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Pathwise optimality of the exponential scheduling rule for wireless channels

Part of: Markov processes Special processes Operations research and management science

Published online by Cambridge University Press:  01 July 2016

Sanjay Shakkottai ,
R. Srikant  and
Alexander L. Stolyar
Sanjay Shakkottai*
Affiliation:
The University of Texas at Austin
R. Srikant*
Affiliation:
University of Illinois at Urbana-Champaign
Alexander L. Stolyar*
Affiliation:
Bell Labs Lucent Technologies
*
∗ Postal address: Wireless Networking and Communications Group, Department of Electrical and Computer Engineering, The University of Texas at Austin, 1 University Station C0803, Austin, TX 78712-0240, USA. Email address: [email protected]
∗∗∗ Postal address: Coordinated Science Laboratory and Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. Email address: [email protected]
∗∗∗∗ Postal address: Mathematical Sciences Research Center, Bell Labs Lucent Technologies, 600 Mountain Avenue, Murray Hill, NJ 07974, USA. Email address: [email protected]
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Abstract

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 {an}, 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 maxnanq̃n(t), where q̃n(t) is the queue length of user n in the heavy-traffic regime.

Keywords

Wireless networkschedulingquality of serviceexponential ruleheavy-traffic limitqueueing networkcomplete resource poolingworkloadstate space collapseoptimality

MSC classification

Primary: 60K25: Queueing theory 90B15: Network models, stochastic 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 36 , Issue 4 , December 2004 , pp. 1021 - 1045
Copyright
Copyright © Applied Probability Trust 2004 

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Footnotes

Partially supported by NSF Grants ACI-0305644, CNS-0325788 and CNS-0347400.

Supported by NSF Grant ITR 00-85929.

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