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

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 the servers in the other pool can only serve 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, not class-dependent, a cμ-type greedy policy is asymptotically optimal in many-server heavy traffic. The key to our optimality proof is a state space collapse result for diffusion-scaled processes under the greedy policy. We employ a framework developed in Dai and Tezcan (2005) to prove the state space collapse in many-server heavy traffic. AMS 2000 subject classifications: Primary 60K25; secondary 90B22, 60F17.