Pricing and equilibrium behavior for a Markovian queue with server vacations

The topic of the talk lies in the intersection of queueing and game theory. More specifically we seek for best balking strategies for the customers in a queueing system with server vacations under various levels of information. The model is the single server Markovian queue with setup times. Whenever a customer leaves this system empty, the server departs immediately to attend to secondary jobs. On the contrary, whenever a customer arrives to an empty system, the server is recalled immediately and it takes an exponential setup time to start service again. We assume a natural reward - cost structure for the customers, which incorporates their desire for service as well as their unwillingness to wait. We examine customers behavior under various levels of information regarding the state of the system at arrival instances. More specifically, a customer may know or not know the state of the server and the number of present customers upon his arrival. We derive equilibrium strategies for the customers under the various levels of information and we study the associated social optimization and profit maximization problems. Analytical and numerical comparisons illustrate further the effect of the information level to the pricing and equilibrium behavior of the system.