LONG term evolution (LTE) has now been operated in

IEEE/ACM TRANSACTIONS ON NETWORKING 1 A Pricing-Aware Resource Scheduing Framework for LTE Networks You-Chiun Wang and Tzung-Yu Tsai Abstract Long term evoution (LTE) is a standard widey used in ceuar networks today. Both resource scheduing and pricing are two critica issues. However, existing studies address them separatey, making the goas of improving system performance and increasing operator revenue conficting. The paper proposes a pricing-aware resource scheduing () framework to conquer this confict. It cassifies users into three eves and has scheduing and pricing modues, which are instaed in a base station and the core network of LTE, respectivey. The scheduing modue uses three-ayer scheduers to assign resource to a fow by considering its packet deay, traffic amount, channe condition, and user eve. The pricing modue uses price easticity of demand in economics to adaptivey adjust the amount of money charged to users. Through experiments by LTE-Sim, we show that achieves a good baance between performance and revenue, and provides quaity of service for the fows with strict deay concerns. Index Terms ceuar network, ong term evoution (LTE), pricing, quaity of service (QoS), resource scheduing. 1 INTRODUCTION LONG term evoution (LTE) has now been operated in many countries to provide 4G service. Comparing with past systems, LTE expoits some efficient techniques, incuding orthogona frequency division mutipe access (OFDMA) [1], carrier aggregation [2], and heterogenous ces [3], to provide high-speed wireess access. Therefore, peope can freey use various broadband appications such as mutimedia streaming and video downoads on their mobie phones. In an LTE ce, the base station caed enodeb (aso abbreviated to enb ) takes charge of scheduing spectra resource to user equipments (UEs). With OFDMA, the downink resource is concretized by a 2D array of physica resource bocks (PRBs) in time and frequency domains. Each PRB carries different number of data bits, depending on the channe quaity of a UE in respect of that PRB. In genera, LTE performance is decided by the way that the enb aocates PRBs to UEs, which we ca LTE resource scheduing, and many methods have been deveoped. They aim at improving system performance by, for exampe, increasing network throughput, keeping fair transmission, or supporting quaity of service (QoS) [4]. On the other hand, the pricing poicy pays an important roe in ceuar networks, as it significanty affects operator revenue. Most operators cassify users into different eves based on the pricing categories. Higher-eve users are charged with a higher rate but can enjoy more resource. According to [5], pricing poicies are categorized into static and dynamic. In a static pricing poicy, users pay a fixed rate no matter how their traffic oads increase. A dynamic pricing poicy charges more money when the user s oad exceeds a threshod. In this way, it can hep increase the operator s revenue. Unfortunatey, the goas of improving system performance and increasing operator revenue may confict, especiay when network resource is insufficient. Let us consider an exampe with two-eve users. Many high-eve users encounter bad channe quaity, whie most ow-eve users have good chan- The authors are with the Department of Computer Science and Engineering, Nationa Sun Yat-sen University, Kaohsiung, 8424, Taiwan. E-mai: ycwang@cse.nsysu.edu.tw; superhawk236@gmai.com ne quaity. To improve performance, one woud give more PRBs to ow-eve users, thereby diminishing revenue. On the contrary, if we give more PRBs to high-eve users, the revenue increases but the performance degrades. However, the investigation of resource scheduing and pricing in LTE is independent. Consequenty, it motivates us to integrate LTE resource scheduing with a pricing poicy, so as to achieve a good baance between performance and revenue. This paper deveops a pricing-aware resource scheduing () framework based on the above observation. Without oss of generaity, we cassify users into three eves: goden (high), siver (medium), and bronze (ow). consists of both scheduing and pricing modues. The scheduing modue empoys a three-ayer scheduing strategy. It first estimates the amount of resource used to support QoS for guaranteedbit-rate (GBR) fows, then aocates PRBs to each fow, and finay checks if some PRBs can be reaocated to improve performance. The pricing modue foows the price easticity of demand (PED) mode [6], where a user s demand is affected by the price. It then adaptivey computes the amount of money charged to users, depending on their resource consumption. Our contributions are threefod. First, this paper indicates that existing studies may face the diemma of improving performance or increasing revenue, as they sove the probems of resource scheduing and pricing separatey. Second, we propose the framework to conquer the diemma by both scheduing and pricing modues, which work from perspectives of engineering (i.e., resource aocation) and economics (i.e., pricing with PED), respectivey. Third, each modue wi refer to the outcome of the other to make its decision, so the resuts of scheduing and pricing in wi tighty coupe. Extensive simuation resuts exhibit that can increase the operator s revenue, improve spectra efficiency, support QoS for GBR fows, and ensure non-gbr transmissions. This paper is organized as foows. Section 2 introduces LTE whie Section 3 surveys reated work. We propose the framework in Section 4 and give some anayses in Section 5. Section 6 evauates performance and Section 7 concudes the paper. We then summarize acronyms in Tabe 1.

