Radio-Aware Scheduler for WiMAX Systems Based on ... - IEEE Xplore

Radio-Aware Scheduler for WiMAX systems based on Time-Utility Function and Game Theory Rosario G. Garroppo, Stefano Giordano, Davide Iacono Dept. of Information Engineering, University of Pisa, Italy Email: [email protected]

Abstract—The paper presents a scheduling algorithm for WiMAX systems, which exploits Time-Utility Functions (TUFs) and game theory. The scheduling decision is performed by means of two steps: the intra-class scheduling step and the inter-class scheduling step. In the first one, each user exploits TUFs to choice the packets to transmit according to QoS requirements. In the second one, the scheduler exploits the game theory to select a specific game solution that provides more or less fairness among the users that have to be served. The available physical network resources (i.e. slots) are taken into account as a constraint to the scheduling decision. The proposed scheduling algorithm follows a cross-layer approach that takes into account application requirements by means of TUFs and physical Channel State Information (CSI) of each user. Several game solutions are compared by means of simulation results in terms of user fairness, user throughput, packet delay and packet expiration rate. The TUFs introduction is also evaluated comparing the different applications performance.

I. I NTRODUCTION In 802.16 systems [1] [2], also known as WiMAX, the contention of the physical/MAC resources at the Base Station (BS) side among different users become a key issue in the system configuration. A bad configuration can result in a bottleneck for application performance, considering that all the uplink and downlink traffic passes through the BS. For tackling these issues the definition of scheduling algorithms is of paramount importance. In this scenario, the paper presents a game theory based scheduling algorithm, which exploits Time-Utility Functions (TUFs) [3]. The algorithm follows a cross-layer approach, considering also the physical layer status. The utilization of TUFs permits to have a flexible framework, which can be tuned according to the needs of the system applications that are active in a specific time. The algorithm divides the scheduling decision in two steps: the first one where user applications requirements are met by means of TUFs, and the second one where the amount of traffic per user to be served is decided. In particular, the scheduling problem among the users is modelled with a cooperative game where each user represents a player. The algorithm in this second step follows certain objective functions specific for different game solutions (such as Utilitarian, Nash etc.), in order to provide more or less fairness among the users. System performance was evaluated by means of simulation analysis. The paper is organized as follows. In Section II, related works are discussed, while Section III reports a brief introduction to WiMAX MAC layer. Section IV presents the proposed

scheduler after a short introduction to TUFs and game theory. The performance analysis is reported in Section V. Section VI summarizes the main results of the paper. II. R ELATED W ORK A summary of scheduling algorithms proposed for WiMAX networks is presented in [4]. The Temporary Removal Scheduler (TRS) presented in [5] consists of identifying packet calls under poor radio conditions and removing them from a scheduling list, which contains the MSs to be served. After a period of TR the packet calls are checked again and if there is a radio channel improvement they are inserted again in the list, otherwise they will wait another cycle. After L cycles the packet calls are inserted in the list independently of their radio channel condition. The proposed work differentiates with TRS because it takes into account not only the CSI (Channel State Information), but also considers the constraints on QoS due to traffic flow requirements. The Opportunistic Deficit Round Robin (O-DRR) scheduler [6] is used in the uplink direction, where the BS polls MSs periodically. If the MSs have a no empty queue and their Signal-to-Interference Ratio (SIR) is above a certain threshold they are enabled to transmit. This procedure is repeated at the beginning of each scheduling epoch. O-DRR does not consider QoS constraints of traffic flow. On the contrary, the proposed algorithm takes into account QoS constraints by means of the TUFs. In [7] the authors summarize some of the cited scheduling algorithms in order to compare their performance. The work in [8] presents a comparison of Game Theoretic Scheduling Criteria for OFDMA systems. In particular the authors investigate on the performance comparison among different game solutions exploited for assigning physical resources to the users in Long Term Evolution (LTE) systems. Differently this work not only considers several game solutions for assigning physical resources to the users, but also takes into account QoS requirements of the applications. III. W I MAX MAC L AYER I NTRODUCTION The wireless nature of WiMAX systems implies diverse CINR (Carrier to Noise and Interference Ratio) experimented by the different subscribers associated to a particular BS. According to [1] and [2] Adaptative Modulation and Coding (AMC) will be applied to the subscribers: subscribers experimenting low CINR will utilize low spectral efficient

