Stability and asymptotic optimality of opportunistic schedulers in wireless systems

We investigate the scheduling of a common resource between several concurrent users when the feasible transmission rate of each user varies randomly over time. Time is slotted and users arrive and depart upon service completion. This may model for example the flow-level behavior of end-users in a narrowband HDR wireless channel (CDMA 1xEV-DO). As performance criteria we consider the stability of the system and the mean delay experienced by the users. Given the complexity of the problem we investigate the fluid-scaled system, which allows to obtain important results and insights for the original system: (1) We characterize for a large class of scheduling policies the stability conditions and identify a set of maximum stable policies, giving in each time slot preference to users being in their best possible channel condition. We find in particular that many opportunistic scheduling policies like Score-Based [9], Proportionally Best [1] or Potential Improvement [4] are stable under the maximum stability conditions, whereas Relative-Best [10] or the cμ-rule are not. (2) We show that choosing the right tie-breaking rule is crucial for the performance (e.g. average delay) as perceived by a user. We prove that a policy is asymptotically optimal if it is maximum stable and the tie-breaking rule gives priority to the user with the highest departure probability. In particular, we show that simple priority-index policies with a myopic tie-breaking rule, are stable and asymptotically optimal. All our findings are validated with extensive numerical experiments.

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

[2]  Riku Jäntti,et al.  Asymptotically fair transmission scheduling over fading channels , 2004, IEEE Transactions on Wireless Communications.

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

[4]  Junshan Zhang,et al.  Traffic aided opportunistic scheduling for wireless networks: algorithms and performance bounds , 2004, Comput. Networks.

[5]  R. Srikant,et al.  Stable scheduling policies for fading wireless channels , 2005, IEEE/ACM Transactions on Networking.

[6]  Ashwin Sampath,et al.  Downlink Scheduling for Multiclass Traffic in LTE , 2009, EURASIP J. Wirel. Commun. Netw..

[7]  Gustavo de Veciana,et al.  Balancing SRPT prioritization vs opportunistic gain in wireless systems with flow dynamics , 2010, 2010 22nd International Teletraffic Congress (lTC 22).

[8]  Sem C. Borst,et al.  Flow-Level Stability of Channel-Aware Scheduling Algorithms , 2006, 2006 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks.

[9]  R. Bass,et al.  Review: P. Billingsley, Convergence of probability measures , 1971 .

[10]  Thomas Bonald.  A Score-Based Opportunistic Scheduler for Fading Radio Channels , 2004 .

[11]  G. Fayolle,et al.  Topics in the Constructive Theory of Countable Markov Chains , 1995 .

[12]  Michael J. Neely,et al.  Order Optimal Delay for Opportunistic Scheduling in Multi-User Wireless Uplinks and Downlinks , 2008, IEEE/ACM Transactions on Networking.

[13]  Samuli Aalto,et al.  Combining opportunistic and size-based scheduling in wireless systems , 2008, MSWiM '08.

[14]  Seung Jun Baek,et al.  Delay-Optimal Opportunistic Scheduling and Approximations: The Log Rule , 2009, INFOCOM 2009.

[15]  Byeong Gi Lee,et al.  Wireless packet scheduling based on the cumulative distribution function of user transmission rates , 2005, IEEE Transactions on Communications.

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

[17]  Gersende Fort,et al.  The ODE method for stability of skip-free Markov chains with applications to MCMC , 2006, math/0607800.

[18]  M. Andrews,et al.  Instability of the proportional fair scheduling algorithm for HDR , 2004, IEEE Transactions on Wireless Communications.

[19]  Urtzi Ayesta,et al.  A modeling framework for optimizing the flow-level scheduling with time-varying channels , 2010, Perform. Evaluation.

[20]  Philippe Robert.  Stochastic Networks and Queues , 2003 .

[21]  J. Dai.  On Positive Harris Recurrence of Multiclass Queueing Networks: A Unified Approach Via Fluid Limit Models , 1995 .

[22]  Sem C. Borst,et al.  Flow-level performance and capacity of wireless networks with user mobility , 2009, Queueing Syst. Theory Appl..

[23]  J. Norris,et al.  Differential equation approximations for Markov chains , 2007, 0710.3269.

[24]  Samuli Aalto,et al.  Flow-level stability and performance of channel-aware priority-based schedulers , 2010, 6th EURO-NGI Conference on Next Generation Internet.

[25]  Lei Ying,et al.  Throughput-Optimal Opportunistic Scheduling in the Presence of Flow-Level Dynamics , 2010, INFOCOM 2010.

[26]  N.B. Shroff,et al.  Optimal opportunistic scheduling in wireless networks , 2003, 2003 IEEE 58th Vehicular Technology Conference. VTC 2003-Fall (IEEE Cat. No.03CH37484).

[27]  Urtzi Ayesta,et al.  Scheduling in a Random Environment: Stability and Asymptotic Optimality , 2011, IEEE/ACM Transactions on Networking.

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

[29]  Sem C. Borst,et al.  Stability of Parallel Queueing Systems with Coupled Service Rates , 2006, Discret. Event Dyn. Syst..

[30]  P. Whittle.  Restless bandits: activity allocation in a changing world , 1988, Journal of Applied Probability.