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Utility Optimization in Congested Queueing Networks

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

N. S. Walton
N. S. Walton*
Affiliation:
University of Cambridge
*
∗Postal address: Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK. Email address: n.s.walton@statslab.cam.ac.uk
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Abstract

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We consider a multiclass single-server queueing network as a model of a packet switching network. The rates packets are sent into this network are controlled by queues which act as congestion windows. By considering a sequence of congestion controls, we analyse a sequence of stationary queueing networks. In this asymptotic regime, the service capacity of the network remains constant and the sequence of congestion controllers act to exploit the network's capacity by increasing the number of packets within the network. We show that the stationary throughput of routes on this sequence of networks converges to an allocation that maximises aggregate utility subject to the network's capacity constraints. To perform this analysis, we require that our utility functions satisfy an exponential concavity condition. This family of utilities includes weighted α-fair utilities for α > 1.

Keywords

Utility optimizationqueueing networkquasi-reversiblelarge deviationcongestion windowcongestion control

MSC classification

Secondary: 90B15: Network models, stochastic 60K25: Queueing theory 90B22: Queues and service 90B18: Communication networks
Type
Research Article
Information
Journal of Applied Probability , Volume 48 , Issue 1 , March 2011 , pp. 68 - 89
Copyright
Copyright © Applied Probability Trust 2011 

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