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On the value function of the M/Cox(r)/1 queue

Part of: Stochastic systems and control Special processes

Published online by Cambridge University Press:  14 July 2016

Sandjai Bhulai
Sandjai Bhulai*
Affiliation:
Vrije Universiteit Amsterdam
*
∗Postal address: Vrije Universiteit Amsterdam, Faculty of Sciences, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands. Email address: sbhulai@few.vu.nl
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Abstract

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We consider a single-server queueing system at which customers arrive according to a Poisson process. The service times of the customers are independent and follow a Coxian distribution of order r. The system is subject to costs per unit time for holding a customer in the system. We give a closed-form expression for the average cost and the corresponding value function. The result can be used to derive nearly optimal policies in controlled queueing systems in which the service times are not necessarily Markovian, by performing a single step of policy iteration. We illustrate this in the model where a controller has to route to several single-server queues. Numerical experiments show that the improved policy has a close-to-optimal value.

Keywords

Coxian distributionM/Cox(r)/1 queueone-step policy improvementoptimal routeingPoisson equationvalue function

MSC classification

Primary: 93E25: Other computational methods
Secondary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 2 , June 2006 , pp. 363 - 376
Copyright
© Applied Probability Trust 2006 

Footnotes

Supported by the Netherlands Organization for Scientific Research (NWO).

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