Pathwise optimality of the exponential scheduling rule for wireless channels

We consider the problem of scheduling the transmissions of multiple data users (flows) sharing the same wireless channel (server). The unique feature of this problem is the fact that the capacity (service rate) of the channel varies randomly with time and asynchronously for different users. We study a scheduling policy called the exponential scheduling rule, which was introduced in an earlier paper. Given a system with N users, and any set of positive numbers {a n }, n = 1, 2,…, N, we show that in a heavy-traffic limit, under a nonrestrictive ‘complete resource pooling’ condition, this algorithm has the property that, for each time t, it (asymptotically) minimizes max n a n q̃ n (t), where q̃ n (t) is the queue length of user n in the heavy-traffic regime.

[1]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[2]  W. Whitt.  Weak convergence theorems for priority queues: preemptive-resume discipline , 1971, Journal of Applied Probability.

[3]  W. C. Jakes,et al.  Microwave Mobile Communications , 1974 .

[4]  Martin I. Reiman,et al.  Some diffusion approximations with state space collapse , 1984 .

[5]  M. Reiman.  A multiclass feedback queue in heavy traffic , 1988 .

[6]  Peter W. Glynn,et al.  Chapter 4 Diffusion approximations , 1990 .

[7]  Jan A. Van Mieghem,et al.  Dynamic Control of Brownian Networks: State Space Collapse and Equivalent Workload Formulations , 1997 .

[8]  Ruth J. Williams,et al.  Diffusion approximations for open multiclass queueing networks: sufficient conditions involving state space collapse , 1998, Queueing Syst. Theory Appl..

[9]  Maury Bramson,et al.  State space collapse with application to heavy traffic limits for multiclass queueing networks , 1998, Queueing Syst. Theory Appl..

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

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

[12]  J. Michael Harrison,et al.  Heavy traffic resource pooling in parallel‐server systems , 1999, Queueing Syst. Theory Appl..

[13]  Ronald J. Williams,et al.  Dynamic scheduling of a system with two parallel servers in heavy traffic with resource pooling: asymptotic optimality of a threshold policy , 2001 .

[14]  R. J. Williams,et al.  Dynamic Scheduling of a System with Two Parallel Servers in Heavy Traac with Complete Resource Pooling: Asymptotic Optimality of a Continuous Review Threshold Policy 1 , 1999 .

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

[16]  Alexander L. Stolyar,et al.  Scheduling for multiple flows sharing a time-varying channel: the exponential rule , 2000 .

[17]  J. Harrison.  Brownian models of open processing networks: canonical representation of workload , 2000 .

[19]  J. Dai,et al.  Heavy Traffic Limits for Some Queueing Networks , 2001 .

[20]  Maury Bramson,et al.  Heavy TraÆ Limits for Some Queueing Networks , 2001 .

[21]  Harold J. Kushner,et al.  Control of mobile communications with time-varying channels in heavy traffic , 2002, IEEE Trans. Autom. Control..

[22]  Philip A. Whiting,et al.  SCHEDULING IN A QUEUING SYSTEM WITH ASYNCHRONOUSLY VARYING SERVICE RATES , 2004, Probability in the Engineering and Informational Sciences.

[23]  D. E. Heyman,et al.  Diffusion Approximations , 2004 .

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

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

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