Delay-Aware Fair Scheduling in Relay-Assisted High-Speed Railway Networks

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1 203 8th International Conference on Communications and Networing in China (CHINACOM) Delay-Aware Fair Scheduling in Relay-Assisted High-Speed Railway Networs Shengfeng Xu, Gang Zhu, Chao Shen, Yan Lei State Key Laboratory of Rail Traffic Control and Safety Beijing Jiaotong University Beijing, P. R. China , gzhu, shenchao, Abstract In this paper, we consider delay-aware fair downlin scheduling with heterogeneous pacet arrivals and delay requirements for a relay-assisted high-speed railway (HSR) networ. Data pacets from multi-users requests are delivered via the twohop networ architecture to achieve a high data transmission rate instead of direct transmission. Our objective is to find a policy that minimizes the average weighted end-to-end (e2e) delay through pacet scheduling under the user fairness constraint. The policy is a two-dimensional vector with the scheduling indexes in the two-hop lin as its elements. We model the problem as an infinite-horizon average reward constrained Marov decision problem (CMDP) when the data arrival process and the channel process are Marovian. To address the challenge of huge complexity of MDP problems, we propose a heuristic and lowcomplexity algorithm. Simulation results show that the proposed algorithm outperforms the other existing schemes in terms of average weighted delay performance and user fairness. Keywords delay-aware, fair scheduling, HSR Networ, two-hop networ architecture, constrained Marov decision problem, heuristic algorithm. I. INTRODUCTION Recently, the high-speed railway (HSR) systems have been developed rapidly all over the world. The passengers on the train will not only enjoy the short journey, but also have a high demand on high-speed Internet services. The cellular networ deployed near the rail lines can provide seamless coverage and data pacets delivery. However, the data transmission rate is limited due to the penetration loss in traditional HSR systems. As an alternative solution, the two-hop HSR networ architecture has been proposed in [ and [2, which becomes a promising one for future broadband mobile communications to provide high data rate service [3 and was evaluated as a better choice in case of large penetration loss [4. We consider a relay-assisted two-hop HSR networ architecture in this wor. The two-hop lin consists of the basic station (BS)-relay station (RS) lin and the RS-Users lin. The data pacets are delivered via RS to achieve a high data transmission rate instead of direct transmission. The users on the train request the data service delivery when the train is moving. For a large number of onboard users with service requests, the resource contention among multiple users should be resolved and the efficient scheduling scheme should be proposed. An efficient scheduling scheme not only considers the highly dynamic channel due to moving at extremely high speeds, but also needs less complexity. In addition, delay and user fairness requirements in data pacets delivery for such a two-hop networ mae the scheduling challenging. Previous wor has been done to improve system performance on scheduling and resource allocation in HSR networs. In order to support the end-to-end (e2e) realtime data application, [5 studied a circuit domain latency model and employed a priority scheduling algorithm to estimate approximate service latency. In HSR networs with the cell array architecture, [6 proposed a scheduling and resource allocation mechanism to maximize the service rate by considering the channel variations and handover information. The optimal resource allocation problem in a cellular/infostation integrated networ has been studied in [7, considering the intermittent networ connectivity and multi-service demands. However, the formulation and solution cannot be directly applied to two-hop data pacet delivery to users. How to efficiently do scheduling among multiple users in such a networ with the two-hop lin is an interesting problem. In this paper, we investigate fair downlin scheduling problem for a relay-assisted HSR networ, taing account of heterogeneous pacet arrivals and delay requirements. Motivated by the observations in [8, we model the scheduling problem as an infinite-horizon average reward constrained Marov decision problem (CMDP), where the control actions are functions of the instantaneous channel state information (CSI) as well as the queue state information (QSI). We assume that the data arrival process and the channel process are Marovian. Transmission scheduling decisions are made at discrete-time instants. Our objective is to find a