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Queueing problems with two parallel servers
Author(s) -
Chun Youngsub,
Jeong Heo Eun
Publication year - 2008
Publication title -
international journal of economic theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.351
H-Index - 11
eISSN - 1742-7363
pISSN - 1742-7355
DOI - 10.1111/j.1742-7363.2008.00077.x
Subject(s) - transfer (computing) , queueing theory , server , computer science , mathematical economics , order (exchange) , queueing system , service (business) , mathematical optimization , microeconomics , economics , computer network , mathematics , finance , parallel computing , economy
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.