2 IEEE/ACM TRANSACTIONS ON NETWORKING acronym CBR CQI FLS GBR HOL LTE MCS M-LWDF PCRF PED PF P-GW PRB QCI TTI UE TABLE 1: Summary of common acronyms. Core network MME enb fu name constant-bit-rate channe quaity indicator frame ayer scheduing guaranteed-bit-rate head-of-ine ong term evoution moduation and coding scheme modified argest weighted deay first network oad based pricing price-aware resource scheduing poicy contro and charging rue function price easticity of demand proportiona fairness packet data network gateway physica resource bock QoS (quaity of service) cass identifier subscriber cass based pricing transmission time interva user equipment S-GW LTE ces PCRF P-GW UE Externa network Data ink Signa ink Wireess ink Fig. 1: LTE structure, where we omit some components in the core network. LTE divides resource into non-overapping PRBs, each with.5ms duration and 18kHz bandwidth. PRBs are nonsharabe 1, so a PRB cannot be given to mutipe UEs. The enb is responsibe for aocating PRBs, in which s scheduing modue is instaed. The minimum period to aocate PRBs is caed a transmission time interva (TTI = 1ms). When the bandwidth of downink channe is 1.4, 3, 5, 1, 15, or 2 MHz, the enb can provide 6, 15, 25, 5, 75, or 1 PRBs in a TTI. Through a moduation and coding scheme (MCS), each PRB carries different number of bits. In genera, a more compex MCS aows the PRB to carry more data, but it requires the UE to have better channe condition. To hep the enb seect the proper MCS, each UE has to report the channe quaity indicator (CQI), which reveas its channe quaity in every TTI. A UE can have mutipe fows, where each fow has a queue at the enb to be its packet container. Packets are stamped with arriva time once they are generated, and the enb sends a queue s packets in a FIFO manner. The head-of-ine (HOL) packet deay of a fow is defined by the eapsing time of the first packet in the queue after its arriva. LTE uses QoS cass identifier (QCI) to depict the QoS demand of a fow, which incudes packet deay budget and packet oss rate. The packet deay budget is the maximum toerant time that each packet can be deayed between P-GW and its UE. When the deay of a packet exceeds the budget, the packet is invaid. The packet oss rate imits the maximum probabiity that a packet is not received by its UE (e.g. due to interference or expiration). LTE categorizes fows into GBR and non-gbr ones. GBR fows mainy support rea-time appications with strict deay constraints, such as VoIP, ive-streaming video, and on-ine games. Non-GBR fows are often used for other service with oose deadines (e.g., TCP-based service). Thus, GBR fows usuay have smaer QCI vaues and packet deay budgets than non-gbr fows. 2 LTE OVERVIEW 2.1 Network Structure LTE network consists of mutipe ces and a core network, as Fig. 1 shows. UEs are served by the enb in a ce. The core network deas with the management job, and has three main components: 1) Mobiity management entity (MME) processes signaing between each UE and the core network. 2) Serving gateway (S-GW) routes data packets and acts as the mobiity anchor when a UE moves among ces. 3) Packet data network gateway (P-GW) connects to the externa network. It aso performs poicy enforcement and supports user charging. Charging contro is done by the cooperation of poicy and charging rues function (PCRF) and P-GW [7]. PCRF is the decision center to manage each fow in P-GW, and checks if the fow s behavior foows its subscription profie. PCRF has an appication function to provide dynamic charging and QoS data to check fows. LTE supports offine and onine charging. Offine charging provides statistics for event- and session-based charging. Onine charging heps P-GW terminate a user s service when certain conditions are met (e.g., when the amount of traffic exceeds the imitation). Based on this structure, s pricing modue can be instaed in PCRF. 2.2 Downink Communication 3 RELATED WORK 3.1 LTE Resource Scheduing LTE standards eave the resource scheduing probem to impementers, so various soutions are deveoped. Capozzi et a. [4] survey some popuar soutions beow: Max-CQI uses a greedy principe to aocate each PRB to the UE with the maximum channe rate r i. Proportiona fair (PF) considers the average channe rate r avg i to support fairness, and it iterativey picks the UE with the argest r i /r avg i vaue to receive resource. Modified argest weighted deay first (M-LWDF) adds a weight w i and HOL packet deay d i to the PF soution to reduce deay. Exponentia proportiona fair introduces a term exp[(w i d i d avg )/(1+ d avg )] to the PF soution, where d avg is the average packet atency. Both LOG-RULE and EXP-RULE refer to the spectra efficiencyψ i of a UE, and seect a fow that has the maximum vaue of (ψ i ogx) and (ψ i expy) to get each PRB, where X and Y are terms defined in LOG-RULE and EXP-RULE, respectivey. Some work adopts a muti-ayer strategy to aocate PRBs. Luo et a. [8] deveop a cross-ayer framework to support video deivery. They refer to the deay requirement, signa distortion, and past rate of each video fow to decide its PRB aocation and coding scheme. In [9], a two-ayer scheduer is designed to support mutimedia service. One ayer computes the amount of data that each fow has to send in a TTI to meet its deay 1. It occurs when the network uses SISO (singe-input singe-output) or SU-MIMO (singe-user mutipe-input and mutipe-output) for communication.

A PRICING-AWARE RESOURCE SCHEDULING FRAMEWORK FOR LTE NETWORKS 3 demand by the discrete-time inear contro theory. Then, the other ayer gives PRBs to each fow by using PF for fairness concern. The work of [1] proposes a doube-ayer scheme to schedue LTE downink resource. The first ayer transates the scheduing probem to a bankruptcy game and then soves it by the Shapey vaue. Based on the resut, the next ayer aocates PRBs according to EXP-RULE. A number of approaches reduce rea-time packet dropping by considering their deadines. The work of [11] appies the eariest-deadine-first method to PF, so as to support fairness whie ensure that the packets whose deadines wi expire soon can be sent first. In [12], a virtua queue is used to predict the incoming of future packets based on the existing packets in each queue. Then, [12] discards the packets that cannot satisfy their deay demands to avoid unnecessary transmission. The study of [13] divides fows into urgent and non-urgent ones, where urgent fows are given with a high priority to send their packets. Non-urgent fows, incuding non-rea-time fows and rea-time fows whose packets have not expired yet, are given with the same (ow) priority for transmission. Wang and Hsieh [14] use max-cqi to compute the preiminary PRB aocation, and tax non-urgent fows with reaocatabe PRBs. Such PRBs are given to those fows in danger of packet dropping. Few studies combine resource scheduing with other factors. For exampe, [15] proposes a scheduing method with power saving. Each UE is assigned with a priority (F i (r g /r avg i ) 2 +Q i ) ˆd i ε i if it is a GBR UE, and(f i +Q i ) ε i otherwise, where F i uses the PF concept, r g is the average throughput of GBR UEs, Q i is u i s queue status, ˆdi is a deay factor, and ε i is a DRX (discontinuous reception) indicator for power saving. Then, UEs can use their priorities to compete for PRBs. To the best of our knowedge, none of existing work considers integrating resource scheduing with a pricing poicy in LTE. This motivates us to deveop the framework with both scheduing and pricing modues, so as to baance between system performance and operator revenue. 