policy that minimizes the average weighted e2e delay through pacet scheduling under the user fairness constraint. The policy is a two-dimensional vector with the scheduling indexes in the two-hop lin as its elements. The above CMDP problem is converted into an unconstrained MDP by Lagrange theory and can be solved by the value iteration algorithm. However, the computational complexity for determining the optimal policy increases exponentially with the increase of system state space. To address the challenge of huge complexity of MDP problems, we propose a heuristic scheduling algorithm and its advantage is validated via simulation results. The remainder of the paper is organized as follows. Section IEEE

2 II provides the details of the system model. Section III presents the CMDP problem formulation and discusses the general solution. In section IV, we propose a heuristic scheduling algorithm. Section V shows the numerical results and some discussions. Finally, Section VI maes some conclusions. Notations: In this paper, A is the cardinality of set A. E[ denotes expectation. Pr[ is the probability measure. x = maxn Z n x} and [x + = maxx, 0}. CC Bacbone Networ Users II. SYSTEM MODEL AP Fig.. CS RS BS Antenna System Model Buffers Buffers A two-hop HSR networ architecture is shown in Fig.. This architecture consists of a central controller (CC), a content server (CS), several BSs, a RS and K users on the train. The CC can communicate with the BSs and the CS, and maes the scheduling decision. The cellular networ deployed near the rail line can provide seamless coverage and data pacets delivery. The BSs are connected to the CS in the Internet via wireline lins. For simplicity, we assume that the bandwidth of the lin from the bacbone networ to the BSs is sufficiently large so that the pacets can be transmitted to BSs with a negligible delay. The RS with powerful antennas is installed on the train to communicate with the BSs. The RS is further connected to an access point (AP) which can be accessed by the users based on wireless local area networ (WLAN) technologies. With this two-hop architecture, radio signals do not need to penetrate into the carriages so that radio signal penetration loss problem can be avoided. We consider that K users with service requests on the train, to each one, a separate portion of the buffers in CS and RS is allocated Q CS,, Q CS,2,..., Q CS,K } and Q R,, Q R,2,..., Q R,K }, respectively. The two buffers in the CS and RS are in tandem. We assume that the buffers are sufficiently large and the pacet dropping rate is considered negligible. Let Q(t) = Q CS, (t), } Q R, (t), } be the joint QSI of the CS and RS respectively, where Q CS, (t) and Q R, (t) denote the number of pacets at the beginning of the t-th slot in the -th user s queue at CS and RS, respectively. The application streams of these K heterogeneous users have different pacet arrival rates and delay requirements. Data pacets from the higher layer application arrive into the buffers and are queued until they are transmitted. The pacet arrival process for each user is assumed to be i.i.d. across slots and all the pacets have equal size of G bits. Let A (t) denotes the number of pacets arriving into the -th user s buffer in CS at time-slot t. Suppose in general, A (t)} forms an ergodic Marov chain and Poisson distributed bursty traffic with average pacet arrival rate = E[A (t) for each user. The distribution of A (t) for Poisson traffic can be given as Pr[A (t) = i = exp( T B ) (T B ) i, i N, () i! where T B is the time-slot period. Let x (t) 0, } and y (t) 0, } denote the time-slot allocation index for the user in the BS-RS lin and RS-Users lin, respectively. The index is set to be if the corresponding user is scheduled at time-slot t and is set to 0 otherwise. and 2 denote the scheduled user index in the BS-RS lin and RS-Users lin, respectively. Finite state Marov chain (FSMC) models have been accepted in the literatures as an effective approach for characterizing the HSR fading channels [9[0. In this paper, we adopt the FSMC channel models to describe the channel state transition for the two wireless lins. The channel from BS to the RS follows Rician distribution while the channel between RS and the users can be treated as Rayleigh fading. Let H(t) = H BS,R (t)} H R, (t), } be the joint CSI, where H BS,R is the channel gain between the BS and the RS, and H R, is the channel gain between the RS and the user. We assume that the channel gains remain constant for the duration of the slot and change across slots in an i.i.d. manner. The derivations of channel state transition probability for the Rician channel and Rayleigh channel have been shown in [9 and [. For the