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1 results

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

  • Part of
  • Sandjai Bhulai
  • Journal:
    Journal of Applied Probability / Volume 43 / Issue 2 / June 2006
    Published online by Cambridge University Press:
    14 July 2016, pp. 363-376
    Print publication:
    June 2006
    • Article
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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.