User-initiated Data Plan Trading via A Personal Hotspot Market

Transcription

1 1 User-initiated Data Pan Trading via A Persona Hotspot Market Xuehe Wang, Lingjie Duan, and Rui Zhang Abstract Mobie data services are becoming the main driver of a wireess service provider s WSP s) revenue growth, and two-part tariff data pans each incuding a ump-sum fee and a per-unit charge) are usuay provided to wireess users. Some users can easiy use up their monthy data quota and may pay for costy data over-usage. Motivated by users diverse usage behavior more or ess than the subscribed data quotas), this paper proposes a new type of user-initiated network for ceuar users to trade data pans by everaging persona hotspots PHs) with users smartphones. A user with data surpus can set up a PH and share the ceuar data connection to another user with data deficit in the vicinity. Due to users randomness in data usage, incentive to trade, and user mobiity to enter or eave the PH connection range, the anaysis on the user-initiated network is chaenging. To overcome these issues, we propose a PH-market for users with diverse data usage behaviors and random user mobiity to directy trade data as seers and buyers, by designing a market-cearing price. It is shown that the PH-market greaty saves a users expected costs when the existence condition of the PH-market is met. Finay, as this PH-market wi chaenge the WSP s revenue coection especiay the surcharge from users data over-usage), we anayze the WSP s response to the PH-market and propose two effective countermeasure strategies by either reducing the seing users data quota in their data pans the PH-market s suppy) or increasing the buying users data quota the PH-market s demand). When we have more than one WSPs and they are competitive, we show one WSP can take advantage from the PH-market by indirecty seing more data to the other WSP s users. Index Terms Two-part tariff data pans, persona hotspot, network economics, market-cearing price X. Wang and L. Duan are with the Piar of Engineering Systems and Design, Singapore University of Technoogy and Design, Singapore e-mai: xuehe wang@sutd.edu.sg; ingjie duan@sutd.edu.sg). R. Zhang is with the Department of Eectrica and Computer Engineering, Nationa University of Singapore, Singapore emai: eezhang@nus.edu.sg).

2 2 I. INTRODUCTION With the rapid deveopments of mobie Internet technoogies and socia services, the mobie data services are becoming the main driver of revenue growth of a wireess service provider WSP) [1]. Most WSPs e.g., AT&T and China Mobie) in the word are providing two-part tariff data pans to wireess users. After subscribing to a two-part tariff data pan denoted by B, P, p), a user is given a monthy data cap B at a fixed ump-sum fee P and shoud pay for extra data beyond B at a costy unit price p. Due to the diversity of users data usage behaviors, some users have eftover data, whie some others face data deficit and need to pay costy extra fee to the WSP. Thus, it is beneficia for users to potentiay trade monthy data themseves and save their tota costs. With the technoogica advancements in smartphones, many iphones and Android phones can now set up persona hotspots PHs) to share the ceuar data connections to nearby wireess devices [2]. The physica coverage of a hotspot ranges hundreds of feet ike WiFi and is expected to further increase in the future [3]. However, the deveopment of such user-initiated PH networks is sti ack of a cear business mode and a user ony shares the PH connection with his own or friends devices. Now we provide an iustrative exampe to te the users economic benefits by everaging PHs for data pan trading. User 1 and user 2 stay in the same workpace most of the time and they subscribe to the same two-part tariff data pan B, P, p)=3 GB, CNY 100, CNY 0.3 per MB) provided by China Mobie, where CNY represents Chinese Yuan or Renminbi RMB). Assume users 1 and 2 can precisey predict their monthy usages to be 2 GB and 3.8 GB before trading, respectivey. Their origina costs are CNY 100 without any surcharge and CNY 340 with CNY 240 surcharge, respectivey. By seing 0.8 GB as a part of the unused data from user 1 to 2 at a reasonabe price CNY 0.2 per MB ower than p), user 2 s cost is reduced to CNY 260 and user 1 even gains revenue, i.e., CNY 60, after paying to the WSP. As user 2 s over-usage cost paid to the WSP becomes 0 after trading data, the WSP s revenue from these two users is reduced from CNY 440 to CNY 200. In practice, a user s data usage is random and he cannot predict his future data demand exacty before trading. Under such uncertainty, we are interested to find who the seer or buyer is and how much data to trade. In this paper, we propose a nove PH-market for demand-heterogeneous users to trade their monthy data pans via PHs. To successfuy reaize the PH-market, we face another two chaenges besides usage randomness: users incentive to trade and their random mobiity to enter

3 3 or eave the PH-range. To provide strong incentives for users to participate and trade in the PHmarket, the trading price shoud be designed carefuy to baance the data suppy and demand and ensure the reduction of a users costs. In addition, users are mobie and their arriva or departure wi affect the reationship between suppy and demand in the PH-market, making it difficut for users to estimate their costs. Our main contributions are summarized as foows: A nove PH-market for data pan trading: We propose a PH-market for heterogeneous users to trade their data pan monthy as seers or buyers. We propose and anayze a marketcearing price to baance the data suppy and demand in the PH-market. We show that the PH-market exists when user types are diverse in subscribed data pan or usage behavior. Users behaviors under random mobiity: Despite users mobiity to enter or eave the PHrange and the PH-market s variation, we anayze users optima trading data amounts and show that their average monthy costs reduce in the PH-market. WSP s countermeasures to PH-market: As the WSP s revenue decreases due to the userinitiated PH-market, we provide two user-acceptabe countermeasures for the WSP to reduce its revenue oss reducing the seing users data quota and/or increasing the buying users data quota. For the situations when there are more than one WSPs competing with each other, we discuss the evoution of the WSPs data pans in the PH-market and show that at the equiibrium, the WSPs compete to set their data pans to meet a customers maximum data usage against the PH-market. To our best knowedge, this paper is the first work discussing user-initiated data pan trading by everaging PH connections. There are some other works that consider generic user cooperation through incentive design, and two types of incentive mechanisms caed reputation-based and market-based or credit-based) systems have been investigated. In reputation-based systems, users gain trust as rewards by cooperation and receive punishments for uncooperative behaviors e.g., [4], [5]). In market-based or credit-based) systems, users receive payments or credits) by cooperating with other users e.g., [6] [10]). Motivated by the 2CM 2nd exchange market) data trading patform introduced by China Mobie Hong Kong 1, there have been a handfu of works deaing with eftover data trading to improve data users payoffs via WSP-coordinated market [11], [12]. In the WSP-provided market investigated in [11], [12], the WSP serves as a trading patform manager to match the suppy and demand of data users by charging transaction fee. 1 intro.htm

