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

Shone, Robert and Knight, Vincent and Harper, Paul and Williams, Janet and Minty, John (2015) Containment of socially optimal policies in multiple-facility Markovian queueing systems. Journal of the Operational Research Society, 67. pp. 629-643. ISSN 0160-5682

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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.

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Journal of the Operational Research Society
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06 Jan 2020 12:10
Last Modified:
22 Nov 2022 08:32