Dynamic admission control in a call center with one shared and two dedicated service facilities

Admission control of a call center is addressed through a Markovian loss system with two classes of calls and three stations, one dedicated for each class, and one shared station. Each class is identified by different revenues, service and arrival rates. We show that serving a call in its dedicated station, whenever possible, is optimal. For the shared station, we establish the existence of optimal monotone thresholds, and of preferred class(es) under certain conditions.