Queueing Problems with Two Parallel Servers

20 Pages Posted: 16 Mar 2007

See all articles by Youngsub Chun

Youngsub Chun

Seoul National University - School of Economics

Eun Jeong Heo

University of Rochester

Date Written: March 2007

Abstract

A group of agents are waiting for their job to be processed in a facility. We assume that each agent needs the same amount of processing time and incurs waiting costs. The facility has two parallel servers, being able to serve two agents at a time. We are interested in finding the order to serve agents and the (positive or negative) monetary compensations they should receive. We introduce two rules for the problem, the minimal transfer rule and the maximal transfer rule. We show that these two rules correspond to the Shapley (1953) value of the queueing games with two servers, as discussed similarly by Maniquet (2003) and Chun (2006a) for queueing problems with one serve, when the worth of each coalition is appropriately defined. If the worth of a coalition is defined by assuming the coalitional members are served before the non-coalitional members, then the minimal transfer rule is obtained. On the other hand, if it is defined by assuming the coalitional members are served after the non-coalitional members, then the maximal transfer rule is obtained.

Keywords: queueing problems with two servers, Shapley value, minimal, transfer rule, maximal transfer rule

JEL Classification: C71, D63, D73

Suggested Citation

Chun, Youngsub and Heo, Eun Jeong, Queueing Problems with Two Parallel Servers (March 2007). ISER Discussion Paper No. 683, Available at SSRN: https://ssrn.com/abstract=970807 or http://dx.doi.org/10.2139/ssrn.970807

Youngsub Chun (Contact Author)

Seoul National University - School of Economics ( email )

San 56-1, Silim-dong, Kwanak-ku
Seoul 151-742
Korea

Eun Jeong Heo

University of Rochester ( email )

Department of Economics
300 Crittenden Blvd
Rochester, NY 14627
United States

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