## Advances in Applied Probability

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

### FCFS infinite bipartite matching of servers and customers

Caldentey René, Kaplan Edward H., and Weiss Gideon

#### 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
*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}.

#### Article information

**Source**

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

**Dates**

First available in Project Euclid: 18 September 2009

**Permanent link to this document**

https://projecteuclid.org/euclid.aap/1253281061

**Digital Object Identifier**

doi:10.1239/aap/1253281061

**Mathematical Reviews number (MathSciNet)**

MR2571314

**Zentralblatt MATH identifier**

1247.90099

**Subjects**

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]

**Keywords**

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

#### Citation

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. https://projecteuclid.org/euclid.aap/1253281061.