Fair Dynamic Routing in Large-Scale Heterogeneous-Server Systems
نویسندگان
چکیده
In a call center, there is a natural trade-off between minimizing customer wait time and fairly dividing the workload amongst agents of different skill levels. The relevant control is the routing policy; that is, the decision concerning which agent should handle an arriving call when more than one agent is available. We formulate an optimization problem for a call center with heterogeneous agent pools, in which each pool is distinguished by the speed at which agents in that pool handle calls. The objective is to minimize steady-state expected customer wait time subject to a “fairness” constraint on the workload division. We first solve the optimization problem by formulating it as a Markov Decision Process (MDP), and solving a related Linear Program. We note that this approach does not in general lead to an optimal policy that has a simple structure. Fortunately, the optimal policy does appear to have a simple structure as the system size grows large, in the Halfin-Whitt many-server heavy-traffic limit regime. Therefore, we solve the diffusion control problem that arises in this regime, and interpret its solution as a policy for the original system. The resulting routing policy is a threshold policy that determines server pool priorities based on the total number of customers in the system. We prove that a continuous modification of our proposed threshold routing policy is asymptotically optimal in the Halfin-Whitt limit regime. We furthermore present simulation results to illustrate that our proposed threshold routing policy outperforms a common routing policy used in call centers (that routes to the agent that has been idle the longest).
منابع مشابه
Fair Dynamic Routing in Large-Scale Heterogeneous-Server Systems: Technical Appendix
In this technical appendix we provide proofs for the various results stated in the manuscript titled: “Fair Dynamic Routing in Large-Scale Heterogeneous-Server Systems”. The technical appendix is divided into two subsections. Section A provides results that are useful to prove the Lemmas, Propositions, and Theorems stated in Sections 3 and 4 of the main paper. Section B shows the proofs of all ...
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عنوان ژورنال:
- Operations Research
دوره 58 شماره
صفحات -
تاریخ انتشار 2010