## Abstract

We consider an infinite sequence of customers of types C = {1,2,..., I} and an infinite quence servers of types & = {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 r_{i.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 r_{i.j}.

Original language | English |
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Pages (from-to) | 695-730 |

Number of pages | 36 |

Journal | Advances in Applied Probability |

Volume | 41 |

Issue number | 3 |

DOIs | |

State | Published - 2009 |

## Keywords

- First-come-first-served
- Infinite bipartite matching
- Markov chain
- Service systems

## ASJC Scopus subject areas

- Statistics and Probability
- Applied Mathematics