Staffing and Control of Instant Messaging Contact Centers

In addition to traditional call centers, many companies have started building a new kind of customer contact center, in which agents communicate with customers via instant messaging (IM) over the Internet rather than phone calls. A distinctive feature of the service centers based on IM is that one agent can serve multiple customers in parallel. We choose to model such a center as a server pool consisting of many limited processor-sharing servers. We characterize the underlying stochastic processes by establishing a fluid approximation in the many-server heavy-traffic regime. The limiting behavior of the stochastic processes is shown to involve a stochastic averaging principle, and the fluid approximation provides insights into the optimal staffing and control for such service centers.