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Fcfs infinite bipartite matching of servers and customers

Part of: Markov processes Computer system organization Operations research and management science

Published online by Cambridge University Press:  01 July 2016

René Caldentey ,
Edward H. Kaplan  and
Gideon Weiss
René Caldentey*
Affiliation:
New York University
Edward H. Kaplan*
Affiliation:
Yale School of Management, Yale School of Medicine, and Yale School of Engineering and Applied Science
Gideon Weiss*
Affiliation:
University of Haifa
*
∗ Postal address: IOMS Department, Stern Business School, New York University, New York. Email address: rcaldent@stern.nyu.edu
∗∗ Postal address: Yale School of Management, Box 208200, New Haven, CT 06520-8200, USA. Email address: edward.kaplan@yale.edu
∗∗∗ Postal address: Department of Statistics, The University of Haifa, Mount Carmel 31905, Israel. Email address: gweiss@stat.haifa.ac.il
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Abstract

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We consider an infinite sequence of customers of types and an infinite sequence of servers of types 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.

Keywords

Service systemsfirst-come–first-servedinfinite bipartite matchingMarkov chain

MSC classification

Primary: 90B22: Queues and service
Secondary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) 68M20: Performance evaluation; queueing; scheduling
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 41 , Issue 3 , September 2009 , pp. 695 - 730
Copyright
Copyright © Applied Probability Trust 2009 

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