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Queueing problems with two parallel servers

Youngsub Chun and Eun Jeong Heo

International Journal of Economic Theory, 2008, vol. 4, issue 2, 299-315

Abstract: Agents are waiting for their jobs to be processed at a service facility. All agents need the same processing time but have different waiting costs per unit of time. The facility has two parallel servers and can serve two agents at a time. We are interested in finding the order in which to serve agents and the (positive or negative) monetary transfers they should receive. We introduce two rules, the “minimal transfer rule” and the “maximal transfer rule”. We show that they correspond to the Shapley (1953) values of associated queueing games, for two alternative definitions of the worth of a coalition. The two‐server queueing games correspond to the games similarly defined by Maniquet (2003) and Chun (2006a) for one server. If the worth of a coalition is defined by assuming that the coalitional members are served before the non‐coalitional members, then the minimal transfer rule is obtained. If it is defined by assuming that the coalitional members are served after the non‐coalitional members, then the maximal transfer rule is obtained.

Date: 2008
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