4 4 Unike these works, we propose a user-initiated market in which each user can freey trade his optima data amount by everaging PHs without the WSP s invovement. Moreover, we further expore the WSP s countermeasures to the user-initiated trading in the PH-market as we as studying the competition between WSPs. It is worth noting that today s WiFi connections are mosty encrypted, so are many smartphone Apps e.g., Appe emai, Aipay) [13] [15]. Therefore, the security and the privacy of a user can be assumed to be guaranteed in the PH-market as users can encrypt the transmitted data and add encryption to data downoaded via PHs, same as in conventiona WiFi. The rest of this paper is organized as foows. The system mode before introducing the PHmarket is given in Section II. In Section III, the PH-market is formay introduced incuding the anaysis of the user behavior and the trading price. In Section IV, we study the WSP s useracceptabe countermeasures to the PH-market. The equiibrium data pans for the case with two WSPs competing with each other are anayzed in Section V. Section VI concudes this paper. II. SYSTEM MODEL WITHOUT PH-MARKET In this section, we provide the WSP and user modes before introducing the PH-market. The key parameters which wi be used throughout the paper are summarized in Tabe I. TABLE I: Key Parameters Symbo B, B h P, P h p D, D h d, d h r λ, λ h K, K h ξ, ξ h π Description subscribed data quota of ight users/heavy users subscription fee of ight users/heavy users unit price for extra data maximum monthy data usage of ight users/heavy users minimum monthy data usage of ight users/heavy users PH-range the density of ight users/heavy users the random number of ight users/heavy users within the PH-range r the average number of ight users/heavy users within the PH-range r trading price We consider two types of users according to their monthy data usage behaviors: K ightusage users and K h heavy-usage users. Our mode and anaysis can be extended to more than two user types without major change of the key insights see Appendix B for detais). Each type of users know their monthy data usage distribution through historica records and experience. Each

5 5 ight user s monthy data usage x is a random variabe with probabiity density function f x ) on the possibe usage range d x D, where d and D are the minimum and maximum monthy data usage of ight users, respectivey. Note that any two ight users reaized usages are generay different at the end of each month. Simiary, each heavy user s monthy data usage x h is a random variabe with probabiity density function f h x h ) on the possibe usage range d h x D h. For anaysis tractabiity, we assume each user type s usage foows a uniform distribution as in [12], [16], i.e., f x ) = 1 and f h x h ) = 1. One can imagine that a heavy user generay demands more data than a ight user, thus, d < d h, D < D h, and thus d +D 2 < d h+d h 2. Our resuts can be extended to Gaussian distribution for data usage without major change of engineering insights see Appendix A for detais). Given there are ony two user types, it is optima for the WSP to offer at most two two-part tariff data pans with one targeting at each user type [17], i.e., B, P, p) for ight users and B h, P h, p) for heavy users. We reasonaby set the unit extra data prices for these two pans identica 2. For exampe, two popuar data pans provided by China Mobie in Beijing are 1 GB, CNY 50, CNY 0.29 per MB) and 3 GB, CNY 100, CNY 0.29 per MB) 3 with identica unit price. How different data pans, such as unimited data pan, impact the PH-market is discussed in Appendix C. Generay, the data quota B chosen by ight users shoud be arger than their minimum monthy data usage d. To save budget, the data quota B aso shoud not be arger than the ight users maximum monthy data usage D. Thus, we assume that d B D. By choosing data pan B, P, p), a ight user s reaized monthy cost for using an arbitrary x [d, D ] amount of data is C x B, P, p)) = P + px B ) +, 1) where x) + = maxx, 0). Since the ight user s monthy data usage x is a random variabe, by taking expectation of C x B, P, p)) in 1) over any possibe x, the expected monthy cost is EC B, P, p)) = P + pd B ) 2 2D d ). 2) 2 If the surcharge prices are different, our anaysis can be extended. The resuting difference is that in the data trading study in Section III, a user with ower surcharge price may want to over-se data to those with higher surcharge price. 3

6 6 Simiar to the ight user s case, we assume that d h B h D h. By subscribing to the ong-term data pan B h, P h, p), a heavy user s reaized monthy cost for using an arbitrary x h [d h, D h ] amount of data is and his expected monthy cost is C h x h B h, P h, p)) = P h + px h B h ) +, 3) EC h B h, P h, p)) = P h + pd h B h ) 2 2D h d h ). 4) By coecting ump-sum fees and the surcharges on over-usage from the two types of users, the expected monthy revenue of the WSP is R = K P + pd B ) 2 2D d ) ) + K h P h + pd h B h ) 2 2D h d h ) ). 5) According to 5), the WSP s expected revenue decreases with both B and B h and increases with P, P h and p. Intuitivey, the WSP wants to induce over-usage charge on both types of users, and prefers high ump-sum fees and costy unit prices to increase its revenue. However, in practice, the WSP may not be abe to freey decide data quotas and prices, depending on the users acceptance and market competition. In the foowing sections, we introduce the PH-market, where users can trade data freey among themseves. III. USER-INITIATED DATA PLAN TRADING VIA PH-MARKET In this section, we propose the PH-market by aowing users in the PH-range to trade data with each other. By creating a ow-power PH, a host user can ony share ceuar data connection with those within the PH-range around 50 meters). The PH range is determined based on the buying users QoS requirement on SNR and data rate) and affects the economic benefit for sharing. As buying users QoS requirement reduces and aows weaker received power, PH-range increases to cover more buying users. Based on the buying users QoS requirement refected by the minimum received power P r, we now determine the PH-range r, by ensuring the actua received power P r is no smaer than