3.2 Pricing in Ceuar Networks Past 2G networks use circuit switching for communication, so operators can simpy charge each ca by its duration. After 2.5G, the technique changes to packet switching, and thus 2G pricing becomes inappicabe [16]. Hence, various pricing poicies are deveoped in response to the technica change [17]: 1) Fixed price charging sets a constant renta fee for users, so the operator need not record bandwidth consumption. However, the operator cannot increase its revenue when network traffic grows, and some users may overuse the network. 2) Metered charging asks users to pay for network connection on a monthy basis and charge them for metered usage of the service. However, the usage is measured by time, so it is unfair for the users who eave sessions open without sending packets. 3) Packet charging computes the expense charged to a user based on the number of packets sent in a session. It provides accurate pricing but reies on a packet counting method, which compicates the biing system. 4) Expected capacity charging ets users pay for different amount of money by their expected bandwidth usage, so the price to each user is predictabe. However, the operator has to continuay monitor the actua bandwidth spent by each user. 5) Edge pricing aims at the case when a user stays in two ces such that his packets are reayed by two base stations. This poicy simpifies the charging mechanism by making each base station consut oca charging information, without exchanging their biing data. 6) Paris-Metro charging aows users to assign a preferred cass with an associated cost for their different traffic (e.g., business mai is viewed more important than persona mai, so a high cass is given to business mai). The poicy provides fexiity, but it aso adds overhead to users for traffic-cass decision. Different pricing methods for 3G and 4G networks are aso proposed. The fat-rate pricing method [5] works ike fixed price charging, where the fee wi not change no matter how network traffic grows. The pricing method [18] divides users into goden, siver, and bronze eves. It charges a user by the eve i and the number n i of PRBs used: C i = P f ( i ) n i, (1) where P f ( ) is the fixed charge by eves (in units of PRB). The network oad based pricing () method [19] considers both network oad L and QCI. When L increases, users are charged for more money, so the operator s revenue increases accordingy. Specificay, each user is charged for C i = P v ( i ) (ê ê αx ) L, (2) where ê is the Euer s number and α restricts the QCI vaue x to [1..9]. In Eq. (2), P v ( ) is the variabe charge and depends on a oad threshod δ. When L δ, P v ( i ) is set to a constant P c, which means that each user is charged fairy if network oad is ight. Otherwise, we set P v (G) > P v (S) > P v (B), where G, S, and B denote goden, siver, and bronze eves, respectivey. The subscriber cass based pricing () method [2] aso considers three-eve users. When L δ, it charges users by Eq. (1). When L > δ, charges users by C i = (P f (G)+P e ) n i if i = G, (2P f (G)+P e ) n i if i = S, (2P f (G)+P f (S)+P e ) n i if i = B, where P e is the extra charging computed by κ/(n A n G ). Here, κ is a pricing constant, n A is the number of tota PRBs, and n G is the number of PRBs reserved for goden users. is expected to greaty increase operator revenue when the network becomes overoaded. However, such high pricing in Eq. (3) aso degrades users wiingness to use the service, thereby hurting system performance. That is why we propose the framework to integrate resource scheduing with pricing. aso adopts PED to avoid overcharging users, so as to improve performance whie keeping high revenue. 4 THE FRAMEWORK This section proposes the framework. We first give the assumption and architecture of our framework. Then, we present both scheduing and pricing modues in, foowed by the design rationae. Afterward, we discuss how to extend the framework to the muti-ce environment. 4.1 Assumption and Architecture We cassify users into eves of goden (G), siver (S), and bronze (B), with priorities of G > S > B. The enb assigns PRBs to UEs by referring to these priorities. PCRF then measures the amount of resource spent by each UE and charges its user accordingy, where goden, siver, and bronze users are charged with high, medium, and ow unit prices, respectivey. Some previous studies restrict the type of fows that a UE can (3)

4 IEEE/ACM TRANSACTIONS ON NETWORKING GBR fows Non-GBR fows CQI...... Scheduing modue (in enb) Pricing modue (in PCRF) 1st-ayer scheduer: GBR estimation FLS GBR transmission need g i,j(k) 2nd-ayer scheduer: PRB aocation Enhanced max-cqi Enhanced M-LWDF 3rd-ayer scheduer: Opportunistic resource reaocation PRB aocation User eve Fow type Cassification Goden Variabe charge Siver Bronze P v(g) P v(s) P v(b) Charging strategy PED mode C G, C S, C B Fig. 2: System architecture of the framework. TABLE 2: Summary of notations used in. notation definition d i,j HOL packet deay of fow f i,j f i,j the jth fow of a UE u i g i,j (k) fow f i,j s transmission need in the kth frame i user eve of UE u i p i,j a PRB aocated to fow f i,j q i,j (k) fow f i,j s queue ength in the kth frame r i, r avg i the current and average channe rate of UE u i w i,j the weight defined by M-LWDF for fow f i,j C i the amount of money charged to UE u i E d coefficient of price easticity G, S, B goden, siver, and bronze eves L network oad P c,p e constant and extra charges P f ( ),P v( ) fixed and variabe charges by the user eve Wi P price-based weight for UE u i δ oad threshod ξ GBR,ξ NGBR two ratios for the portion of reaocated PRBs Ψ R GBR,ΨR NGBR two sets of reaocated PRBs use (e.g., [2] does not aow bronze UEs to have GBR fows). In this paper, we assume that each UE can transmit any type of fows for fexibiity and practicabiity. Fig. 2 gives the system architecture of our framework, which consists of scheduing and pricing modues instaed in an enb and PCRF, respectivey. The scheduing modue contains three ayers of scheduers. The 1st-ayer scheduer, GBR estimation, measures how much resource that each GBR fow requires to satisfy its deay constraint. We borrow the idea from frame ayer scheduing (FLS) [9] to do the measurement. The 2nd-ayer scheduer, PRB aocation, then decides the number of PRBs given to each