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Dynamic Control of N-Systems with Many Servers: Asymptotic Optimality of a Static Priority Policy in Heavy Traffic

Industrial and Enterprise Systems Engineering, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
ttezcan{at}uiuc.edu
dai{at}isye.gatech.edu

We consider a class of parallel server systems that are known as N-systems. In an N-system, there are two customer classes that are catered by servers in two pools. Servers in one of the pools are cross-trained and can serve customers from both classes, whereas all of the servers in the other pool can serve only one of the customer classes. A customer reneges from his queue if his waiting time in the queue exceeds his patience. Our objective is to minimize the total cost that includes a linear holding cost and a reneging cost. We prove that, when the service speed is pool dependent, but not class dependent, a cµ-type greedy policy is asymptotically optimal in many-server heavy traffic.

Subject classifications: N-systems; parallel server systems; asymptotic optimality; many-server limit; heavy-traffic limit; Halfin-Whitt regime.
History: Received December 2006; revision received October 2007; accepted November 2007.