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Service-Level Differentiation in Many-Server Service Systems via Queue-Ratio Routing

Kellogg School of Management, Northwestern University, Evanston, Illinois 60208
Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027
i-gurvich{at}kellogg.northwestern.edu
ww2040{at}columbia.edu

Motivated by telephone call centers, we study large-scale service systems with multiple customer classes and multiple agent pools, each with many agents. To minimize staffing costs subject to service-level constraints, where we delicately balance the service levels (SLs) of the different classes, we propose a family of routing rules called fixed-queue-ratio (FQR) rules. With FQR, a newly available agent next serves the customer from the head of the queue of the class (from among those he is eligible to serve) whose queue length most exceeds a specified proportion of the total queue length. The proportions can be set to achieve desired SL targets. The FQR rule achieves an important state-space collapse (SSC) as the total arrival rate increases, in which the individual queue lengths evolve as fixed proportions of the total queue length. In the current paper we consider a variety of service-level types and exploit SSC to construct asymptotically optimal solutions for the staffing-and-routing problem. The key assumption in the current paper is that the service rates depend only on the agent pool.

Subject classifications: queues; networks; multiple classes; server pools; queues; optimization; design; staffing; routing; queues; limit theorems; asymptotic optimality; many-server heavy-traffic limits.
History: Received January 2007; revision received January 2009; accepted April 2009.