7 7 WSP Stage I Stage II B, P, p) B h, P h, p) Data pans Light users Heavy users Data buying from K ight users PH-range r Data seing to K h heavy users PH-range r Fig. 1: Stackeberg game incuding one WSP and two types of users randomy distributed in the ceuar network. A typica user can ony trade data with users within the PH-range r. Both user types foow homogeneous Poisson point processes PPPs) with user densities λ and λ h, respectivey P r. We consider a typica signa propagation mode by considering the pathoss 4, and received power at the buying user of distance d from the PH is d ζ P r = P t c 0, 6) where P t is the maximum PH s transmission power, c 0 is a constant equa to the pathoss at a reference distance r 0, and ζ is the pathoss exponent vaued between 2 and 4. We need to ensure that the received power P r in 6) of the buying user at the PH ce-edge user with d = r is sti Pr, we determine the maximum PH-range r as ) 1 c0 P ζ t r = r0. 7) P r From 7), a seing user wi try to serve buying users within range r and a buying user wi try to connect to a PH within r. The successfu connection or trading event sti depends on the users mobiity and popuation densities. Suppose the ight users and heavy users foow independent homogeneous Poisson point processes PPPs) with user densities λ and λ h, respectivey see Fig. 1). The number of neighboring r ζ 0 4 Simiar resuts of 6) and 7) can be obtained if more genera fading channe is considered, where the required received power and maximum PH-range can be modified accordingy with a given maximum outage probabiity and fading distribution [18].

8 8 users inside the PH-range is random and can greaty affect the opportunity to trade data. Let K and K h denote the random numbers of ight users and heavy users within the PH-range r of a typica user buyer or seer), respectivey. As both user types ocations foow homogeneous PPP, K and K h within the PH-range r foow Poisson distributions with means ξ and ξ h = πr 2 λ = πr 2 λ h, respectivey. Each mean formua is increasing in the PH-range r and the corresponding user density. The probabiity mass function of K i is given by P i K i ) = ξk i i K i! e ξ i, K i 0, i {, h}. 8) We formuate the two-stage interaction between the WSP and heterogeneous users as a Stackeberg game see Fig. 1), expained as foows: In Stage I, the WSP decides and charges data pans asting for ong-term, e.g., two years 5 ) B, P, p) and B h, P h, p) to the ight users and heavy users in the ceuar network before introducing the PH-market, respectivey. Yet the WSP can sti change them in a useracceptabe way after introducing the PH-market. In Stage II, the two types of users coud choose to trade data with each other in the PHmarket on the basis of the data pans provided by the WSP. We use backward induction to first anayze users behaviors in the PH-market at Stage II and then the WSP s countermeasure against the PH-market at Stage I. As data usage is not reaized yet, a user decides to buy or se data under usage uncertainty and his beief on the other users trading behavior. It is sti possibe to incur over-usage surcharge by the WSP. We denote the trading price per unit data as π. This trading price shoud be ess than unit surcharge price p; otherwise, users wi directy purchase data from the WSP once facing data deficit within each month. In the foowing, given an arbitrary trading price π, we predict and anayze users seing and buying behavior. To reaize such trading, we then enforce a market-cearing price π by using the prediction of users behavior to match suppy with demand. A. Users Trading Behavior in the PH-market Given Price π A ight heavy) users are symmetric and have the same decision in seing or buying data. As ong as their costs are reduced, they wi a participate in the PH-market. In this section, we 5

9 9 anayze the situation when the ight users are data seers and heavy users are data buyers. For the situation when the ight users are data buyers and heavy users are data seers, the anaysis is simiar. First, we anayze a ight user s expected monthy cost when he acts as a seer in the PH-market. After seing data to heavy users, the remaining data quota may not be enough for the ight user himsef and he may need to buy data from the WSP eventuay. Note that d B ; otherwise, the ight user wi not se any data and the PH-market does not exist. Denote s as the amount of sod data to the PH-market. Due to the buying/heavy users mobiity, a seing/ight user decides to se data amount s continuousy over time but cannot find any buyer with probabiity P h 0) = e ξ h within the PH-range r. The expected sod data of the ight user is 1 e ξ h)s 6. To guarantee the basic data usage of the seer himsef, the expected sod data shoud be ess than the maximum eftover data, i.e., 1 e ξ h )s B d. Then, by ocay consuming any reaized x amount of data, the monthy cost of the ight user is given as C x s, π) = P π1 e ξ h )s + px B 1 e ξ h )s)) +. 9) Different from 1), π1 e ξ h )s is the revenue received by the ight user due to seing 1 e ξ h )s amount of data at price π and px B 1 e ξ h )s)) + is the surcharge for over-usage if any). As x [d, D ] is random foowing uniform distribution, by taking expectation of C x s, π) in 9) over any possibe x, the expected monthy cost is EC s, π) = P π1 e ξ h )s + p 2D d ) D B + 1 e ξ h )s) 2. 10) Since EC s, π) is convex with respect to s, by setting the derivative dec s, π)/ds = 0, we obtain the optima shared data s π) shown in the foowing emma. Lemma 3.1: The optima sod data s π) for the ight user is given as πd d ) D s p +B, if π > pd B ) π) = 1 e ξ h ; 0, otherwise. And the optima expected cost of the ight user in the PH-market is 11) EC π) = P + πd B ) π2 D d ). 12) 2p 6 Here we assume the there is enough data demand from the seer given buyer appearance. This wi be ensured through our trading pricing as designed ater.

