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 consider two types of policies for assigning customers to idle servers – a random assignment and assignment to the longest idle server (ALIS) We survey some results for four different situations: - For a loss system we find conditions for reversibility and insensitivity. - For a manufacturing type system, in which there is enough capacity to serve all jobs, we discuss a product form solution and waiting times. - For an infinite matching model in which an infinite sequence of customers of i.i.d. types, and infinite sequence of servers of i.i.d. types are matched according to first come first, we obtain a product form stationary distribution for this system, which we use to calculate matching rates. - For a call center model with overload and abandonments we make some plausible observations

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