Abstract

We consider a system where jobs of several types are served by servers of several types, and a bipartite graph between server types and job types describes feasible assignments.

This is a common situation in manufacturing, call centers with skill based routing, matching of parent-child in adoption or matching in kidney transplants etc.

We consider the case of first come first served policy: jobs are assigned to the first available feasible server in order of their arrivals. We will survey some results for three different situations: For stable system, in which there is enough capacity to serve all jobs with no congestion, we discuss a product form solution.

For an overloaded system with reneging, we emphasize a global first come first served property under fluid scaling.

For a balanced model we consider the matching of an infinite sequence of jobs and an infinite sequence of servers, and discuss its modeling by some Markov chains.

This talk surveys work with Rene Caldentey and Ed Kaplan, and work by Jeremy Visschers, Ivo Adan and Cor Hurkens, and by Rishy Talreja and Ward Whitt.