Cooperation and sharing costs in a tandem queueing network

Dan Bendel and Moshe Haviv

European Journal of Operational Research, 2018, vol. 271, issue 3, 926-933

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.

Keywords: Queueing; Tandem queues; Cooperative games; Cost allocation; Core; Shapley value (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0377221718303801
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:271:y:2018:i:3:p:926-933

DOI: 10.1016/j.ejor.2018.04.049

Access Statistics for this article

European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

More articles in European Journal of Operational Research from Elsevier
Bibliographic data for series maintained by Catherine Liu ().