978-1-4244-4148-8/09/$25.00 ©2009 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2009 proceedings.

modulation and coding scheme, whereas those with high values of CINR will utilize high efficient schemes, which permit to obtain higher bit-rate. Table 334 in [2] suggests the modulation scheme associated to different normalized CINR values. The peculiarity of mobile WiMAX is the utilization of Orthogonal Frequency Division Multiple Access (OFDMA) modulation, where the Orthogonal Frequency Division Modulation (OFDM) subcarriers are shared among the users. In particular the subcarriers are always spaced of 10.94 KHz. Thus, the available system profiles are dependent of the subcarriers number which is utilized. For example, the profile of 5 MHz channel bandwidth utilizes a 512 subcarriers OFDMA modulation, whereas the 10 MHz profile utilizes 1024 subcarriers, in order to maintain the same subcarriers spacing. This is very important considering the robustness issue against doppler effect due to node mobility. Further, in WiMAX systems the data subcarriers are grouped into basic resource set units, called slots. A slot is the minimum amount of resources that can be allocated to a certain user and its size in terms of subcarriers is specific of the subchannel allocation algorithm. IV. G AME T HEORY- BASED S CHEDULER D ESCRIPTION In this paper the problem of choosing the user packets to be served is modelled by means of game theory. Game theory considers two classes of games: cooperative and non cooperative. In non cooperative games binding agreements are not allowed, whereas they are possible in cooperative ones. In this last kind of games the players could pursue a common scope. Hence, there is the possibility that some of them associate themselves, creating a coalition, with the aim of improving their profits. Furthermore, cooperative games can be divided in two subclasses: non-transferable and transferable utility games. In the first case, players joined in the winner coalition will receive a predefined payoff, whereas in the second one they can share the winnings. In this work the packet scheduling problem for WiMAX systems is modelled as a cooperative with non-transferable utility game. The constraint taken into account in this work is the limited amount of physical resources (i.e. slots), which limits the number of packets to be transmitted in a frame. In this modeling each user is considered as a player. Obviously each user has several traffic classes which depend on the applications that request network access. Each traffic class is represented by a queue, which is served in a FIFO manner. In order to address the application requirements, a TUF is assigned per traffic class and is specific for that application. The packets belonging to a certain traffic class will be associated with the relative TUF, which determines the amount of utility brought by the service of the packet. The TUF associates the packet utility to its service time, in particular with respect to its deadline. Let dl be the deadline of packet l belonging to traffic class j. Let i be the packet position in the queue associated to traffic class j of user k. The utility can be evaluated as the following:

