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First Come First Served: Infinite Matching with Applications to Queues with Multi-type Customers and Multi-type Servers

Wednesday 27 October 2010, 4.00pm-5.30pm
NAB 2.06, New Academic Building

Professor Gideon Weiss
Department of Statistics
University of Haifa

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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 centres 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 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 discus a product form solution.
  • For an overloaded system with reneging, we emphasize a global first come first served property under fluid scaling.

These queuing models are intimately connected to the following discrete time Markovian model, which is both simpler and more general:

  • There is a infinite sequence of customers with i.i.d. types, and infinite sequence of servers of i.i.d. types and the two are matched according to the bipartite customer server graph, using first come first matched.

We obtain a product form stationary distribution for this system, which we use to calculate matching rates.

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

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Gideon Weiss