Service-Level Differentiation in Many-Server Service Systems: A solution based on fixed-queue-ratio routing, Operations Research
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 stang costs subject to service-level constraints, where we delicately balance the service levels (SLs) of the dierent 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 specied 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 xed 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 stang-and-routing problem. The key assumption in the current paper is that the service rates depend only on the agent pool.
Itai Gurvich, Ward Whitt
Gurvich, Itai, and Ward Whitt. 2010. Service-Level Differentiation in Many-Server Service Systems: A solution based on fixed-queue-ratio routing. Operations Research. 58(2): 31-328.LINK