fow based on the GBR transmission need (from the st-ayer scheduer), user eve (from the pricing modue), and CQI. It enhances the max-cqi and M-LWDF methods [4] to cope with PRB aocation for GBR and non- GBR fows, respectivey. The 3rd-ayer scheduer, opportunistic resource reaocation, finay checks whether it is possibe to exchange the usage of some PRBs by different eves of UEs, so as to improve system performance. It aso invoves extra charge to some users who acquire additiona PRBs by this scheduer, and such information wi feed back to the pricing modue for cacuation. The pricing modue provides variabe charges for different eves of users. The charging strategy is the core of this modue. It takes the PED mode into consideration, where the user demand for service wi depend on its price and fow type. Then, the charging strategy adaptivey adjusts the fee charged to each fow according to the information of fow type and PRB aocation from the scheduing modue. Apparenty, the amount of money charged to a user wi be the sum of fees on a fows that his UE uses. Next, we present the detaied design of both scheduing and pricing modues. Tabe 2 summarizes the notations used in the framework. 4.2 Scheduing Modue 4.2.1 GBR Estimation The 1st-ayer scheduer considers ony GBR fows, as shown in Fig. 2. We adopt FLS to evauate the amount of data that shoud be transmitted for a GBR fow to satisfy its deay requirement (caed transmission need). Specificay, et q i,j (k) and g i,j (k) be the queue ength of a GBR fow f i,j and its transmission need in the kth frame, respectivey, where q i,j (k) q max, g i,j (k), and q max denotes the maximum size of a queue. Then, the variation in queue ength can be described by the foowing equation: q i,j (k +1) q i,j (k) = φ i,j (k) g i,j (k), (4) where φ i,j (k) is the amount of newy generated data to f i,j s queue in the kth frame, and φ i,j (k). To cacuate the transmission need of f i,j, FLS defines a contro rue by g i,j (k) = h i,j (k) q i,j (k), (5) where denotes the discrete-time convoution and h i,j (k) is a puse-response function. According to [9], we can derive g i,j (k) by combining Eqs. (4) and (5) as foows: g i,j (k) = q i,j (k)+ M i,j m=2 ĉ i,j (m) (q i,j (k m+1) q i,j (k m+2) g i,j (k m+1)). (6) In Eq. (6),M i,j is the samping interva for the fow. We can set M i,j = d max i,j 1, where d max i,j is the maximum toerant deay off i,j (in frames). Thus, once the enb transmits at eastg i,j (k) amount of data for a GBR fow during every frame k, we can guarantee that the fow s packets wi never be dropped due to expiration. On the other hand, ĉ i,j (m) is a coefficient that satisfies two conditions [21]: ĉ i,j (m) 1 m Z +, ĉ i,j (m) ĉ i,j (m+1),m 1 with ĉ i,j (m) R. (7) The coefficient ĉ i,j (m) is a rea number between zero and one, and it monotonicay decreases as the parameter m increases (when m 1). One possibe way to satisfy the conditions in Eq. (7) is to set ĉ i,j () =, ĉ i,j (1) = 1, and ĉ i,j (m + 1) = ĉ i,j (m)/2, for m = 1,2,,M i,j 1. In other words, we have ĉ i,j (2) = 1/2, ĉ i,j (3) = 1/4, ĉ i,j (4) = 1/8, and so on. This setting wi be aso used by our simuations in Section 6. We give an exampe in Fig. 3 to demonstrate FLS, where M i,j = 1 frames. In the kth frame, an amount φ i,j (k) = 1 bits of data comes tof i,j s queue. Based on the above setting of coefficient ĉ i,j (m), we can spread the enqueued data over the kth, (k+1)th,, and (k+9)th frames to 5, 25,, and 1 bits, respectivey. Then, supposing that φ i,j (k +1) = 2 bits and φ i,j (k +2) = bit (i.e., no data generated in the (k +2)th frame), we can cacuate the amount of data spread over M i,j observing frames accordingy. Based on Eq. (6), we eventuay

A PRICING-AWARE RESOURCE SCHEDULING FRAMEWORK FOR LTE NETWORKS 5 Enqueued data ϕ i,j(k) = 1 ϕ i,j(k+1) = 2 ϕ i,j(k+1) = Transmission need g i,j(m) Spread enqueued data over frames: 5 25 125 63 31 16 8 4 2 1 k k+1 k+2 k+3 k+4 k+5 k+6 k+7 k+8 k+9 1 5 25 125 63 31 16 8 4 3 k+1 k+2 k+3 k+4 k+5 k+6 k+7 k+8 k+9 5 125 625... k+1 k+2 k+3 k+4 k+5 k+6 k+7 k+8 k+9 k+1 k+11 We omit this part in the exampe. Fig. 3: Cacuate the transmission need of a GBR fow by FLS. obtain g i,j (k) = 5 bits, g i,j (k + 1) = 125 bits, g i,j (k + 2) = 625 bits, and so on, as shown in Fig. 3. 4.2.2 PRB Aocation From Fig. 2, the 1st-ayer scheduer passes the transmission need g i,j (k) of each GBR fow to the 2nd-ayer scheduer, and then the 2nd-ayer scheduer determines PRB aocation for both GBR and non-gbr fows. Specificay, it obeys two priority rues to aocate PRBs: [Priority rue 1] GBR fows are given precedence over non-gbr ones, as they have stringent deay constraints. [Priority rue 2] Goden UEs can acquire network resource first, foowed by siver and bronze UEs. Consequenty, the enb first aocates PRBs to GBR fows to meet rue 1. Since there may not be sufficient resource to serve a GBR fows, we thus modify M-LWDF to seect a GBR fow to receive each PRB. In order to appy rue 2, we define a pricebased weight for each UE u i by W P i = C i C G +C S +C B, (8) where C G, C S, and C B denote the average amount of money charged to a goden, siver, and bronze user, respectivey, and C i {C G,C S,C B }. Such information can be obtained from the pricing modue (discussed in Section 4.3). Then, we seect a fow f i,j to obtain the PRB as foows: f i,j = argmax i,j [( w i,j d i,j r i r avg i ) W P i ], (9) where w i,j is the origina weight defined by M-LWDF. Specificay, w i,j = ogβ i,j /σ i,j, where β i,j is the maximum probabiity of packet dropping (i.e., d i,j > d max i,j ), and σ i,j denotes the expected deay of f i,j. In Eq. (8), the price-based weight Wi P is imited to (, 1], and a higher-eve UE wi have a arger Wi P vaue 2. Thus, there is a higher possibiity to pick its GBR fow to receive the PRB by Eq. (9). The enb then iterativey uses Eq. (9) to aocate each PRB, unti either 1) a PRBs have been consumed or 2) the transmission need g i,j (k) of every GBR fow is satisfied in the current TTI. Afterward, if there sti remain PRBs, the enb distributes them among non-gbr fows. We enhance max-cqi by introducing the price-based weight, so as to increase the overa throughput of non-gbr fows whie come up to rue 2: ( r i Wi P u i = argmax i ). (1) 2. The case of W P i = 1 occurs when a UEs have the same user eve. TABLE 3: CQI tabe defined in LTE. CQI MCS code rate efficiency bits carried vaue eve ( 124) by a PRB 3 1 QPSK 1 78.1523 12.79 2 QPSK 12.2344 19.69 3 QPSK 193.377 31.67 4 QPSK 38.616 5.53 5 QPSK 449.877 73.67 6 QPSK 62 1.1758 98.77 7 16QAM 2 378 1.4766 124.3 8 16QAM 49 1.9141 16.78 9 16QAM 616 2.463 22.13 1 64QAM 466 2.735 229.36 11 64QAM 567 3.3223 279.7 12 64QAM 666 3.923 327.79 13 64QAM 772 4.5234 379.97 14 64QAM 873 5.1152 429.68 15 64QAM 948 5.5547 466.59 1 QPSK: Quadrature phase shift keying 2 QAM: Quadrature ampitude moduation 3 This is an average vaue. The enb then iterativey uses Eq. (1) to aocate the remaining PRBs, unti either 1) a PRBs