BS-RS lin with the bandwidth W, the maximum achievable data rate in bit-per-second is given by R BS = W log( + P BS H BS,R 2 N 0 ), (2) where P BS is the transmit power of the BS and N 0 is the noise power. Liewise, for the RS-Users lin with the bandwidth W 2, we have the maximum achievable data rate for user : R R, = W 2 log( + P R H R, 2 N 0 ), =, 2,..., K, (3) where P R is the transmit power of the RS. Since the pacets have equal size of G bits, the capacity C BS of time-slot t can be denoted as the maximum number of pacets by converting R BS, to pacet-per-second through a proportionality constant, i.e., C BS = R BS T B /G. Similarly, C R, = R R, T B /G. The global system state at time-slot t is denoted by S(t) = (H(t), Q(t)) comprising of the CSI and QSI. Given an observed system state realization, the CC may adopt the scheduling scheme according to a stationary policy. A stationary scheduling policy (Π) maps the system state space S to the action space U, i.e., Π : S U. Π is called feasible if 8

3 the associated actions satisfy the constraints. We assume that the next state S(t + ) only depends on the current state and action but not on the previous states, hence the process S(t)} for a given control policy Π is Marovian with the following state transition probability function: Pr[S(t + ) S(t), Π(S(t)) = (4) Pr[H(t + ) H(t)Pr[Q(t + ) S(t), Π(S(t)), where the channel state transition probability is given by Pr[H(t + ) H(t) = (5) Pr[H BS,R (t + ) H BS,R (t)pr[h R, (t + ) H R, (t), and the queue state update processes are given by (6) and (7). Given a feasible policy Π, the induced Marov chain S(t)} is ergodic and there exists a unique steady state distribution π S [2. By Little s law, the average time that a pacet of the user spends in the e2e system is Q CS,+Q R,. Thus, the average weighted e2e delay of the two-hop relay-assisted HSR networ can be expressed by D = lim T T = E π S [ K = [ T K E Π Q CS, (t) + Q R, (t) ω = ω Q CS, (t) + Q R, (t), (8) where E π S denotes the expectation with respect to the induced steady state distribution. The positive weight variable ω is used to represent delay requirement for user. User fairness constraint is given by R = lim T T T E Π [y (t)t (t) = E π S [y (t)t (t) α, (9) where α (0, denotes proportional factor of user, which reflects that the average rate constraint is proportional to the average arrival rate in order to realize user fairness. T (t) is the instantaneous throughput for user at time-slot t, i.e., T (t) = minc R, (t), Q R, (t)}. Moreover, y (t) = and x (t) = denote that only one user can be scheduled in one lin at time-slot t. III. CMDP PROBLEM FORMULATION In this section, we formulate the delay-aware fair scheduling problem as an infinite-horizon average cost CMDP and discuss the general solution. The objective is to choose an optimal policy so that the average weighted e2e delay (8) is minimized subject to the fairness constraint (9). This problem is an infinite-horizon average cost CMDP with system state space S = Q H and action space U = X Y, where X = x, } and Y = y, } are user selection action spaces. The above CMDP problem can be converted into an unconstrained MDP by Lagrange theory. The Theorem 2.7 from [3 demonstrated that the optimal cost and policy of the CMDP can be found using an unconstrained MDP and Lagrangian approach. We define the Lagrangian as L(Π, β) = lim /T T T EΠ [L(S(t), Π(S(t)), β), where L(S(t), Π(S(t)), β) = (0) K [ Q CS, (t) + Q R, (t) ω β (y (t)t (t) α ), = in which β = [β, β 2,..., β K is the Lagrange multiplier (LM) vector and the corresponding unconstrained MDP is given by G(β) = min L(Π, β) Π } T = min lim E Π [L(S(t), Π(S(t)), β),() Π T T where G(β) gives the Lagrange dual function. It was shown by Theorem 2. in [4 that there exists a LM β 0 such that Π minimizes L(Π, β) and the saddle point condition holds. Given a LM vector, the optimizing policy Π for the unconstrained MDP () can be obtained by solving the associated optimality equation for i =, 2,..., S as: θ + V (S i ) = (2) } min Π(S i ) L(S i, Π(S i ), β) + S j Pr[S j S i, Π(S i )V (S j ) where V (S) is the value function of the MDP and Pr[S j S i, Π(S i ) is the state transition probability which can be obtained from (4). θ = min Π L(Π, β) is the optimal average cost per stage. The value iteration algorithm is an efficient stable iteration algorithm to solve the optimality equation [2. The algorithm operates by calculating successive approximation to the value function V (S). The computation complexity of the algorithm is O( U S 2 ) [2. IV. HEURISTIC ALGORITHM In certain cases of practical interest, it is not possible to adopt the optimal scheduling policy presented above. The system state