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Containment of socially optimal policies in multiple-facility Markovian queueing systems

Research output: Contribution to journalJournal articlepeer-review

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  • Robert Shone
  • Vincent Knight
  • Paul Harper
  • Janet Williams
  • John Minty
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<mark>Journal publication date</mark>25/11/2015
<mark>Journal</mark>Journal of the Operational Research Society
Volume67
Number of pages15
Pages (from-to)629-643
Publication StatusPublished
<mark>Original language</mark>English

Abstract

We consider a Markovian queueing system with N heterogeneous service facilities, each of which has multiple servers available, linear holding costs, a fixed value of service and a first-come-first-serve queue discipline. Customers arriving in the system can be either rejected or sent to one of the N facilities. Two different types of control policies are considered, which we refer to as ‘selfishly optimal’ and ‘socially optimal’. We prove the equivalence of two different Markov Decision Process formulations, and then show that classical M/M/1 queue results from the early literature on behavioural queueing theory can be generalized to multiple dimensions in an elegant way. In particular, the state space of the continuous-time Markov process induced by a socially optimal policy is contained within that of the selfishly optimal policy. We also show that this result holds when customers are divided into an arbitrary number of heterogeneous classes, provided that the service rates remain non-discriminatory.