Dynamic admission control in a call center with one shared and two dedicated service facilities (original) (raw)

Calls of two classes arrive at a call center according to two independent Poisson processes. The center has two dedicated stations, one for each class, and one shared station. All three stations consist of parallel servers and no waiting room. Calls of each type demand exponential service times with different service rates and generate different rewards. Moreover, the service rates are different in the shared and dedicated stations. We assume non-preemptive service. Our objective is to derive the structure of dynamic admission policies that maximize the total expected discounted revenue over an infinite horizon as well as the long-run average revenue. We show that it is optimal to serve a customer in her dedicated station whenever it is possible. For the shared station, we derive a sufficient condition for each class under which it is always optimal to accept customers of that class to the shared station if the dedicated station is full and the shared station has available servers. Furthermore, the optimal admission policy at the shared station can be characterized as a monotonic threshold policy.