On the Asymptotic Optimality of the Gradient Scheduling Algorithm for Multiuser Throughput Allocation

We consider the model whereN queues (users) are served in discrete time by a generalized switch. The switch state is random, and it determines the set of possible service rate choices (scheduling decisions) in each time slot. This model is primarily motivated by the problem of scheduling transmissions ofN data users in a shared time-varying wireless environment, but also includes other applications such as input-queued cross-bar switches and parallel flexible server systems.The objective is to find a scheduling strategy maximizing a concave utility functionH( u1,..., uN ), whereu n s are long-term average service rates (data throughputs) of the users, assuming users always have data to be served.We prove asymptotic optimality of the gradient scheduling algorithm (which generalizes the well-known proportional fair algorithm) for our model, which, in particular, allows for simultaneous service of multiple users and for discrete sets of scheduling decisions. Analysis of the transient dynamics of user throughputs is the key part of this work.

[1]  Leandros Tassiulas,et al.  Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks , 1992 .

[2]  Leandros Tassiulas,et al.  Dynamic server allocation to parallel queues with randomly varying connectivity , 1993, IEEE Trans. Inf. Theory.

[3]  Jean C. Walrand,et al.  Achieving 100% throughput in an input-queued switch , 1996, Proceedings of IEEE INFOCOM '96. Conference on Computer Communications.

[4]  Nick McKeown,et al.  A Starvation-free Algorithm For Achieving 100% Throughput in an Input- Queued Switch , 1999 .

[5]  G. V. van Ryzin,et al.  Optimal dynamic scheduling of a general class of parallel-processing queueing systems , 1998, Advances in Applied Probability.

[6]  J. Harrison Heavy traffic analysis of a system with parallel servers: asymptotic optimality of discrete-review policies , 1998 .

[7]  James Williams On Dynamic Scheduling of a Parallel Server System With Complete Resource Pooling , 1999 .

[8]  Matthew S. Grob,et al.  CDMA/HDR: a bandwidth-efficient high-speed wireless data service for nomadic users , 2000, IEEE Commun. Mag..

[9]  A. Jalali,et al.  Data throughput of CDMA-HDR a high efficiency-high data rate personal communication wireless system , 2000, VTC2000-Spring. 2000 IEEE 51st Vehicular Technology Conference Proceedings (Cat. No.00CH37026).

[10]  Ness B. Shroff,et al.  Opportunistic transmission scheduling with resource-sharing constraints in wireless networks , 2001, IEEE J. Sel. Areas Commun..

[11]  Rajeev Agrawal,et al.  Optimality of Certain Channel Aware Scheduling Policies , 2002 .

[12]  David Tse,et al.  Opportunistic beamforming using dumb antennas , 2002, IEEE Trans. Inf. Theory.

[13]  H. Kushner,et al.  Asymptotic Properties of Proportional-Fair Sharing Algorithms , 2002 .

[14]  Harish Viswanathan,et al.  Downlink capacity evaluation of cellular networks with known-interference cancellation , 2003, IEEE J. Sel. Areas Commun..

[15]  Ness B. Shroff,et al.  A framework for opportunistic scheduling in wireless networks , 2003, Comput. Networks.

[16]  A. Stolyar MaxWeight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic , 2004 .

[17]  S. Ethier,et al.  Markov Processes: Characterization and Convergence , 2005 .

[18]  A. Stolyar On the Stability of Multiclass Queueing Networks: A Relaxed SuÆcient Condition via Limiting Fluid Processes , .