space is enormous, including the channel states in the two-hop lin and the buffer states for each users. The computational load of optimal scheduling increases exponentially with the increase of system state space. To address the challenge of huge complexity of MDP problems, we introduce a heuristic and low-complexity algorithm. Specifically, we split the e2e delay-aware fair scheduling problem into two stages corresponding to the two-hop lin. The scheduling schemes for the two stages are given as follows. A. The scheduling scheme in the first stage The objective of the first stage is to provide enough pacets to each queue in the RS in order to not underusing the time resource in the second stage. Since all the users on the train have the same channel quality in BS-RS lin, we can ignore the channel state effect on scheduling scheme. The motivation of proposing the scheduling scheme includes two aspects. On the one hand, in order to mae the best use of time resource, 9

4 A (t) + [Q Q BS, (t + ) = CS, (t) C BS (t) + if = A (t) + Q CS, (t) if [Q R, (t) C R, (t) + if = 2 minc Q R, (t + ) = BS (t), Q CS, (t)} + [Q R, (t) C R, (t) + if = 2 = Q R, (t) + minc BS (t), Q CS, (t)} if 2 and = Q R, (t) if 2 and (6) (7) in the BS-RS lin, CC should schedule the user with large value Q CS, (t). On the other hand, CC should allocate more resource to the user with small value Q R, (t). Therefore, the scheduling scheme in the first stage is presented as follow: = arg max Q CS,(t)/Q R, (t)}, (3) where smaller value Q R, (t) and larger value Q CS, (t) imply that higher priority for scheduling user. B. The scheduling scheme in the second stage In order to minimize the average weighted e2e delay (8) and satisfy the fairness constraint (9), we propose the scheduling scheme for the RS-Users lin consisting of three parts: instantaneous throughput, pacet utility and user fairness. ) Instantaneous throughput: In order to mae the best use of time resource, instantaneous throughput should be considered into scheduling scheme. As mentioned above, T (t) = minc R, (t), Q R, (t)} for each user. The user with high value T (t) gets the high priority. 2) Pacet utility: We set the pacet utility based on optimization objective (8) as follow: U (t) = ω Q R, (t). (4) The larger the utility is, the higher priority the user gets. 3) User fairness: We consider the long-term average throughput proportional fairness issue. T (t) is the average throughput of user before time-slot t in the tracing time and is updated every time slot as follow [5: T (t + ) = ( t ω ) T (t) + t ω ϕ (t), (5) where t ω is the window size of tracing time, while ϕ (t) is the current scheduling rate of user at time-slot t, T (t) if user is scheduled ϕ (t) =, (6) 0 otherwise Based on the user fairness constraint, we define the throughput proportional fairness parameter ε (t) as the ratio of T (t) to α. ε (t) = T (t) α (7) The fairness index of user, F (t) is defined as F (t) = exp(ε (t) ε (t)), (8) where ε (t) is denoted as ε (t) = ε (t) K. (9) The user with high fairness index gets the high priority. 4) Scheduling Policy: The objective of the scheduling scheme is to reduce the weighted delay while eeping the user fairness. Hence, CC maes the scheduling decision with the criteria given by 2 = arg max T (t)u (t)f (t). (20) The user with largest value would be selected for transmission. V. NUMERICAL RESULTS AND DISCUSSIONS In this section, we present numerical results to illustrate the performance of the proposed heuristic algorithm. For the purpose of comparison, we evaluate two related scheduling policies as reference benchmars. One is the traditional round-robin (RR) scheme which schedules users in a predetermined order. At time-slot t, the (t mod K + )-th user is chosen for the two lins. Another is the Greedy scheme, where user scheduling is done in a greedy method. Specifically, = arg max Q CS,(t)} and 2 = arg max min(c R,(t), Q R, (t))}. We summarize the simulation parameters in Table I. In addition, the Rayleigh fading channel state H R, (t) is selected from the probability density function expressed as f H (h) = h ᾱ exp( h 2 2ᾱ ), h 0 and ᾱ = 2dB. Rician factor is 7 db. 2 TABLE I PARAMETERS IN SIMULATION Parameter Value Parameter Value 5 pacets/time-slot W 4 MHz T B 53µs W 2 0 MHz G 240 bits P BS 47 dbm t ω 50ms P RS 4 dbm Fig. 2 compares the delay performance of the three scheduling schemes with different numbers of users. In order to emphasize different weights, we set the delay weight value ω = +. The proportional factors are equal with α = 0.5 for all users. In this figure, we find that the delay performance for the proposed algorithm is much higher than the RR and Greedy schemes. Furthermore, the average weighted e2e delay per user for these scheduling schemes increases with the number of users grows. 20

