The single server vacation queueing model with geometric abandonments

Abstract

Several recent papers have investigated the customer reneging behavior in queueing systems with vacations, where the customers become impatient during the absence of the server(s). These studies have treated the cases of independent and synchronized abandonments. In the case of independent abandonments, the customers have their own independent patience times and abandon the system when such times expire. In the case of synchronized abandonments, the abandonment opportunities occur according to a certain point process and then all present customers decide simultaneously but independently whether they will abandon the system or not. In the present paper, we complement these studies by considering the case of geometric abandonments. This case arises when the abandonment opportunities occur according to a certain point process and the customers decide sequentially whether they will leave the system or not. We derive explicit expressions and computational schemes for various performance descriptors, including the number of customers in system, the sojourn time of a customer, the duration and the maximum number of customers in a busy period.