have been aocated or 2) the traffic demand of each non-gbr fow is satisfied. Next, we give two remarks for our PRB aocation in the 2nd-ayer scheduer. Remark 1 discusses how to determine the current rate r i of each UE, which is used by both Eqs. (9) and (1). Then, Remark 2 addresses how to estimate the number of PRBs actuay required by a fow. Remark 1 (Determining the current rate r i of a UE). Both max- CQI and M-LWDF methods are deveoped for genera wireess networks [4], so the current rater i of each UE can be easiy determined if there is ony one downink channe. However, LTE adopts OFDMA for downink communication, where PRBs may ocate in different subchannes that encounter frequency seective fading [22]. In other words, r i may not be necessariy the same across a PRBs. Therefore, to make both Eqs. (9) and (1) function we in the LTE environment, the rate r i can be defined by the data rate supported by the current PRB for a UE u i. In fact, the LTE standard [23] defines a CQI tabe shown in Tabe 3 to determine the reationship between efficiency and MCS (incuding the code rate) for each CQI vaue. Through the CQI tabe, we can cacuate the average number of data bits carried by each PRB when a UE has a certain CQI vaue for that PRB. In this way, we can aso determine its current rate r i (for the PRB) accordingy. Remark 2 (Cacuating the number of PRBs used by a fow). As mentioned in Remark 1, a fow may have different channe quaity across its aocated PRBs. To find the effective SINR (signa-to-interference-pus-noise ratio) γ eff on these PRBs, we can empoy the exponentia effective SINR mapping (EESM) approach [24] as foows: γ eff = EESM(Γ,ε) = εn 1 s s e γk/ε, (11) k=1 where Γ is a vector [γ 1,γ 2,,γ s ] of the tone SINR vaue for each subchanne, s is the number of subchannes, and ε is a tunabe parameter (usuay set to one). In the LTE impementation, the enb first uses one PRB to cacuate γ eff by Eq. (11), and then checks if this PRB has sufficient capacity (by consuting Tabe 3) to satisfy the traffic demand of fow

6 IEEE/ACM TRANSACTIONS ON NETWORKING f i,j in the current TTI. If not, the enb iterativey adds the next PRB, recacuates γ eff, and repeats the above check, unti f i,j s demand becomes satisfied or there is no avaiabe PRB. In this way, we can estimate the number of PRBs actuay used by each fow. 4.2.3 Opportunistic Resource Reaocation By introducing the price-based weight W P i to Eqs. (9) and (1), we aow goden UEs to acquire PRBs first (and foowed by siver and bronze UEs). However, such PRB aocation may hurt system performance, especiay when high-eve UEs encounter bad channe condition. In this case, their PRBs can ony use simpe MCS and carry quite few data bits (in other words, the spectra resource is wasted). To dea with the probem, the 3rd-ayer scheduer adopts opportunistic resource reaocation, whose idea is to aow a sma portion of PRBs to be reaocated to ow-eve UEs according to their channe rates. LetΨ GBR andψ NGBR be the sets of PRBs aocated to GBR and non-gbr fows by the 2nd-ayer scheduer, respectivey. We haveψ GBR Ψ NGBR = andψ GBR Ψ NGBR Ψ, where Ψ denotes the set of avaiabe PRBs in the current TTI. Aso, we define two ratios ξ GBR and ξ NGBR to respectivey contro the portion of PRBs to be reaocated inψ GBR andψ NGBR. Beow, we separate our discussion into GBR and non-gbr cases. Let us denote by p i,j the PRB aocated to a fow f i,j of UE u i. For the GBR case, we sort a p i,j in Ψ GBR by its UE s channe rater i in an increasing order. Then, we create a subset Ψ R GBR Ψ GBR of candidate PRBs that can be reaocated. Initiay, we have Ψ R GBR =. Then, for each p i,j Ψ GBR, we add it to Ψ R GBR if the user eve i {G,S} (i.e., goden or siver UEs), unti Ψ R GBR reaches to Ψ GBR ξ GBR, where denotes the number of eements in a set and is the ceiing function. Then, we consider two reaocation rues: [Reaocation rue 1] i = G: If the foowing condition satisfies r i < max{r i i {S,B} and f i,j is GBR}, (12) which means that another GBR fow f i,j owned by a ower-eve UE actuay has a higher channe rate to PRB p i,j, we thus reaocate p i,j to f i,j to improve system performance. If Eq. (12) is vioated, we remove p i,j from Ψ R GBR because there is no gain to reaocate the PRB. [Reaocation rue 2] i = S: If the foowing condition satisfies r i < max{r i i = B and f i,j is GBR}, (13) which impies that GBR fow f i,j owned by a bronze UE has a higher channe rate to p i,j than its origina fow f i,j, we reaocate p i,j to f i,j to increase network throughput. When Eq. (13) is vioated, we remove p i,j from Ψ R GBR as there is no need to reaocate the PRB. After the above examination,ψ R GBR wi remain ony the PRBs that have been reaocated to other fows. The scheduing modue then passes Ψ R GBR to the pricing modue for extra charge (discussed in Section 4.3). We dea with the non-gbr case foowing the above two reaocation rues. Then, the set Ψ R NGBR is aso passed to the pricing modue to cacuate the extra charge for those ow-eve users who get additiona resource by opportunistic resource reaocation. Remark 3 discusses the effect of both parameters ξ GBR and ξ NGBR on PRB aocation. Remark 3 (Impact ofξ GBR andξ NGBR ). Bothξ GBR andξ NGBR are the ratios of GBR and non-gbr PRBs that wi be considered to be reaocated, respectivey. Based on the two reaocation rues in Eqs. (12) and (13), a PRB wi be reaocated if we can find a ower-eve UE that has better channe condition (i.e., arger CQI vaue) to that PRB. In other words, when bothξ GBR and ξ NGBR increase, the overa throughput coud improve as more PRBs can be given to the UEs with the best channe condition. Nevertheess, higher-eve UEs may be forced to give up more PRBs. Let us consider an extreme case where ξ GBR = ξ NGBR = 1 and bronze UEs have better channe condition than others. In this case, the 3rd-ayer scheduer reaocates each PRB to the bronze UE that has the argest CQI vaue. Consequenty, the resut of PRB aocation wi be the same with that of the max-cqi method. However, both goden and siver UEs wi receive no PRB, which vioates the principe of UE cassification. The design of opportunistic resource reaocation is to improve network throughput under the prerequisite that UEs are given with resource based on their priorities (i.e., eves). Obviousy, the vaues of ξ GBR and ξ NGBR shoud not be set too arge. Therefore, we suggest setting ξ GBR.1 and ξ NGBR.1 so that no more than 1% of PRBs wi be reaocated. In this way, the price-based weight W P i can have dominating effect on PRB aocation. We wi aso set both ξ GBR and ξ NGBR to.1 in our simuations. 4.3 Pricing Modue The pricing modue refers to the user eve and the PRB aocation from the scheduing modue to charge each user, as shown in Fig. 2. It aso consuts PED to mode the reaction of user demand to the change of price. Here, we adopt the PEDreated equation in [25], which is used to anayze the effect of price P on user demand D in wireess networks: D = λ P E d, (14) where λ is a scaing constant to represent the demand potentia 3, and E d is the coefficient of price easticity. From Eq. (14), we can derive E d by D 2 / D 1 = ( P1 / P 2 ) Ed E d = n( D 2 / D 1 ) n( P 1 / P 2 ). (15) In genera, a arger E d vaue impies that the user demand is reativey eastic. In other words, when the price increases, the user demand wi decrease more significanty, and vice versa. According to [26], [27], VoIP and video appications have dominated the revenue of most teecommunications operators. It impies that VoIP and video fows shoud have smaer E d vaues, as peope usuay use these appications. Therefore, we set E d to 1.3, 1.7, and 2.1 for VoIP, video, and non-gbr fows, respectivey, based on the suggestion in [25]. To compute the amount of money charged to a fow f i,j based on its consumption of network resource, we improve Eq. (2) as foows: C i,j = [P v ( i )+P e ] (ê ê y ) L, (16) 3. λ can be set to equa to the vaue of D when P = 1.

