Dynamic control in the Single Server Markovian Queue

We explore a queuing system with a non-homogeneous population of customers in the sense of optimizing the social welfare. In particular we modify Naor’s observable M/M/1 queue model, which is the most seminal queueing model involving strategic customers. We assume that some customers obey the central planner, who aims to maximize the social welfare, the others don’t. We consider two levels of control: 1) Static control, in which disciplined customers join or balk as instructed by the central planner. 2) Dynamic control, in which disciplined customers also abandon the queue when instructed. We quantify and compare the benefit from each level of control. In particular, we investigate the additional benefit from having dynamic control instead of static control. ∗Department of Statistics and Operation Research, Tel Aviv University, Israel. Emails: [email protected], [email protected]