Blind Fair Routing in Large-Scale Service Systems with Heterogeneous Customers and Servers

Abstract

In a call center, arriving customers must be routed to available servers, and servers that have just become available must be scheduled to help waiting customers. These dynamic routing and scheduling decisions are very difficult, because customers have different needs and servers have different skill levels. A further complication is that it is preferable that these decisions are made blindly; that is, they depend only on the system state and not on system parameter information such as call arrival rates and service speeds. This is because this information is generally not known with certainty. Ideally, a dynamic control policy for making routing and scheduling decisions balances customer and server needs by keeping customer delays low but still fairly dividing the workload amongst the various servers. In this paper, we propose a blind dynamic control policy for parallel-server systems with multiple customer classes and server pools that is based on the number of customers waiting and the number of agents idling. We show that in the Halfin-Whitt many-server heavy-traffic limiting regime, our proposed blind policy performs extremely well when the objective is to minimize customer holding costs subject to “server fairness,” as defined by how the system idleness is divided among servers. To do this, we formulate an approximating diffusion control problem (DCP) and compare the performance of the nonblind DCP solution to a feasible policy for the DCP that is blind. We establish that the increase in the DCP objective function value is small over a wide range of parameter values. We then use simulation to validate that a small increase in the DCP objective function value is indicative of our proposed blind policy performing very well.

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