10 10 The denominator of s π) tes that the seing/ight users shoud overse data to compensate for the revenue oss due to the probabiity of no buyers within the PH-range r. Note that D B is the probabiity for data-overage beyond B and pd B ) can be viewed as the ight user s average penaty for over-usage. Thus, if the trading price π is arge enough to cover the average penaty for over-usage pd B ), the ight user woud ike to se 1 e ξ h )s π) amount of data. Otherwise, the ight user wi not se any data. From 11), the optima sod data increases with the trading price π and quota B and decreases with the unit price p. Due to π < p, 1 e ξ h )s π) < B d aways hods in 11). Then, we discuss a heavy user s expected monthy cost when he acts as a buyer in the PHmarket. As heavy users cannot exacty predict their future data usage, the data bought from ight users may not cover their monthy data usage. Thus, he may need to buy extra data from the WSP eventuay. Note that B h D h ; otherwise, the heavy user wi not buy any data and the PH-market does not exist. Denote b as the amount of purchased data from the PH-market. Due to the seing/ight users mobiity, a buying/heavy user decides to buy data amount b continuousy over time but cannot find any seer with probabiity P 0) = e ξ within the PH-range r. The expected bought data of the heavy user is 1 e ξ )b. Note that 1 e ξ )b shoud be ess or equa to D h B h, i.e., 1 e ξ )b Dh B h, since each buyer s data usage is upper-bounded by D h. Then, in the PH-market, the monthy cost of heavy user for ocay consuming any reaized x h amount of data is given as C h x h b, π) = P h + π1 e ξ )b + px h B h + 1 e ξ )b)) +. 13) Here, π1 e ξ )b is the payment to ight users from buying 1 e ξ )b amount of data at price π and px h B h + 1 e ξ )b)) + is the surcharge for over-usage if any). As the heavy user s data usage x h [d h, D h ] is random foowing uniform distribution, by taking expectation of C h x h b, π) over any possibe x h, the expected monthy cost of heavy user is EC h b, π) = P h + π1 e ξ p )b + 2D h d h ) D h B h 1 e ξ )b) 2. 14) Since EC h b, π) is convex with respect to b, by setting the derivative dec h b, π)/db = 0, we obtain the optima bought data b π) shown in the foowing emma. Lemma 3.2: The optima bought data b π) for the heavy user is given as D h B h π ) b p, if π < pd h B h ) π) = 1 e ξ ; 0, otherwise. 15)

11 11 And the optima expected cost of the heavy user in the PH-market is ECh π) = P h + πd h B h ) π2 D h d h ). 16) 2p The denominator of b π) tes that the buying/heavy users shoud overbuy data to compensate for the extra payment to the WSP due to the probabiity of no seers within the PH-range r. Note that D h B h is the probabiity for data-overage beyond B h and pd h B h ) can be viewed as the heavy user s average penaty for over-usage. Thus, the average penaty pd h B h ) shoud be arger than the unit trading price π to stimuate heavy users to buy 1 e ξ )b π) amount of data in the PH-market. From 15), the optima bought data decreases with respect to the trading price π and quota B h and increases with the unit data price p. Obviousy, 1 e ξ )b π) D h B h. Remark 3.1: From 12) and 16), we can concude that if the ight/heavy users act as buyers/seers, the structure of their optima expected costs in the PH-market is the same as 12) and 16), respectivey. B. Market-cearing Price and PH-market Existence According to Lemmas 3.1 and 3.2, if pd B ) < π < pd h B h ), the ight users and heavy users woud ike to join the PH-market and act as seers and buyers, respectivey. Simiary, we can show that if pd h B h ) < π < pd B ), the ight users and heavy users act as buyers and seers, respectivey. Yet prior anaysis of trading behavior is based on the assumption that the data suppy aways equas data demand. Thus, to ensure this assumption hods and the prior anaysis is feasibe, we decide a market-cearing price by a baance between the average tota suppy and the average tota demand: P K )K s eπ) = P h K h )K h b eπ), 17) K =1 K h =1 where s eπ) = 1 e ξ h )s π) and b eπ) = 1 e ξ )b π) are the expected sod data of the ight user and the expected bought data of the heavy user, respectivey. Note that K and K h foow Poisson distributions with means ξ = πr 2 λ and ξ h = πr 2 λ h, respectivey, thus, 17) is equivaent to λ s eπ) = λ h b eπ), 18) which shows the tota suppy per unit area is equa to the tota demand per unit area.

12 12 Theorem 3.1: The equiibrium trading price for market-cearing is given as π λ ) = pd h B h ) + λ λ h D B )). 19) λ h D h d h ) + λ λ h D d ) Furthermore, for any positive λ > 0 and λ h > 0, the equiibrium trading price π λ λ h ) encourages a users to participate by ensuring the foowing inequaity: If the ight users act as seers and heavy users act as buyers, pd B ) D d If the ight users act as buyers and heavy users act as seers, pd h B h ) D h d h < π λ λ h ) < pd h B h ) D h d h ; 20) < π λ λ h ) < pd B ) D d. 21) Proof: To derive the average tota suppy and demand, we take the expectation of K s eπ) and K h b eπ) over K and K h, respectivey. Since K =0 P K )K = πr 2 λ and K h =0 P hk h )K h = πr 2 λ h, by setting K =0 P K )K s eπ) = K h =0 P hk h )K h b eπ), we have π λ λ h ) as shown in 19). It is easy to check that for the situation when the ight users are buyers and the heavy users are seers, the equiibrium trading price is the same as 19). Take derivative of π y) with respect to y, where y = λ λ h, we can concude that: If pd B ) < pd h B h ), then dπ y) < 0, which means that π λ dy /λ h ) decreases as λ /λ h increases. If pd B ) > pd h B h ), π λ /λ h ) is a increasing function of λ /λ h. Note that 0 < λ /λ h < +. As y 0, π y) pd h B h ). As y +, π y) pd B ). Thus, the proof is competed. Theorem 3.1 iustrates that the trading price π λ λ h ) baances data suppy and demand in the PH-market: it increases as more users woud ike to buy data and decreases as more users woud ike to se data. As shown in Fig. 2, the equiibrium trading price decreases with the ratio λ /λ h when the ight users act as seers and heavy users act as buyers. In the foowing, we wi use π and π λ λ h ) interchangeaby when no confusion is caused. The PH-market s existence condition is given in the foowing theorem. Theorem 3.2: The PH-market s existence condition is D B If D B If D B D h B h. Furthermore, < D h B h, the ight users act as data seers and heavy users act as data buyers; > D h B h, the heavy users act as data seers and ight users act as data buyers. Proof: According to 20), when D B < D h B h, the ight users woud ike to se data and heavy users woud ike to buy data in the PH-market. From 21), when D B ight users serve as buyers and heavy users serve as seers. When D B > D h B h, the = D h B h, both of the

