4 shows that the feasblty condton s more lkely to be volated when the demands are unbalanced or XB s small. Under the mod ed mechansm, the allocaton scheme of cellular resource s denoted by a n o ~ ~ ~1; X ~ 2 s the fracton of cellular vector, m = 1; 2, where m ; ; X m ; ; X1 ; X2 22

23 resource allocated n regon m, and t s a functon of the reported types of hotspots and the demand contngency. The mod ed procurement mechansm for two regons s descrbed as follows: The cellular servce provder announces a payment-bandwdth schedule P ( ; ; X ~ 1 ; X ~ 2 ), an allocaton scheme of cellular resource n m ; ; X ~ 1 ; X ~ o 2, and a bandwdth allocaton schedule q = Q ; ; X ~ 1 ; X ~ 2 ; m ; ; X ~ 1 ; X ~ 2, m = 1; 2; Hotspot reports the prvate cost parameter ; Hotspot provdes bandwdth q = Q ; ; X ~ 1 ; X ~ 2 ; m ; ; X ~ 1 ; X ~ 2 to the cellular servce provder, and ts payment s P = P ( ; ; ~ X 1 ; ~ X 2 ). Let s de ne y m as the optmal amount of cellular capacty allocated to regon m when we don t consder the constrant y m 0, so y m s the soluton to the followng congeston cost mnmzaton problem when Y m s the optmal procurement quantty n regon m: mn y 1 ;y 2 s:t: 2X C 0 ( X ~ m Y m y m ) m=1 2X y m = X B : m=1 and ym = ( X ~ m X) (Ym Y ) " X = ( X ~ m X) Q ; ; X ~ 1 ; X ~ 2 2 m 1 2 nx Q ; ; X ~ 1 ; X ~ # 2 ; =1 where Q ; ; ~ X 1 ; ~ X 2 s gven by equaton 4.5 when M = 2. The optmal mod ed mechansm (P ; q ; m) for the cellular servce provder s gven by the followng proposton: 23

24 Proposton 5 If M = 2 and the feasblty condton s not sats ed, the optmal allocaton allocaton scheme of cellular resource s gven by m ; ; X ~ 1 ; X ~ 2 = 8 >< >: 0, f y m < 0; y m =X B, f 0 y m X B ; 1, f y m > X B ; We denote Q ; ; ~ X 1 ; ~ X 2 the optmal bandwdth allocaton schedule q q as the soluton gven by equaton 4.5. If m = y m =X B, s gven by = Q ; ; ~ X 1 ; ~ X 2 ; 2 m: If m = 0 or 1, q s gven by C 0 0 ~X m mx B X 2 m q = c (q ; ) + c (q ; )H( ); 2 m;! (5.1) The optmal payment schedule P ( ; ; X ~ 1 ; X ~ 2 ), for = 1; 2; :::n, s gven by: Z P ( ; ; X ~ 1 ; X ~ 2 ) = C (q ; ) + C (q ; ) d: (5.2) Proof. See Appendx. We bre y outlne the steps of the proof here. Frst, we need to show that the proposed mechansm s ncentve compatble: Gven the mod ed mechansm (P each hotspot does not have an ncentve to msreport ts prvate cost parameter. ; q ; m), Then, we need to show that the proposed mechansm s optmal for the cellular servce provder. The ntuton s that when the feasblty condton s sats ed, the mod ed mechansm s equvalent to the optmal mechansm descrbed n Proposton 4. Note that when the feasblty condton s sats ed, t s optmal for the cellular servce provder to organze a global 24