⎧ 0 if t ≥ dl ⎪ ⎪ ⎨ 0 if packet i − 1 in the queue j k ul = of user k is not served ⎪ ⎪ ⎩ fj (t, dl ) otherwise (1) where t represents the time when the scheduling decision is made. The first constraint implies that the utility of serving a packet, which is already expired, will bring no utility. The second constraint represents the FIFO service order of the user queues. The function fj (t, dl ) will be defined in the following sections and is specific for the particular traffic class j. The proposed scheduling algorithm is divided in two steps: in the first one inter-class scheduling is performed, where each user/player builds its strategy set; in the second one the intraclass scheduling is performed, where the scheduler chooses a game solution among those available in the feasible set. The set of all possible combinations of strategies is determined by the constraint on the available physical resources (i.e. slots) and represents the game feasible set F . 1) Inter-class Scheduling Algorithm: Inter-class scheduling is used to allocate the resources among the several traffic classes. In this step each user lists his packets, produced by different applications, in decreasing order of their utility. This list represents the preferred service order of the packets of each user, in other words this list has to be served from the first element to the least one. The packet utility depends on the TUF associated to the packet application. Note that the FIFO service order of the applications queues is preserved taking into account the second constraint in (1). In this point of view a packet can’t be put in the list before packets that precede it in the user application queue. The strategies set Sk for user k is composed by all possible combinations of its N packets, with the constraint dictated by the user preferred service order. Sk = {s1 ; s2 ; ..sN } s.t. si = the first i − th packets of the list are served (2) 2) Intra-class Scheduling Algorithm: In this scenario each user has its own strategies set (i.e. preferred service order list) and the scheduling algorithm has to choose which combination of them to serve. Considering the different signal quality among the users, each packet will utilize a certain amount of slots available in the MAC frame. The set of all possible combinations of users strategies, under the constraint of available slots, represents the game feasible set F . Each strategies combination represents a coalition. The payoff Rkf for player/user k for a coalition f is its throughput in that specific coalition. Utilizing this model, the scheduling algorithm can choose the coalition to be served according to different game solutions that provide more or less fairness among the users/players. In particular in this work the following solutions are considered.


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Utilitarian Solution: In this solution the scheduling algorithm will choose the coalition that has the highest overall payoff. In other words the solution consists in the coalition for which the sum of the players’ throughputs is maximized. This solution can be formulated as the following: f Rk (3) US = argmaxF k

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Obviously this solution does not consider fairness issues, packets that belong to user with bad quality signal will not be chosen firstly, because they employ a bigger amount of slots to obtain the same throughput as users experimenting a good quality signal. In this point of view serving packets of users having a bad quality signal will be resource wastage. Nash Solution: In this solution the scheduler will choose the coalition that has the highest Nash value, which is evaluated as the following: f Rk (4) NS = argmaxF k

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The Nash solution brings to more fairness among the players than the Utilitarian one. In fact a coalition where a player has a null payoff (i.e. it has no packet served) will have a null Nash value. In this point of view the only coalitions taken into account are those which have some packets served for each player. Kalai-Smorodinsky Solution: In this solution the ideal payoff Rk,max for each player (say utopia point) is evaluated. In other words the utopia point for a specific player is the throughput that it can reach, in the ideal situation where it is the only player in the game. The scheduler follows a weighted max-min solution as the following:

Rkf (5) KS = argmaxF mink Rk,max Egalitarian Solution: In this solution the scheduler follows the max-min throughput concept:

(6) ES = argmaxF mink Rkf

A. Time-Utility Function Definition Introduced by Jensen [3], Time-Utility Functions (TUFs) allow the semantics of soft time constraints to be precisely specified. A TUF, which is a generalization of the deadline constraint, specifies the utility to the system resulting from the completion of an activity as a function of its completion time. Examples of TUFs are represented in Fig.1. In the figures, A and D represent the packet maximum utility and deadline respectively. Note that TUF (a) is suitable for very high priority traffic packets, which have to be sent as soon as possible and which does not care about other transmission. TUF (b) is typical of delay sensitive applications,

Fig. 1.