13 Equiibrium trading price π * λ /λ h Fig. 2: Equiibrium trading price π versus λ /λ h when the ight users act as seers and heavy users act as buyers optima sod data and bought data are 0, which impies that users wi not trade data with each other and the PH-market does not exist. The PH-market s existence condition when ight users act as seers and heavy users act as buyers is equivaent to pd B ) < pd h B h ). Note that pd B ) can be viewed as the ight user s average penaty for over-usage and pd h B h ) can be viewed as the heavy user s average penaty for over-usage. Therefore, the condition pd B ) < pd h B h ) indicates that if the ight user has a smaer penaty than the heavy user, it is worthwhie for the ight users to se data and heavy users to buy data in the PH-market at a midde price. Simiary, if pd B ) < pd h B h ), i.e., the heavy user has a smaer penaty than the ight user, then, the heavy users woud ike to be data seers and ight users woud be data buyers. C. Robustness of Trading Efficiency under User Mobiity and Usage Randomness In the above anaysis, we have shown the reduction in users expected monthy costs in the PH-market. In this section, we divide a month into many time sots and consider the user s actua monthy cost under the circumstance that users can trade data during a month randomy based on the number of neighboring users and the data demand/suppy in each time sot. If the tota data suppy is arger than the tota data demand in a certain time sot, the seers can ony se the amount of required data to the buyers, and vice versa. When a user s monthy trading data reaches his expected trading amount i.e., 1 e ξ h )s π) for the data seers and 1 e ξ )b π) for the data buyers) derived from Lemma 3.1 and 3.2, he wi not trade data this month any

14 14 Light user s monthy cost CNY) Average actua cost without PH market Actua cost without PH market Average actua cost in PH market Actua cost in PH market Month a) ight user Heavy user s monthy cost CNY) 900 Average actua cost without PH market 800 Actua cost without PH market 700 Average actua cost in PH market Actua cost in PH market Month b) heavy user Fig. 3: The typica user s actua monthy cost more. In the foowing simuation, we show that the typica user s average actua monthy cost in the PH-market is smaer than that without PH-market. Consider an exampe where there are 60 users per unit area. We assume λ h : λ = 3 : 7, i.e., λ h = 18 users per unit area and λ = 42 users per unit area. Suppose heavy and ight users subscribe to the data pan B, P, p) =3 GB, CNY 140, CNY 0.3 per MB) and B h, P h, p) =6 GB, CNY 180, CNY 0.3 per MB), respectivey. Set D = 3.5 GB, d = 2 GB, D h = 7.5 GB, d h = 5.5 GB. Each user s actua monthy data usage is generated randomy according to a uniform distribution. Given the trading price π, it is shown in Fig. 3a) and Fig. 3b) that the typica ight user s seer) or heavy user s buyer) actua cost in the PH-market may be arger than his actua cost without PH-market for a certain month. But his average actua monthy cost reduces in PH-market compared to that without PH-market. IV. WSP S COUNTERMEASURES TO PH-MARKET A users benefit from data pan trading and baancing in the proposed PH-market, but the WSP can no onger surcharge users for data over-usage as much as the case without data trading. In this section, we wi investigate the WSP s countermeasures to the PH-market in Stage I. Without oss of generaity, we consider the WSP s monthy revenue in one unit area in the foowing sections, i.e, on average λ ight users and λ h heavy users trade data in the PH-market.

15 15 By trading data at price π given in 19), the WSP s expected monthy revenue per unit area changes from 5) to R P H = λ EC π ) + λ h EC h π ). 22) Since EC π ) < EC B, P, p)) and EC h π ) < EC h B h, P h, p)), we have R P H < R. Equation 22) tes that the WSP can reduce its revenue oss due to PH-market by simpy raising the subscription fee P, P h and surcharge price p or decreasing the subscribed quota B and B h to resut in more data over-usages among users. However, such data pan change wi vioate the existing contracts with users and users can hardy agree. In order to et the users accept the contract change, the WSP shoud ensure the reduction for the users expected monthy costs whie increasing its expected revenue. In the foowing, we discuss some user-acceptabe strategies for the WSP to defend the PHmarket and reduce its revenue oss due to the PH-market under the situation when ight users are data seers and heavy users are data buyers in the PH-market originay, i.e., D B < D h B h. For the situation when D B > D h B h at the first pace, the anaysis is simiar with some minor modifications. Remark 4.1: For the case with one data pan, i.e., P = P h = P, B = B h = B, the WSP cannot find any user-acceptabe strategy to reduce its revenue oss due to PH-market, no matter it decides to keep users in the PH-market or drive them out of the market. A. Acceptabe Reduction of Data Suppy in PH-market As the ight users may have eftover data and account for the data suppy in the PH-market, one possibe countermeasure strategy for the WSP is to decrease each ight user s data quota from B to B. To ensure ight users agreement for contract change, the WSP aso reduce the ump-sum fee P to P that in the PH-market. such that each ight user s expected cost is further reduced compared to Since the initia status of the PH-market is D B condition D B < D h B h, from the PH-market s existence D h B h, we can see that decreasing B can drive the users out of the PHmarket. If B is further decreased such that D B > D h B h, a users join the PH-market again and the ight users serve as buyers and heavy users serve as seers. However, the WSP s expected revenue decreases after joining the PH-market. Therefore, when B is reduced to B = D D h B h D d ), i.e., D B = D h B h, the WSP wi not further reduce B to et D B > D h B h.

