Dynamic Control of N-Systems With Many Servers: Asymptotic Optimality of a Static Priority Policy in Heavy Traffic
Source: Georgia Institute of Technology
This paper considers 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. The objective is to minimize the total cost that includes a linear holding cost and a reneging cost. The authors prove that, when the service speed is pool-dependent, but not class-dependent, a ci-type greedy policy is asymptotically optimal in many-server heavy traffic.