A PRICING-AWARE RESOURCE SCHEDULING FRAMEWORK FOR LTE NETWORKS 7 where the variabe charge is defined by P c if L δ, P P v ( i ) = v (G) if L > δ and i = G, (17) P v (S) if L > δ and i = S, P v (B) if L > δ and i = B, y is fow f i,j s QCI 4, and the network oad is defined by the number of used PRBs L = the number of avaiabe PRBs. (18) In Eq. (16),P e is the extra charge incurred whenf i,j uses PRBs in Ψ R GBR or ΨR NGBR. With the PED mode, we define P e = γ E d, (19) whereγ max{e d, f i,j }. For exampe, we can setγ = 2.5, so P e wi be 1.2,.8, and.4 for VoIP, video, and non-gbr fows. Such setting is feasibe due to two reasons. First, VoIP service has the owest price easticity, so we can charge more money to increase operator revenue without significanty degrading user demands. Second, since non-gbr service has the highest price easticity, we can reduce its extra charge to encourage users to utiize such service. Notice that if fow f i,j does not use any PRB inψ R GBR ΨR NGBR, its user need not pay for such extra charge. Then, the amount of money charged to a user u i wi be the sum of charges to a its fows: C i = C i,j. (2) f i,j u i In addition, the average amount of money charged to a goden user can be derived by { u {C i i i=g} C G = N G if N G > (21) otherwise, where N G is the number of goden users. Simiary, we can compute C S and C B (i.e., the average amount of money charged to a siver and bronze user, respectivey) foowing Eq. (21). As iustrated in Fig. 2, the parameters C G, C S, and C B wi change depending on the number of PRBs aocated to different eves of UEs (determined by the scheduing modue), and they are necessary to cacuate the price-based weightw P i in Eq. (8) used by the 2nd-ayer scheduer. This reationship exhibits that both scheduing and pricing modues can tighty coupe with each other. 4.4 Design Rationae Most studies discussed in Section 3 independenty cope with the resource scheduing and pricing probems in LTE. They aim at either improving system performance or increasing operator revenue. However, the two objectives may confict with each other if we do not take both of them into consideration. Specificay, when we simpy aocate most resource to the fows with better channe quaity to improve performance, the priority of high-eve users woud be omitted by the scheduer. On the contrary, if we want to increase revenue by giving most resource to high-eve users, performance may degrade when their UEs encounter worse channe condition. To conquer this diemma, our framework proposes two tighty-couped modues to hande PRB aocation and 4. There were originay nine QCIs defined in LTE Reease-8 standard [28]. However, LTE Reease-13 standard [7] adds four new QCIs, 65, 66, 69, and 7, for some specia appications such as mission critica data. We thus restrict y to range between 1 and 9 in Eq. (16) for backward compatibiity. user charge, as shown in Fig. 2. The scheduing modue reies on the information of user eve and charge from the pricing modue to cacuate the price-based weight Wi P, which pays a critica roe in assigning PRBs for transmission. On the other hand, the pricing modue estimates user charge based on PRB aocation and two sets Ψ R GBR and ΨR NGBR outputted from the scheduing modue. In this way, the framework can baance between system performance and operator revenue. In the scheduing modue, there are three specia designs to support QoS for GRB fows: We empoy FLS in the 1st-ayer scheduer to estimate the amount of data transmission required to meet the deay constraint of each GBR fow. Thus, the enb can try its best to satisfy the transmission needs by the 2ndayer scheduer. Notice that we modify FLS to compute ony the transmission amount used to avoid a GBR fow dropping its packets. When some users request a arge amount of GBR traffic, non-gbr users can sti have network resource to use their service. For the priority rues in Section 4.2.2, we give rue 1 precedence over rue 2 to guarantee GBR transmissions of ow-eve users. Let us consider an exampe where goden users send a huge amount of non-gbr data. If we simpy satisfy their demands first, siver and bronze users wi never have a chance to receive network resource (i.e., starvation), even though they have deaycritica GBR traffic. To sove this probem, the enb first satisfies the necessary GBR demands (i.e., rue 1), and then gives the remaining PRBs to non-gbr fows. When deaing with the GBR and non-gbr cases, rue 2 can ensure that goden users have a higher priority to receive resource. GBR and non-gbr fows are schedued in different ways. We use the enhanced M-LWDF method to schedue GBR fows, which takes care of the urgent degree (i.e., packet deay) of each fow. Non-GBR fows are schedued by the enhanced max-cqi method for performance concern. Furthermore, we propose the mechanism of opportunistic resource reaocation to adjust the scheduing resut by repacing some bad PRB aocation. In particuar, we pick those PRBs assigned to high-eve UEs that encounter worse channe condition, and check if each of such PRBs can be reaocated to another UE with a ower user eve but better channe quaity. In this case, these ow-eve users have to pay for extra fee (i.e., P e in Eq. (16)) to receive the reaocating PRBs by the pricing modue. Moreover, our pricing modue uses Eq. (19) to adjust the extra fee according to different service types, which considers the price easticity defined by the economic PED mode. It thus heps increase operator revenue without significanty degrading user demands. 4.5 Extending to the Muti-ce Environment Ti now, the discussion of our scheduing modue aims at a singe-ce environment. However, it can be easiy extended to a muti-ce environment. Beow, we consider three types of LTE muti-ce networks, as shown in Fig. 4: Homogeneous ces: This is the simpest case. Each enb independenty manages the spectra resource in its ce without affecting other enbs. Therefore, we can directy appy our scheduing modue to each individua enb.