16 16 The mechanism design of the data pan is shown as foows. After decreasing B, if B > D D h B h D d ), i.e., D B < D h B h, then ight users are sti data seers and heavy users are sti data buyers in the PH-market. Since ony the ight user s data pan is revised, the WSP ony needs to consider the ight users acceptance to this change. Therefore, the WSP aims to find B, P to maximize R P H and decrease the expected monthy costs of the ight users by a reasonaby sma constant ε > 0, 7 i.e., for an ε > 0, where R P H is given in 22) and EC P H From 24), the reationship between P and B is given as max R P H B, P ) 23) B,P s.t. EC π ) EC P H ε, 24) is the origina cost of ight users in the PH-market. P ε + EC P H + π ) 2 D d ) π D B ). 25) 2p According to 22), the WSP s expected revenue increases with P, thus, the expected revenue that the WSP aims to maximize becomes ) R P H B ) = λ EC P H + π ) 2 D d ) π D B ) ε + λ h p P h + π ) 2 D h d h ) 2p Since R P H is a concave function with respect to B, by setting dr P H db = 0, we obtain B that maximizes R P H as shown in the foowing emma. Lemma 4.1: The optima monthy data cap B B ). 26) for the ight user provided by the WSP is given = D D h B h D h d h D d ). 27) The WSP s optima data pan design for the ight users is given as foows. Proposition 4.1: To reduce the revenue oss due to PH-market and decrease the ight user s expected cost simutaneousy, the optima data pan for the ight user provided by the WSP is given as: for a reasonaby sma ε > 0, B = D D h B h D h d h D d ), 28) 7 If ε is arge, which impies that the users expected monthy costs are reduced a ot, the WSP s revenue may be smaer than that before adjusting the data pan. Therefore, the WSP woud reduce the users expected costs by a reasonaby sma constant ε to make users accept the data pan change whie ensuring its own revenue increase. The upper bound of ε can be cacuated easiy by ensuring the WSP s expected revenue after adjusting the data pan is arger than that before adjusting the data pan.

17 17 P which drives the users out of the PH-market. Under the optima data pan, the ight user s expected cost is = ε + EC P H pd B ) 2 2D d ), 29) EC B, P, p)) = EC P H ε, 30) and the WSP s expected revenue is given as R = λ EC P H ε) + λ h P h + pd ) h B h ) 2. 31) 2D h d h ) Proof: Note that R P H B ) decreases with B when B D D h B h D d ). Therefore, the WSP woud ike to set B = B = D D h B h D d ) to maximize its expected revenue, which drives the users out of the PH-market since D B = D h B h. Then, the subscription fee P, the ight user s expected monthy cost EC B, P, p)) and the WSP s expected revenue R can be cacuated easiy. Actuay, we can check that R P H B ) is identica to R when B = D D h B h D d ). Remark 4.2: Even though the WSP s expected revenue is improved by adjusting the ight user s data pan, it is sti ess than its origina expected revenue without PH-market. This is because the ight user s expected cost is reduced in the PH-market, i,e., EC P H EC P H ε < EC B, P, p)) = P + pd B ) 2 2 for any ε > 0. ) < EC B, P, p)). Thus, Besides presenting anaytica resuts, we aso use numerica resuts with practica data to iustrate the impact of the data pan change to WSP s revenue. 1) Numerica Resuts: Consider the same system as shown in Section III-C. We can cacuate the expected monthy cost of the ight user and heavy user before trading data are CNY 165 and CNY , respectivey. Since π = CNY per MB, pd B ) = 0.1, pd h B h ) = 0.225, pd B ) < π < pd h B h ) is satisfied. Therefore, ight users act as seers and heavy users act as buyers. The expected monthy cost of the ight user and heavy user are CNY and CNY , respectivey, which are ess than their expected monthy costs before joining PH-market. In this exampe, we set ε = It is observed in Fig. 4 that the WSP s expected revenue increases as B decreases in the PH-market and achieves its maximum vaue when B = D D h B h D d ). When the WSP reduces B to B P to P = D D h B h D d ) = GB and = CNY, its expected monthy revenue becomes CNY , which is arger than its origina expected monthy revenue CNY after PH-market trading but is sti ess than its origina expected revenue CNY before PH-market trading. Furthermore,

18 18 WSP s expected monthy revenue CNY) 1.33 x Expected revenue Origina revenue in PH market Origina revenue without PH market Light user s subscribed quota B GB) Fig. 4: WSP s expected monthy revenue versus ight user s subscribed quota B we can check that the expected monthy cost of the ight user decreases to CNY , which is ess than his origina cost for both the situations with or without PH-market. B. Acceptabe Reduction of Data Demand in PH-market Since heavy users may not have adequate data quota and account for the data demand in the PH-market, the WSP coud increase each heavy user s subscribed quota from B h to B + h prevent them from trading data with ight users. In order to improve the expected revenue, the WSP aso increases the subscription fee from P h to P + h, and at the same time, guarantees that the heavy users expected monthy costs are reduced compared to their origina expected costs in the PH-market. According to the initia status of the PH-market D B to < D h B h, increasing B h to D h D B D h d h ) can drive the users out of the PH-market. Moreover, if B h is further increased such that D B > D h B h, users trade data again and the heavy users become seers and ight users become buyers. As a resut, the WSP s expected revenue decreases in the PH-market. Therefore, the WSP wi not further increase B h such that B h > D h D B D h d h ) to et users trade data again once the PH-market is driven out. After increasing B h, if B h < D h D B D h d h ), i.e., D B < D h B h, the roes of the ight users and the heavy users remain unchanged. As ony the heavy user s data pan is modified, the WSP ony considers the heavy users acceptance to this change. Therefore, the WSP aims to

