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

Author

Listed:
  • Rob Shone

    (Cardiff University, Cardiff, UK)

  • Vincent A Knight

    (Cardiff University, Cardiff, UK)

  • Paul R Harper

    (Cardiff University, Cardiff, UK)

  • Janet E Williams

    (Cardiff University, Cardiff, UK)

  • John Minty

    (Cardiff University, Cardiff, UK)

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.

Suggested Citation

  • Rob Shone & Vincent A Knight & Paul R Harper & Janet E Williams & John Minty, 2016. "Containment of socially optimal policies in multiple-facility Markovian queueing systems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(4), pages 629-643, April.
    • Handle: RePEc:pal:jorsoc:v:67:y:2016:i:4:p:629-643
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    Cited by:

    1. Rob Shone & Vincent A. Knight & Paul R. Harper, 2020. "A conservative index heuristic for routing problems with multiple heterogeneous service facilities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(3), pages 511-543, December.
    2. Hanukov, Gabi & Avinadav, Tal & Chernonog, Tatyana & Yechiali, Uri, 2020. "A service system with perishable products where customers are either fastidious or strategic," International Journal of Production Economics, Elsevier, vol. 228(C).

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