8 IEEE/ACM TRANSACTIONS ON NETWORKING (a) homogeneous ces enb Reay stations (c) ces with reay stations Pico-ce Macro-ce (b) heterogeneous ces Fig. 4: Three types of LTE muti-ce networks. Heterogeneous ces: A arge macro-ce may contain severa sma pico-ces. In this case, they may cause signa interference with each other. To conquer this probem, LTE adopts the technique of enhanced interce interference coordination (eicic) [29]. In eicic, the macro-ce enb wi seect some sots (caed amost bank subframe, abbreviated to ABS ) to transmit ony ow-power signas. Thus, pico-ce enbs can send their data without interference in ABS sots. To appy our scheduing modue to such networks, the macro-ce enb wi aocate PRBs ony in non-abs sots. On the other hand, pico-ce enbs can aocate PRBs in ABS sots. Ces with reay stations: Each UE can choose to receive data directy from the enb or via a reay station. In this network, the enb and a reay stations share the same spectra resource. Therefore, the enb wi partition PRBs into three groups: 1) PRBs for the data from the enb directy to UEs, 2) PRBs for the data from the enb to reay stations, and 3) PRBs for the data from reay stations to UEs. How to cacuate the number of PRBs in each group can refer to our previous work [3]. After the partition, both the enb and reay stations can separatey use our scheduing modue to aocate PRBs in the corresponding groups. On the other hand, since we insta the pricing modue in PCRF (referring to the LTE structure in Fig. 1), there is no need to modify the modue when we switch from the singe-ce environment to a muti-ce network. The major reason is that each piece of data wi be associated with the destination enb, so it is easy to aow PCRF to cacuate the amount of data received by each UE in the network. 5 THEORETICAL ANALYSIS In this section, we give anaysis on performance and compexity of the framework. For performance anaysis, we aim at whether the scheduing modue can guarantee deay bound of GBR fows (i.e., QoS support). In particuar, our scheduing modue uses FLS to cacuate the GBR transmission need in the 1st ayer. The objective of FLS is to support boundedinput, bounded-output (BIBO) stabiity [21], where the output of a system remains bounded in ampitude, provided that the input is aso bounded. In other words, the enb wi never seek to aocate an infinite bandwidth due to the reason that the system input (i.e., the incoming data rate) is bounded in ampitude as any practica appication cannot produce an infinite packet rate. Lemma 1 shows that FLS satisfies BIBO stabiity and aso indicates its deay bound for GBR fows. Lemma 1. FLS is BIBO stabe and ensures that the queuing deay of any GBR fow f i,j is smaer than M i,j + 1, where M i,j is the fow s samping interva. Proof: The proof can be found in Theorem 1 of [9]. With Lemma 1, the foowing theorem then proves that the scheduing modue in can meet the deay requirement of GBR fows when the enb has sufficient downink resource. Theorem 1. GivenR k PRBs supported by an enb in thekth frame, where the minimum number of data bits carried by each PRB is kept above b min, then the scheduing modue in can guarantee that there is no packet dropping of GBR fows due to expiration if the foowing equation hods for any k: R k b min f i,j g i,j (k). (22) Proof: The scheduing modue uses FLS in its 1st-ayer scheduer and sets the samping intervam i,j of each GBR fow f i,j to d max i,j 1, where d max i,j is the maximum toerant deay. According to Lemma 1, if the enb can aocate enough resource to meet the transmission demandg i,j (k) off i,j by Eq. (6), each of f i,j s packet must be deivered before the deadine d max i,j. In fact, Eq. (22) indicates the condition of whether the enb has sufficient PRBs, where the eft term is the tota number of data bits that can be sent out in the kth frame, whie the right term is the amount of overa GBR transmission need that shoud be satisfied in the frame. Based on priority rue 1 in Section 4.2.2, GBR fows can aways obtain PRBs for transmission first in the 2nd-ayer scheduer. This rue impies that the enb must aocate enough PRBs for each GBR fow to avoid dropping its packets, no matter there exist non-gbr fows. Then, the 3rdayer scheduer deas with GBR and non-gbr PRB reaocation independenty. Thus, there is no possibiity that some GBR PRBs wi be reaocated to non-gbr fows. Therefore, the scheduing modue can meet the deay requirement of every GBR fow if Eq. (22) hods for any k, thereby proving this theorem. On the other hand, our pricing modue enhances the method discussed in Section 3.2, which empoys the inearity factor to estimate the amount of money charged to users: f L (x) = A (ê ê Bx ), (23) where A decides the base eve of price whie B adjusts the deduction of price when using high bit rate or voume transfers. It has been shown in [19] that the inearity factor of charging increases operator revenue whie considering price easticity. Moreover, Theorem 2 shows that our pricing modue can further improve revenue than the method. Theorem 2. With the same resut of PRB aocation, the pricing modue in can receive revenue no ess than. Proof: By comparing the pricing equations of and the pricing modue in Eq. (2) and Eq. (16), it is apparent that the pricing modue wi ask users for extra charge P e. Such charge

