ABSTRACT
In this chapter, the behaviors of impatient clients on a single server retry queue with different server breaks are studied. According to the Poisson process, the client arrives at the queuing system, and the client receives the service immediately while the server is not busy with any other customer. If not, they must rejoin an orbit to receive their services randomly. Service time is distributed exponentially. Customers wait in orbit to retry their service and retry rates are also distributed exponentially. When there are no clients on the system, the server allows vacations for a random period. When the server returns to duty after completing the vacation, the server may leave for another short vacation if there is no one on the system. All holiday samples, such as differentiated vacations, are distributed exponentially. As the server provides services to clients, the clients in orbit become impatient with an individual timer, and it is assumed that this individual timer is distributed exponentially. The probability generator technique is applied to obtain the size probability of the steady-state system. In addition, several performance metrics are also presented. At the end of the chapter, a numerical example is presented to study the system’s behavior when the system parameters are modified.