25 aucton that ncludes all hotspots from d erent regons. When the feasblty condton s not sats ed, an optmal mechansm s to allocate all cellular capacty to one regon, and then organze a separate local aucton for each regon. We show that the expected payo of the cellular servce provder n our mod ed mechansm s the same as the payo under two separate local auctons when the feasblty condton s not sats ed. We can extend our mod ed mechansm to the case that M > 2. The approach s that the multple regon case can be converted to the case that M = 2. Let s denote y mk, for k = 1; 2; :::M and m = 1; 2; :::; k, as the soluton to the followng congeston cost mnmzaton problem: mn y mk s:t: kx C 0 ( X ~ m Y mk y mk ) (5.3) m=1 kx y mk = X B ; m=1 where Y mk s the optmal procurement quantty n regon m when the partcpatng hotspot 2 [ k j=1 j: Y mk = P 2 Q m k ; ; X ~ 1 ; X ~ 2 ; :::; X ~ k. Q k ; ; X ~ 1 ; X ~ 2 ; :::; X ~ k s gven by equaton 4.5 when the partcpatng hotspot 2 [ k j=1 j. We sort y mk nto descendng order n an terated way. Step (1) y 1M y 2M ::: y MM ; Step (2) for regon m = 1; 2; :::; M 1 n Step 1, we solve the mnmzaton problem 5.3 when k = M 1, and sort y mm 1 : y 1M 1 y 2M 1 ::: y M 1;M 1,...; Step (k + 1) for regon m = 1; 2; :::; M k n step k, we solve the mnmzaton problem 5.3 when k = M k, and sort y m;m k : y 1M k y 2M k ::: y M k;m k, k = 2; 3; :::; M 1. The optmal mod ed mechansm when M > 2 s gven by the followng proposton: Proposton 6 If M > 2 and the feasblty condton 4.3 s not sats ed, the optmal allocaton scheme of cellular resource s gven by the followng terated process: If y MM 0, then m = y mm =X B, for m = 1; 2; :::; M. If y MM < 0, then M = 0, and f y M 1;M 1 0, then m = y mm 1 =X B, for m = 1; 2; :::; M 1. If y M 1;M 1 < 0, then M 1 = 0, :::; and 25

26 f y M k;m k 0, then m = y mm k =X B, for m = 1; 2; :::; M k. If y M k;m k < 0, then M k = 0. If m = y mm k =X B, the optmal bandwdth allocaton schedule q q = Q M k ; ; X ~ 1 ; X ~ 2 ; :::; X ~ M k, for 2 m: s gven by If m = 0, q s gven by: C 0 0 = c (q ~X m X 2 m q! ; ) + c (q ; )H( ); for 2 m; (5.4) The optmal payment schedule P, for = 1; 2; :::n s gven by: P Z = C (q ; ) + C (q ; ) d: (5.5) 6 Smulaton Studes Applyng our model to the network data from one of the largest U.S. servce provders, we address the followng queston n ths secton: As compared wth the standard VCG aucton, how much can our optmal procurement aucton mprove the cellular network s expected payo? The Monte Carlo smulaton results demonstrate that, as compared wth the standard VCG aucton, our contngent procurement aucton sgn cantly mproves the cellular network s expected payo. We also evaluate the mpact of the cellular capacty and the relatve cost of deployng cellular resources on the performance d erence between these two mechansms. Before we do the comparson, we wll rst revew the mult-unt VCG aucton for procurement n our context. The followng lst descrbes the VCG procurement aucton: Invte each hotspot to report ts cost parameter. Denote the submtted cost para- 26

27 meters as f 1 ; 2 ; ; n g. Under the VCG mechansm, the socally e cent allocaton mnmzes the sum of the expected congeston cost of the cellular servce provder and the cost of hotspots. Accordng to equaton 4.2, we have the sum of the expected congeston cost, and the mnmzaton problem s formalzed as follows: mn M q 1 ;q 2 ;:::;q k Z 1 Z Z 1 0 C 0 ( X Y )dg( ~ X 1 ; ~ X 2 ; ; ~ X M ) + nx C(q ; ) =1 s:t: q 0; for = 1; 2; :::; n; Y = 1 MX Y = 1 MX q : M M =1 =1 Let ( 1 ; 2 ; ; k ) be the optmal value of the objectve functon, and let (q1; q2; ; qn) be an optmal soluton to the cost mnmzaton problem. Let ( ) be the optmal value of the objectve functon wth the addtonal constrant q = 0 (.e., hotspot does not partcpate n the aucton). The cellular servce provder wll pay hotspot accordng to the followng: P = ( ) ( 1 ; 2 ; ; n ) + C(q ; ) (6.1) where ( ) ( 1 ; 2 ; ; n ) s the bonus payment to hotspot, representng the postve externalty that hotspot s mposng on the cost mnmzaton problem. The cellular servce provder pays hotspot ts cost C(q ; ), plus ts contrbuton to the cost mnmzaton problem. Ths payment nternalzes the externalty. Hotspot provdes capacty q and receves payment P. Note that the VCG aucton s both truth-tellng and socally e cent by standard arguments. All hotspots bd ther cost parameters truthfully, rrespectve of other hotspots 27