Examples of TUF

such as VoIP. The packet utility rises very quickly respect to the service delay, in order to encourage its service. TUF (c) can be associated to streaming applications that can tolerate delay slightly higher than VoIP one. TUF (d), instead, is typical for BE traffic, where no requirements are guaranteed. In this work we assumed D = 50 ms, this means that the TUF (b) changes its trend at 7.5 and 15 ms (before the typical inter-arrival time of voice packets, which is 20 ms). On the contrary the trend change of TUF (c) happens at 20 ms and at 30 ms for the TUF (d). V. S IMULATION A NALYSIS The proposed scheduler was developed in C++ language in order to evaluate its performance. In the analysis of the proposed scheduling algorithm a 5 WiMAX users scenario was set up. Each WiMAX user is considered as a terminal that provided network access to several hosts, and therefore it aggregated all their traffics. In this work we focused on the downlink subframe, but it is possible to evaluate the scheduler performance even in uplink according to the downlink/uplink ratio. The 5 MHz profile was utilized with a frame duration of Tf = 5 ms and a downlink/uplink ratio of DLR = 3. The mandatory Downlink Partial Usage of Subcarriers (DL-PUSC) subchannel allocation algorithm was considered. In this subchannel allocation algorithm a slot is composed of 24 subcarriers by two OFDM symbols, for an overall number of data subcarriers of CdSl = 48. A 10% of OFDM symbols was assigned to preamble and signalling data. The user CINRs were fixed a priori, in order to compare the different game solutions considered in this work. In particular: User 0 had a CINR of 27.85 dB; User 1 had a CINR of 20.5 dB; User 2 had a CINR of 19 dB; User 3 had a CINR of 14.8 dB; User 4 had a CINR of 8.42 dB. Taking into account the parameters in [2] it is possible to evaluate the available physical resources. The number of slots


SlDL present in a downlink subframe is given by the following equation: C symb · NOF DM · DLR (7) SlDL = d (DLR + 1) · CdSl where Cdsymb represents the data subcarriers in any OFDM symbol, which are 360 in a 5 MHz profile, and NOF DM represents the number of OFDM symbols in one frame, which is 48 in a 5 ms frame. Assuming that all the users are experimenting the same signal quality (i.e. they are utilizing the same modulation scheme according to the AMC) and let bsub be the bit per data subcarrier. Assuming also that all slots are utilized, the rate R of the downlink WiMAX subframe can be evaluated according the following: R=

SlDL · CdSl · bsub Tf

4) Best Effort packet size: uniform random value between 64 and 1500 bytes. The packets of each traffic flow have been generated according to a Poisson process, characterized by intensity λ. Each user could generate all the four traffic flows described above (i.e. voice, video, data and BE). As performance parameter, the frame utilization is defined as the ratio between the used and the whole MAC frame resources, expressed in terms of subcarriers and slots. In order to take into account the diverse CINRs experimented by the users, the four buffers associated to the considered traffic classes are implemented for each user set in the simulation scenario. All traffic classes offer an equal amount of offered load, and each of them is characterized by an intensity Poisson parameter λi , expressed in terms of packets/s, evaluated according to: λi =

(8)

For example, when all the served users utilize the highest spectral efficient scheme (i.e. 64-QAM with coding rate equal to r = 5/6, for an overall bit per symbol equal to bsub = 5), the downlink WiMAX subframe can serve the maximum load, which is Rmax = 11.8 Mbit/s. On the contrary, when all the users utilize the least spectral efficient scheme (i.e. QPSK with coding rate r = 1/3, for an overall bit per symbol equal to bsub = 0.67) the rate that the downlink WiMAX subframe can serve is Rmin = 1.73 Mbit/s. In this scenario the proposed scheduler takes into account the user’s CINR and consequently its modulation scheme. In particular, a queue is assigned to each traffic flow of each user. Then each user creates its strategies set, the scheduler evaluates the number of slots needed for the transmission of the users’ packets. The scheduler chooses the coalition to serve according to the game solution chosen, as explained in section IV. The scheduler assumes that the constraint limiting the feasible set F is the number of slots provided by the WiMAX MAC frame according to the assumed subchannel allocation algorithm. Furthermore the scheduler considers not only the utility values associated to the packets, which are estimated using the TUF and the waiting time in the buffer of each packet, but also the CINR and the modulation scheme adopted by each user. The overall offered load among the users was set to the 95% of the maximum rate that can be sustained from the WiMAX frame (i.e. R = 11.8 Mbit/s). Considering the users’ CINR and (8) the network was overloaded. In this analysis the statistical characteristics of the different traffic flows represent a common assumption. In particular, 4 classes of traffic were considered, each one characterized by the following packet size: 1) Voice packet size: 200 bytes; 2) Video packet size: 1500 bytes with probability of 0.9 and 512 with probability of 0.1; 3) Data packet size: 64 bytes with probability of 0.33, 512 bytes with probability of 0.33, 1500 bytes with probability 0.34;

