Delay-optimal opportunistic scheduling and approximations: The log rule

Bilal Sadiq, Seung Jun Baek, Gustavo De Veciana

Research output: Contribution to journalArticlepeer-review

84 Citations (Scopus)


This paper considers the design of multiuser opportunistic packet schedulers for users sharing a time-varying wireless channel from performance and robustness points of view. For a simplified model falling in the classical Markov decision process framework, we numerically compute and characterize mean-delay-optimal scheduling policies. The computed policies exhibit radial sum-rate monotonicity: As users' queues grow linearly, the scheduler allocates service in a manner that deemphasizes the balancing of unequal queues in favor of maximizing current system throughput (being opportunistic). This is in sharp contrast to previously proposed throughput-optimal policies, e.g., Exp rule and MaxWeight (with any positive exponent of queue length). In order to meet performance and robustness objectives, we propose a new class of policies, called the Log rule, that are radial sum-rate monotone (RSM) and provably throughput-optimal. In fact, it can also be shown that an RSM policy minimizes the asymptotic probability of sum-queue overflow. We use extensive simulations to explore various possible design objectives for opportunistic schedulers. When users see heterogenous channels, we find that emphasizing queue balancing, e.g., Exp rule and MaxWeight, may excessively compromise the overall delay. Finally, we discuss approaches to implement the proposed policies for scheduling and resource allocation in OFDMA-based multichannel systems.

Original languageEnglish
Article number5559458
Pages (from-to)405-418
Number of pages14
JournalIEEE/ACM Transactions on Networking
Issue number2
Publication statusPublished - 2011 Apr


  • Delay/throughput optimality
  • Markov decision process
  • OFDMA resource allocation
  • opportunistic scheduling
  • radial sum-rate monotonicity (RSM)

ASJC Scopus subject areas

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Electrical and Electronic Engineering


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