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

Shone, Rob, Knight, Vincent A., Harper, Paul R., Williams, Janet E. and Minty, John 2016. Containment of socially optimal policies in multiple-facility Markovian queueing systems. Journal of the Operational Research Society 67 (4) , pp. 629-643. 10.1057/jors.2015.98

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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Additional Information: Published online 25 November 2015
Publisher: Taylor & Francis
ISSN: 0160-5682
Funders: EPSRC
Date of First Compliant Deposit: 30 March 2016
Date of Acceptance: 13 October 2015
Last Modified: 17 Nov 2020 18:00

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