28 Fgure 5: Area Map of A Typcal Cell Sector bds. The VCG mechansm guarantees the mnmum total cost. However, t leads to an overpayment to hotspots that s shown n the smulaton.15 In our smulatons, we consder a typcal urban neghborhood n New York Cty, NY, USA, as shown n Fgure 5. We de ne a cell sector as the range of the cell tower. Our dataset conssts of the locaton nformaton of 14,576 cell towers from a large cellular provder n the U.S. In our smulaton study, we pck a cell tower n New York Cty from the full lst of cell towers and smulate the moble data demand n ths sector. In Fgure 5, T represents the cell tower, and others are 69 WF hotspots n the gven cell sector.16 Followng Dong et al. (2012), we set the communcaton range for a cell tower as 250m, and set the communcaton range for W-F as 100m. The followng steps descrbe the procedure of smulatons: Generatng tra c demands n the gven cell sector: To gan a sense of the populaton densty n the coverage area of the cell tower, we use 2010 census data, whch contans the land area coverage and populaton densty of each zp code. Combnng the market 15 Note that ths VCG mechansm s not contngent on the realzed demand. We also smulate the performance of a contngent VCG mechansm. The basc results of performance comparson reman unchanged. 16 Locatons of commercal WF hotspots are from 28

29 share of ths servce provder for the rst quarter , we estmate the number of users n the gven cell sector. On average, smartphone users consume about 1GB data per month, but the usage patterns of moble data s hghly uneven. 18 Paul et al. (2011) and Jn et al. (2012) found that a small number of heavy users contrbute to a majorty of data usage n the network. To consder the heterogenety of data usage and the e ects of peak hours, we smulate ndvdual data usage from the byte dstrbuton n Jn et al. (2012). 19 Generatng WF regons n the cell sector: Dong et al. (2012) showed that the approprate number of WF regons n a cell sector s sx. Followng ther approach, we generate sx WF regons by clusterng the WF hotspots usng k-means. In Fgure 5, Regon A, Regon B,..., and Regon F ndcate whch regon the WF hotspots belong to. Generatng tra c demands n each WF regon: We use two d erent methods to place users n the cell sector and assgn them to the correspondng WF regons accordng to ther locatons. (1) All users are randomly placed n the cell sector. (2) All users are placed accordng to the denstes of the hotspots. 20 After placng all the users, a nearest hotspot s calculated for each user locaton. If the dstance between the nearest hotspot found and the user locaton s less than the hotspot range (100m), the user s counted as one of the regonal populaton accordng to the WF regon; otherwse, the user s consdered as n the regon wth no hotspots (regon 0). We run 1, See 18 See ercewreless.com/specal-reports/average-androd-os-smartphone-data-use-acrosster-1-wreless-carrers-thr-1#xzz2zspdos5z. 19 We obtan the quantles of the byte dstrbuton from Jn et al. (2012) and generate ndvdual usage usng the Johnson System. We also adjust the usage by consderng the e ect of peak hours, see 20 To calculate the denstes of the hotspots for d erent locatons, we dvde the square crcumscrbng the cell sector nto a 20 by 20 array of grds. By default, each grd has a weght of 1, except the grds whose centers are not n the range of the tower. The grd s weght s ncreased by the number of hotspots whose locatons are nsde the grd. Then, a lst of grd ndces s created accordng to the weght of each grd. Fnally, for each user, a grd ndex s rst unformly chosen from the lst, and then the locaton of the user s unformly chosen from the range of the grd wth the grd ndex just pcked. 29

30 Fgure 6: The Performance Comparon of the Procurement Mechansms for the Servce Provder smulatons to generate tra c demands n each WF regon. Generatng cell tower capacty: The cell tower capacty s set to three carrers, that s, three tmes 3.84 MHz (Dong et al. 2012). Data spectral e cency vares across towers from 0.5 to 2 bps/hz. 21 We set spectral e cency to be 1 by default and then vary the spectral e cency to evaluate ts mpact. Note that when the user demand for moble data s below 80% of the cell tower capacty, the cellular servce provder faces no congeston cost. Usng the algorthms n Secton 4.2 and Secton 5, we conduct a varety of smulatons to compute the correspondng allocaton under the VCG mechansm and our contngent procurement aucton (CPA). The relatve cost of deployng cellular resources as compared wth WF resources a ects the bandwdth allocaton result. Dong et al. (2012) assumed that spectrum cost s always hgher than WF and that WF s always preferred when the cellular servce provder s overloaded. Joseph et al. (2004) assumed that the relatve cost of deployng cellular resources as compared wth WF resources s 4:1. We follow ther assumptons and set the parameter values: C 0 (x) = 0:5 ax 2, and C (x; ) = (0:5 + ) x 2, 21 See cent_use_spectrum.pdf 30