### FCFS infinite bipartite matching of servers and customers

Caldentey René, Kaplan Edward H., and Weiss Gideon
Source: Adv. in Appl. Probab. Volume 41, Number 3 (2009), 695-730.

#### Abstract

We consider an infinite sequence of customers of types 𝓒={1,2,...,I} and an infinite sequence of servers of types 𝓢={1,2,...,J}, where a server of type j can serve a subset of customer types C(j) and where a customer of type~$i$ can be served by a subset of server types S(i). We assume that the types of customers and servers in the infinite sequences are random, independent, and identically distributed, and that customers and servers are matched according to their order in the sequence, on a first-come--first-served (FCFS) basis. We investigate this process of infinite bipartite matching. In particular, we are interested in the rate ri,j that customers of type i are assigned to servers of type j. We present a countable state Markov chain to describe this process, and for some previously unsolved instances, we prove ergodicity and existence of limiting rates, and calculate ri,j.

First Page:
Primary Subjects: 90B22
Secondary Subjects: 60J20, 68M20
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Permanent link to this document: http://projecteuclid.org/euclid.aap/1253281061
Digital Object Identifier: doi:10.1239/aap/1253281061
Mathematical Reviews number (MathSciNet): MR2571314
Zentralblatt MATH identifier: 05625065

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