Queueing Problems with Two Parallel Servers

Youngsub Chun

Chapter Chapter 10 in Fair Queueing, 2016, pp 141-157 from Springer

Abstract: Abstract We generalize the queueing problem by assuming that the facility has two parallel servers so that two agents can be served at the same time. Once again, we are interested in finding the order in which to serve agents and the monetary transfers they should receive. Similarly to the queueing problem with one server, we introduce the “minimal transfer rule” and the “maximal transfer rule” for the queueing problem with two parallel servers and show that they correspond to the Shapley (Contributions to the theory of games II. Princeton University Press, Princeton, 1953) value of queueing games with two parallel servers, for two alternative definitions of the worth of a coalition. 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. If it is defined by assuming the coalitional members are served after the non-coalitional members, then the maximal transfer rule is obtained.

Date: 2016
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Journal Article: Queueing problems with two parallel servers (2008)
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DOI: 10.1007/978-3-319-33771-5_10

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