A Queuing System with Dual Services

A queuing system with dual services, i.e., the primary service and the auxiliary service, is considered in the present article. The server has to allocate part of its capacity to process the additional service when the auxiliary service is requested. We show that the possible optimal auxiliary capacity is actually on the convex envelope of the auxiliary cost function. Also, the optimal control policy is that the allocated capacity for auxiliary service is monotonically non-increasing in the number of people in the queue. Practical implications are discussed at the end.