Cooperation and sharing costs in a tandem queueing network

Dan Bendel, Moshe Haviv*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We consider a tandem network of queues with a Poisson arrival process to the first queue. Service times are assumed to be exponential. In cases where they are not, we additionally assume a processor sharing service discipline in all servers. Consecutive servers may cooperate by pooling resources which leads to the formation of a single combined server that satisfies the aggregated service demands with a greater service rate. On this basis we define a cooperative game with transferable utility, where the cost of a coalition is the steady-state mean total number of customers in the system formed by its members. We show that the game is subadditive, leading to full cooperation being socially optimal. We then show the non-emptiness of the core, despite the characteristic function being neither monotone, nor concave. Finally, we derive several well-known solution concepts, including the Shapley value, the Banzhaf, value and the nucleolus, for the case where servers have equal mean service demands. In particular, we show that all three values coincide in this case.

Original languageEnglish
Pages (from-to)926-933
Number of pages8
JournalEuropean Journal of Operational Research
Volume271
Issue number3
DOIs
StatePublished - 16 Dec 2018

Bibliographical note

Publisher Copyright:
© 2018 Elsevier B.V.

Keywords

  • Cooperative games
  • Core
  • Cost allocation
  • Queueing
  • Shapley value
  • Tandem queues

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