5 Fig. 3 indicates the long-term average throughput proportional fairness under the three scheduling schemes for the problem with K = 8. We set the proportional factors from user to user K are 0.4, 0.3, 0.4, 0.5, 0.6, 0.7, 0.7, 0.6 and the delay weight ω = for all users. For user, the leftmost bar shows fairness parameter ε (t) for the proposed algorithms, and the remaining bars represent the fairness parameter for the other two schemes. Simulation results show that the proposed algorithm outperforms the RR and Greedy schemes in respect of throughput proportional fairness. Average weighted e2e delay per user/ms Throughput proportional fairness Heuristic algorithm RR Greedy Number of users Fig Average weighted e2e delay per user vs. the number of users Heuristic algorithm RR Greedy User Index Fig. 3. Throughput proportional fairness for K = 8 VI. CONCLUSION This paper investgates delay-aware fair downlin scheduling problem with heterogeneous pacet arrivals and delay requirements in a relay-assisted HSR networ. We model the problem as an infinite-horizon average reward CMDP when the data arrival process and the channel process are Marovian. To address the challenge of huge complexity of MDP problems, we propose a heuristic and low-complexity algorithm. Simulation results show that the proposed algorithm outperforms RR and Greedy schemes in terms of average weighted delay performance and user fairness. For future wor, we will investigate the distributed algorithm with low complexity by exploiting the properties of CMDP. In addition, modeling for the scheduling problem under the practical HSR scene (e.g., the accurate channel models in the two-hop lin and the various numbers of the total users with service requests) is an interesting issue. ACKNOWLEDGMENT This wor was supported by the Fundamental Research Funds for the Central Universities under Grant number 203YJS0 and Key Project of State Key Lab of Rail Traffic and Control under Grant number RCS202ZZ004. REFERENCES [ D. Foum and V. Frost, A survey on methods for broadband internet access on trains, IEEE Communications Surveys & Tutorials, vol. 2, no. 2, pp. 7 85, 200. [2 J. Wang, H. Zhu, and N. J. Gomes, Distributed antenna systems for mobile communications in high speed trains, IEEE J. Sel. Areas Commun., vol. 30, no. 4, pp , 202. [3 L. Tian, J. Li, Y. Huang, J. Shi, and J. Zhou, Seamless dual-lin handover scheme in broadband wireless communication systems for high-speed rail, IEEE J. Sel. Areas Commun., vol. 30, no. 4, pp , 202. [4 J. You, Z. Zhong, R. Xu, and G. Wang, Transmission schemes for highspeed railway: Direct or relay? in Proceedings of International Wireless Communications and Mobile Computing Conference, 202, pp [5 Y. Yang, Z. Huang, Z. Zhong, and X. Fu, A study of real-time data transmission model of train-to-ground control in high-speed railways, in Proceedings of IEEE Vehicular Technology Conference Fall, 200, pp. 5. [6 O. B. Karimi, J. Liu, and C. Wang, Seamless wireless connectivity for multimedia services in high speed trains, IEEE J. Sel. Areas Commun., vol. 30, no. 4, pp , 202. [7 H. Liang and W. H. Zhuang, Efficient on-demand data service delivery to high-speed trains in cellular/infostation integrated networs, IEEE J. Sel. Areas Commun., vol. 30, no. 4, pp , May 202. [8 M. Moghaddari, E. Hossain, and L. B. Le, Delay-optimal fair scheduling and resource allocation in multiuser wireless relay networs, in Proceedings of International Conference on Communications, 202, pp [9 S. Lin, Z. Zhong, L. Cai, and Y. Luo, Finite state marov modelling for high speed railway wireless communication channel, Proceedings of IEEE Globecom, 202. [0 L. Zhu, F. R. Yu, B. Ning, and T. Tang, Cross-layer design for video transmissions in metro passenger information systems, IEEE Trans. Veh. Technol., vol. 60, no. 3, pp. 7 8, 20. [ H. S. Wang and N. Moayeri, Finite-state marov channel - a useful model for radio communication channels, IEEE Trans. Veh. Technol., vol. 44, no., pp. 63 7, 995. [2 M. Puterman, Marov Decision Processes: Discrete Stochastic Dynamic Programming. Hoboen, NJ: Wiley, 994. [3 E. Altman, Constrained Marov Decision Processes: Stochastic Modeling. London, U.K.: Chapman and Hall/CRC Press, 999. [4 V. Borar, An actor-critic algorithm for constrained marov decision processes, Systems and Control Letters, vol. 54, pp , [5 R. Zhou, H. N. Nguyen, and I. Sasase, Pacet scheduling for cellular relay networs by considering relay selection, channel quality, and pacet utility, Journal of Communications and Networs, vol., no. 5, pp ,

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