A PRICING-AWARE RESOURCE SCHEDULING FRAMEWORK FOR LTE NETWORKS 9 occurs ony when a user receives PRBs from the opportunistic resource reaocation method. In other words, if there is no PRB reaocation, our pricing modue wi compute the same amount of money with. Otherwise, it can further improve revenue comparing with due to extra charge P e. We then anayze the computationa compexity. Lemma 2 discusses the compexity to run the scheduing modue on each enb, whie Lemma 3 shows the compexity to conduct the pricing modue by PCRF. Theorem 3 finay gives the overa compexity of our framework. Lemma 2. LetN GBR andn NGBR be the number of GBR and non- GBR fows in theth ce, respectivey. Then, the worst-case compexity of the scheduing modue for the th ce is O(N GBR (D max 1))+O(R max{n GBR,N NGBR }), where D max and R are the maximum toerant deay of fows (in frames) and the number of PRBs (in a TTI) in the ce. Proof: The scheduing modue conducts the three-ayer scheduers in sequence (referring to Fig. 2), so we anayze the computationa compexity of each scheduer separatey. Specificay, the 1st-ayer scheduer adopts FLS to compute the GBR transmission need, which reies on Eq. (6) to do the computation. Obviousy, the computation of g i,j (k) for a fow f i,j requires (M i,j 1) mutipications and (3(M i,j 1)+1) sums, so the compexity of Eq. (6) is O(M i,j ). Because there are N GBR GBR fows, so we have to repeat Eq. (6) for N GBR times, which spends time of O(N GBR M max ), where M max = max{m i,j }. As mentioned in Section 4.2.1, we set M i,j = d max i,j 1, so M max = D max 1. Thus, the compexity of the 1st-ayer scheduer wi be O(N GBR (D max 1)). The 2nd-ayer scheduer first uses the enhanced M-LWDF scheme to aocate PRBs to GBR fows. From Eq. (9), it takes O(N GBR ) time to aocate each PRB because we have to check every GBR fow. If there sti remain PRBs, we use the enhance max-cqi scheme to distribute PRBs among non- GBR fows. Based on Eq. (1), it requires O(N NGBR ) time to assign a PRB since we shoud examine every non-gbr fow. When N GBR N NGBR, the worst case occurs if a PRBs are aocated to GBR fows. If N GBR < N NGBR, the worst case occurs when the resource is given to ony non-gbr fows. Thus, the compexity of the 2nd-ayer scheduer wi be O(R max{n GBR,N NGBR }). In the 3rd-ayer scheduer, two cases are considered. For the GBR case, the enb reaocates at most ξ GBR R PRBs to siver and bronze UEs by Eqs. (12) and (13), so the compexity is O(ξ GBR R (N GBR,S +N GBR,B )), wheren GBR,S andn GBR,B respectivey denote the number of GBR fows owned by siver and bronze UEs. Simiary, the non-gbr case wi spend time ofo(ξ NGBR R (N NGBR,S +N NGBR,B )), wheren NGBR,S and N NGBR,B are the number of non-gbr fows owned by siver and bronze UEs, respectivey. Thus, the tota compexity is O(N GBR (D max 1)) + O(R max{n GBR,N NGBR }) + O(ξ GBR R (N GBR,S + N GBR,B ))+O(ξ NGBR R (N NGBR,S +N NGBR,B )). Because ξ GBR 1, ξ NGBR 1, N GBR,S + N GBR,B N GBR, and N NGBR,S + N NGBR,B N NGBR, we can simpify the compexity too(n GBR (D max 1))+O(R max{n GBR,N NGBR }), thereby proving the emma. Lemma 3. Suppose that N is the tota number of fows in an LTE network. Then, the computationa compexity of the pricing modue is O(N) in the worst case. TABLE 4: Simuation parameters. enb-reated parameters: bandwidth 2MHz number of PRBs 1 (12 subcarriers per PRB) ce range 15 meters frame structure frequency division dupexing (FDD) MCS QPSK, 16QAM, 64QAM UE-reated parameters: 36, 48, 6, 72, 84, 96, 18 mobiity mode random direction moving speed 3km/h GBR fows VoIP (8.4kbps) and H.264 video (242kbps) non-gbr fows CBR (4kbps) channe-reated parameters: propagation oss urban macro-ce mode path oss 128.1+37.6ogL, where L is the distance between the enb and a UE in kiometers shadowing fading og-norma distribution with db mean and 8dB standard deviation penetration oss 1dB fast fading Jakes mode (for Rayeigh fading) pricing-reated parameters: (price unit: mu/prb) fat-rate method P c = 3 method P f (G) = 11,P f (S) = 6,P f (B) = 4 method α = 1,P c = 2.6 P v(g) =.9,P v(s) =.7,P v(b) =.5 method κ = 52 P f (G) = 9,P f (S) = 8,P f (B) = 4 framework γ = 2.5,P c = 2.6 P v(g) =.9,P v(s) =.7,P v(b) =.5 Proof: The pricing modue uses Eq. (16) to compute the fee of each fow, where the variabe chargep v ( i ), extra charge P e, and QCI index y can be determined by the fow itsef. Moreover, the network oad can be cacuated once by Eq. (18). Thus, it takes O(N) time to compute the charges for a fows in the network by Eq. (16). Then, cacuating the fee to each UE requires O(N) time in Eq. (2), because each fow beongs to ony one UE. Due to the same reason, it aso spendso(n) time to find the vaues ofc G,C S, andc B by Eq. (21). Therefore, the worst-case compexity of the pricing modue wi be O(N) + O(N)+O(N) = O(N). Theorem 3. Given N GBR GBR fows and N NGBR non-gbr fows in an LTE network, the computationa compexity of the framework iso(n GBR (D 1))+O(R max{n GBR,N NGBR })+ O(N GBR +N NGBR ), whered is the maximum toerant deay of a fows (in frames) and R is the maximum number of PRBs supported by a ce (in a TTI) in the worst case. Proof: Based on the discussion in Section 4.5, each enb conducts the scheduing modue independenty. LetLdenotes the set of a ces in the LTE network. By Lemma 2, the overa compexity to conduct the scheduing modue wi be L O(N GBR (D max 1))+O(R max{n GBR,N NGBR }) = O(N GBR (D 1))+O(R max{n GBR,N NGBR }). (24) By combining Eq. (24) with Lemma 3, where N is repaced by (N GBR +N NGBR ), we can thus prove the theorem. 6 PERFORMANCE EVALUATION We use LTE-Sim [31] to verify the efficiency of the framework. Tabe 4 ists the parameters of our simuations. We consider an LTE macro-ce where the enb distributes 1 PRBs among UEs in every TTI. Each UE foows the random