Ivo Adan, Antonis Economou and Stella Kapodistria. Synchronized reneging in queueing systems with vacations

Abstract. We study a single-server queueing model with multiple vacations and impatient customers, where the source of the impatience is the absence of the server. In the literature, the standard assumption is that the customers perform independent abandonments. However, in some real situations, it is plausible to assume that the customers abandon the system simultaneously. This is the case in remote systems where some of the customers decide to abandon the system, when a transport facility becomes available.

We study two cases. In the first case the customers decide whether to abandon the system or not at the times when the vacation period finishes. While in the second case we suppose that the abandonments are possible only at the event epochs of a point process which is set on, every time that a vacation time begins. At the decision epochs, every present customer remains in the system with probability q or abandons the system with probability p=1-q, independently of the others. In both cases, a key issue is the study of the number of customers at the start of a busy period. Based on this study, we obtain the partial probability generating function of the number of customers at an arbitrary point during a busy period-server is up- and during an idle period-server is down. Finally we discuss further aspects and possible extensions of these models.