Advances in Applied Probability

FCFS infinite bipartite matching of servers and customers

Caldentey René, Kaplan Edward H., and Weiss Gideon

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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.

Article information

Adv. in Appl. Probab. Volume 41, Number 3 (2009), 695-730.

First available in Project Euclid: 18 September 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 90B22: Queues and service [See also 60K25, 68M20]
Secondary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40] 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]

Service systems first-come--first-served infinite bipartite matching Markov chain


René, Caldentey; Edward H., Kaplan; Gideon, Weiss. FCFS infinite bipartite matching of servers and customers. Adv. in Appl. Probab. 41 (2009), no. 3, 695--730. doi:10.1239/aap/1253281061.

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