19 19 find B h and P h i.e., for an ε > 0, to maximize R P H without increasing the heavy user s expected monthy cost, where R P H is given in 22) and EC P H h max R P H B h, P h ) 32) B h,p h s.t. EC h π ) EC P H h ε, 33) is the origina cost of heavy users in the PH-market. According to 33), the reationship between P h and B h is given as P h ECh P H ε + π ) 2 D h d h ) π D h B h ). 34) 2p Since the WSP s expected revenue R P H increases with P h, thus, the expected revenue that the WSP aims to maximize becomes R + P H B h) ) ) =λ P + π ) 2 D d ) + λ h ECh P H ε + π ) 2 D h d h ) π D h B h ). 2p p Since R + P H is a concave function with respect to B h, by setting dr+ P H db h maximizes R + P H shown in the foowing emma. Lemma 4.2: The optima monthy data cap B h given as 35) = 0, we obtain B h that for the heavy user provided by the WSP is B h = D h D B D d D h d h ). 36) The WSP s optima data pan design for the heavy users is given as foows. Proposition 4.2: To reduce the revenue oss due to PH-market and decrease the heavy user s expected cost simutaneousy, the optima data pan for the heavy user provided by the WSP is given as: for a reasonaby sma ε > 0, B + h P + h which drives the users out of the PH-market. = B h = D h D B D d D h d h ), 37) H = ε + ECP h pd h B + h )2 2D h d h ), 38) Under the optima data pan, the heavy user s expected cost is EC h B + h, P + h and the WSP s expected revenue is given as R + = λ P + pd ) B ) 2 2D d ) The proof is simiar to that of Proposition 4.1 and is thus omitted., p)) = ECP H h ε, 39) + λ h EC P H h ε). 40)

20 20 V. COMPETITIVE WSPS COUNTERMEASURES TO PH-MARKET In previous sections, we have studied the WSP s countermeasures to the PH-market under the condition that there is ony one WSP existing in the PH-market. In reaity, there may exist more than one WSPs providing a variety of data pans, e.g., two major WSPs in China: China Mobie and China UniCom. In this section, we consider the situation when there are two WSPs each offering one data pan to wireess users. Suppose WSP 1 offers data pan B, P, p) to ight users and WSP 2 offers data pan B h, P h, p) to heavy users and the ight users act as seers and heavy users act as buyers in the PH-market at the first pace, i.e., D B < D h B h. 8 If WSPs 1 and 2 are fuy cooperative to maximize the tota revenue, the anaysis and resuts are the same as in Section IV. We are thus interested in how the two WSPs compete with each other and what the impact of the PH-market is on them. In this section, we anayze competitive WSPs countermeasure to PH-market. Before introducing the PH-market, the WSP 1 s expected monthy revenue is R 1 = λ P + pd ) B ) 2, 41) 2D d ) and the WSP 2 s expected revenue is R 2 = λ h P h + pd ) h B h ) 2. 42) 2D h d h ) After the PH-market appears, the WSP 1 s expected revenue becomes ) RP 1 H = λ P + π ) 2 D d ), 43) 2p and WSP 2 s expected revenue becomes ) RP 2 H = λ h P h + π ) 2 D h d h ). 44) 2p Note that after introducing the PH-market, the WSP 1 s expected revenue increases as the ight users woud pay more surcharge fee due to the data sod to heavy users, and the WSP 2 s expected revenue decreases as the heavy users woud buy ess data from it. That is to say, the PH-market benefits the WSP whose customers serve as seers in the PH-market but exerts a detrimenta effect on the WSP whose customers serve as buyers. In the foowing, we wi anayze the WSPs response to the PH-market. 8 For the case when D B > D h B h at the first pace, the anaysis is simiar with some minor modifications.

21 21 A. WSP 2 s Countermeasure to PH-market As the WSP 1 s expected revenue increases in the PH-market, it wi not vioate its data pan first. However, the WSP 2 s expected revenue decreases in the PH-market. In order to reduce the revenue oss due to the PH-market and ensure heavy users acceptance to the contract change, the WSP 2 aims to revise the data pan as B h, P h, p) to maximize its expected revenue without any adversey effect on heavy users at the beginning of the first month. as Lemma 5.1: The optima monthy data cap B h for the heavy users offered by WSP 2 is given which satisfies D B Then P h where EC P H h B h = min{d h D B )D h d h ) 2D d ) D h B h. can be set accordingy as: for a reasonaby sma ε > 0, + λ D B ) 2λ h, D h }, 45) P h = ECP h H ε + π ) 2 D h d h ) π D h 2p B h ), 46) is the expected cost of heavy users in the PH-market at previous month. Proof: See Appendix D. After the WSP 2 adjusts its data pan to B h, P h, p), the heavy users and ight users exchange roes and WSP 2 gains benefit in the PH-market. However, the WSP 1 s expected revenue decreases under such change and it coud increase B to resist it. B. WSP 1 s Response to WSP 2 s Countermeasure In order to reduce the revenue oss due to WSP 2 s data pan change, the WSP 1 aims to revise the data pan as B, P, p) to maximize its expected revenue without any adversey effect on ight users at the beginning of the second month. as Lemma 5.2: The optima monthy data cap B B = min{d D h B h )D d ) 2D h d h ) which satisfies D B D h B h. Then P is cacuated accordingy as: for a reasonaby sma ε > 0, where EC P H P for the ight users offered by WSP 1 is given + λ hd h B h ) 2λ, D }, 47) = ε + EC P H + π ) 2 D d ) π D 2p B ), 48) is the expected cost of ight users in the PH-market at previous month.