R·ρ 4 · E(Si )

(9)

where ρ is the utilization factor fixed to ρ = 95%, and E(Si ) is the mean packet size of traffic flow i. A. Simulation Results During the simulation L = 100000 frames were generated, which correspond to 500 seconds of simulation. Considering Fig.1, TUF (b) was assigned to voice traffic, TUF (c) to video traffic and TUF (d) to data and BE traffic. The User Fairness Index (UFI) was evaluated considering the throughput of each user. In particular: K ( k=0 Rk )2 (10) UFI = K K · k=0 (Rk )2 where Rk represents the average throughput of the user k during the simulation and K the number of users. Table I shows the global statistics collected for the different game solutions (see Sec. IV-2). Note that frame utilization in terms of slots is higher than the one in terms of subcarriers. This is due to the fact that a packet, which requires a certain amount of slots to be transmitted, maybe does not need all the subcarriers provided by these slots. In this point of view there is resource wastage because some subcarriers contained in its assigned slots remain not utilized. Furthermore, whilst Egalitarian solution provided the highest UFI, it had also the highest delay and expiration rate. On the contrary, Utilitarian solution provided the lowest delay, but also the lowest UFI. Nash solution supplied the lowest expiration rate. KalaiSmorodinsky solution had almost the same UFI of Nash solution, but had a higher delay and expiration rate. Fig. 2 and 3 show throughput performance for each user and per application respectively. In particular, Fig. 2 shows how Utilitarian solution gives much more transmission opportunities to users that have a high signal quality. Indeed user 1, 2 and 3, which have the highest CINR, reached the maximum throughput above 2.2 Mbit/s. On the contrary user 5, which has the worst one, reached almost zero throughput. Nash, Kalai-Smorodinsky and Egalitarian Solution try to give more fairness among users. In these solutions user 5 reached a


Packets Generated Expiration Rate Average Delay [ms] Frame Utilization (Sub.) Frame Utilization (Slot) UFI

US 1461100 0.25 5.37 0.961 0.984 0.76

NS 1457816 0.217 14.61 0.96 0.983 0.86

KS 1461062 0.252 16.66 0.9 0.927 0.85

ES 1458368 0.34 16.81 0.71 0.73 0.96

TABLE I G ENERAL S CHEDULER P ERFORMANCE FOR D IFFERENT G AME S OLUTIONS

Fig. 4. Fig. 2.

User Throughput for different Game Solutions

higher throughput than the null one obtained in the Utilitarian solution. Further in the Egalitarian solution each user reached quite the same throughput with the exception of user 5. However user 5, obtained the highest throughput compared to other game solutions (i.e. above 500 kbit/s). Note that thanks to the inter-class scheduling voice and video traffic reached a higher priority than data and BE traffic. This is reflected in Fig. 3 where voice and video traffic reached a higher throughput than the data and BE one in all solutions. Note that in the Utilitarian solution even data and BE traffic reached a high throughput, but this is mainly due to the high CINR users’ traffic.

Fig. 3.

Voice Average Delay for different Game Solutions

Application Throughput for different Game Solutions

From the simulation results we observed that only user 5 experimented a certain voice packets expiration rate among all game solutions. In particular in the Utilitarian solution it was 0.95. This means that almost all its voice packets, which had the highest priority, expired. This is reflected in Fig. 2 where user 5 obtained an almost null throughput. Even in Kalai-Smorodinsky solution user 5 experimented a certain expiration rate (i.e. 0.25). On the contrary in Nash and

Egalitarian solutions the voice expiration rate for user 5 was almost null. For the other users the expiration rate was null, except for user 4 who experimented in the Utilitarian solution a very low expiration rate (about 0.005). Fig. 4 shows the voice packets average delay. Note that for all the users, with the exception of user 5, the voice packet delay was under the 20 ms (which is the typical inter-arrival time of voice packets) for all the game solutions. User 5, instead, experimented at least 20 ms packet delay in the Egualitarian solution and a higher one in the other solutions. Taking into account the packet expiration rate shown in Fig. 2, the most important packet delay values for user 5 are the Nash and Egualitarian ones, where the expiration rate was near 0. Fig. 5 shows the video packet expiration rate. Note that all video packets of user 5 expired for all game solutions, only in the Egalitarian solution some packets were served, which is the one that brings the highest fairness. User 1, 2 and 3 experimented a null or quasi null expiration rate for Utilitarian and Nash solutions. Respect to the Nash solution, in Kalai-Smorodinsky user 3 experimented a higher expiration rate to reduce the user 4 one. In the Egalitarian solution, instead, all users, with the exception of user 5, experimented approximately the same expiration rate (i.e. 0.3 ÷ 0.4). Fig. 6 shows the video packet delays. For all users, except user 5, video packet delay remained below 32 ms for all the solutions. Note that for user 1 and 2 the average video packet delay was near 0 ms in Utilitarian and Nash solutions. For Data and BE traffics the performance reflected the trend of video ones, but with worse results, with higher delay and expiration rate. This is clearly shown in Fig. 7 and 8. The BE performance were not reported since they were very similar to Data ones as both traffic classes were associated to the same TUF. This means that the TUFs can determine the performance of a traffic flow giving to it a certain amount of priority that


can be tuned a priori according to applications requirements. Moreover a certain fairness level among users in the network can be reached selecting a particular game solution according to the network provider wishes. Summarizing, the results show that the Utilitarian solution exploits very well the network resources. Nash solution can exploit network resources as well as Utilitarian one, providing much more fairness. This is reflected in the per user throughput shown in Fig. 2 and in the packet expiration rate for voice traffic, where user 5 obtained a zero expiration rate in Nash solution and 0.95 in the Utilitarian one. Egualitarian solution provides the highest user fairness (i.e. UFI = 0.96), but it has also the highest resources wastage (i.e. frame utilization = 0.73). Kalai-Smorodinsky solution seems to be not as good as game solution, because it is very similar to Nash solution considering its performance, but it provides a less fairness index and frame utilization than Nash one.

Fig. 5.

Video Expiration Ratio for different Game Solutions

Fig. 8.

Data Average Delay for different Game Solutions

VI. C ONCLUSION A game theory-based scheduling algorithm for WiMAX network is presented. The scheduling decision is made in two steps: the intra-class scheduling step and the inter-class scheduling step. In the former TUFs are exploited in order to tune priority among the user packets of different applications. In the latter game theory is exploited in order to give more or less fairness among the users. Simulation results show that Utilitarian solution exploits better the network resources (i.e. slots), but provides not much fairness among the users. Egalitarian solution provides the highest fairness among the users, but it has the lowest resource utilization. Nash solution revealed the best choice in this scenario, because it provides a good fairness and has high resources utilization as well as Utilitarian one. The utilization of TUFs revealed a benefit for voice and video traffic, which experimented a lower delay and expiration rate than data and BE traffic. In this point of view the TUF construction can determine significantly specific traffic flow performance and their design have to be deeply investigated in future work. ACKNOWLEDGMENT This work was supported by the Italian Ministry of Instruction, University and Research (MIUR) under the PRIN 2007 research project “SESAME” (Scalable Efficient Secure Autonomic MEsh networks). R EFERENCES

Fig. 6.

Video Average Delay for different Game Solutions

Fig. 7.

Data Expiration Ratio for different Game Solutions

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