22 22 Trading via PH-market Light users seer) Heavy users buyer) WSP 1 increases B to B at stage/month k + 1 WSP 2 increases B h to B h at stage/month k Trading via PH-market Light users buyer) Heavy users seer) Fig. 5: WSP s data pan updating process The proof is simiar to that of Lemma 5.1 and thus we omit it here. After the WSP 1 modifies its data pan to B, P, p), the ight users and heavy users exchange roes again, and the WSP 1 gains benefit in the PH-market whie the WSP 2 s expected revenue decreases. C. Convergence of Competitive WSPs Data Pans According to the above discussion, when ight users act as seers and heavy users act as buyers, the WSP 2 increases B h to B h given in 45) to maximize its expected revenue and exchange the roes of the ight users and heavy users at the beginning of month k. Then, WSP 1 increases B to B shown in 47) to exchange the roes of the heavy users and ight users at month k + 1. The WSP s data pan updating process is shown in Fig. 5. The user-acceptabe equiibrium data pans for the two WSPs case is summarized in the foowing theorem. Theorem 5.1: For the two-wsps case, the data pan updating process is repeated unti B h = D h and B = D, and the user-acceptabe equiibrium data pans for the WSP 1 and WSP 2 are D, P, p) and D h, P h, p), respectivey, where P and P h can be cacuated through 48) and 46), respectivey. In addition, from any initia data pans, the equiibrium data pans can be achieved at most 3 months. Proof: According to 45) and 47), when B = D and B h = D h, we have B h = D h and B = D, which indicates that the equiibrium points are achieved. Then, P and P h are cacuated through 48) and 46), respectivey. Since D B not exist at the equiibrium data pan. = D h B h = 0, the PH-market does

23 Subscribed quota B h GB) Subscribed quota B GB) Month Fig. 6: Evoution of WSPs data pans WSP 1 s expected monthy revenue CNY) Expected revenue Origina revenue without PH market Origina revenue in PH market Month a) WSP 1 WSP 2 s expected monthy revenue CNY) Expected revenue Origina revenue without PH market Origina revenue in PH market Month b) WSP 2 Fig. 7: Evoution of WSP s expected revenue Note that if D h d h + λ λ h > 0, then D d + λ h λ < 0. Therefore, according to 45) and 47), B h = D h at first month or third month and B = D at the second month, which means that the equiibrium data pans can be achieved at 2 months or 3 months. At the equiibrium data pans, both WSP 1 and WSP 2 set the subscribed quota B, B h as the maximum monthy data usage of ight users and heavy users, i.e., D, D h, respectivey. Therefore, the subscribed quota is adequate for a users and the PH-market no onger exists.

24 24 Light user s expected monthy cost CNY) Expected cost Origina cost in PH market Month a) ight user Heavy user s expected monthy cost CNY) Expected cost Origina cost in PH market Month b) heavy user Fig. 8: Evoution of user s expected monthy cost D. Numerica Resuts Consider the same system as shown in Section III-C. Starting from the initia data pans, it is shown in Fig. 6 that the equiibrium data pans are achieved within 2 months. At the equiibrium data pans, WSP 1 s expected monthy revenue decreases whie WSP 2 s expected monthy revenue increases compared to their origina expected monthy revenues in the PH-market see Fig. 7a) and Fig. 7b). However, the expected revenues of both WSP 1 and WSP 2 cannot reach their origina revenues without PH-market. After updating the data pans, the expected monthy costs of the ight users and heavy users are reduced see Fig. 8a) and Fig. 8b)). VI. CONCLUSION This paper studies the data trading between ceuar users enabed by WiFi persona hotspots. In the PH-market we proposed, we anayze a users expected costs by taking users random data usage, incentive to trade, and user mobiity into account and a market-cearing price is derived. Furthermore, we aso expore how the WSP adjusts the data pans to reduce its revenue oss due to the PH-market by user-acceptabe strategies for the cases with two data pans and competing WSPs, respectivey. One of our possibe future work is to extend to the static trading price to the dynamic pricing, yet this can be bothering to users, as he not ony needs to check his usage over time but aso the dynamic trading price. Another future direction coud be users data pan changing.

25 25 A. Gaussian Distribution for Data Usage APPENDICES In this subsection, we show that our resuts aso appy to other distribution for data usage. Consider the case when the ight user s and heavy user s monthy data usage x, x h foow a Gaussian distribution with mean µ, µ h and variance σ 2, σ2 h, respectivey. By checking the firstorder condition of the user s expected monthy cost, we have the foowing resuts. Lemma 6.1: The optima sod data s π) for the ight user is B µ 2σ erf π p ), if π > 1 erf B s 2σ µ )) p 1 e π) = ; ξ h 2 0, otherwise. 49) where erfx) = 2 π x 0 e t2 dt. And the optima bought data b π) for the heavy user is 2σh erf π p ) B h+µ h, if π < 1 erf B 2σh h µ h )) p b 1 e π) = ; ξ 2 0, otherwise. 50) Theorem 6.1: The equiibrium trading price for market-cearing under Gaussian distribution is given as For any positive λ, λ h π λ λ ) = 1 erf λ h participate by ensuring the foowing inequaity: λ h B µ ) + B h µ h 2σh + λ 2σ λ h ) ) p 2. 51) > 0, the equiibrium trading price π λ λ h ) encourages a users to If the ight users act as seers and heavy users act as buyers, 1 erf B µ ) p ) 2σ 2 < π λ ) < 1 erf B h µ h p )) λ h 2σh 2 ; 52) If the ight users act as buyers and heavy users act as seers, 1 erf B h µ ) h p ) 2σh 2 < π λ ) < 1 erf B µ p )) λ h 2σ 2. 53) The proof is simiar as the case under uniform distribution and thus omitted here. When the ight users act as seers and heavy users act as buyers, the equiibrium trading price decreases with the ratio λ /λ h, which coincides with the situation under uniform distribution see Fig. 2). It is shown in Fig. 9 that when the ight users act as seers and heavy users act as buyers, the ight user s equiibrium expected cost decreases as the trading price increases more heavy users woud ike to buy data), whie the heavy user s equiibrium expected cost increases with