A discrete-time queueing system with changes in the vacation times

Abstract

This paper considers a discrete-time queueing system in which an arriving customer can decide to follow a last come first served (LCFS) service discipline or to become a negative customer that eliminates the one at service, if any. After service completion, the server can opt for a vacation time or it can remain on duty. Changes in the vacation times as well as their associated distribution are thoroughly studied. An extensive analysis of the system is carried out and, using a probability generating function approach, steady-state performance measures such as the first moments of the busy period of the queue content and of customers delay are obtained. Finally, some numerical examples to show the influence of the parameters on several performance characteristics are given.

From Exhaustive Vacation Queues to Preemptive Priority Queues with General Interarrival Times

“…If not, the server leaves for another vacation of random duration; see, e.g., the works of Doshi (1986), Takagi (1991) or Tian and Zhang (2006) for references to M/G/1-type vacation models. Some recent advances on queues with vacations are presented by Woźniak et al (2014), Dudin et al (2016) and Atencia (2016).…”

Analysis of an N–Policy GI/M/1 Queue in a Multi–Phase Service Environmentwith Disasters

“…During the past two decades, the topic of disasters has been studied extensively by many researchers; the interested readers are referred to the works of Towsley and Tripathi (1991), Artalejo and Gómez-Corral (1998), Krishna Kumar and Arivudainambi (2000), Economou Sudhesh et al (2016) analyzed an N-policy M/M/1 queue with disastrous breakdown, and derived the closed-form expressions of system size probabilities in transient state and in steady state. For the discrete-time queueing models, there also exist a large volume of references (see, e.g., Atencia and Moreno, 2004;Park et al, 2009;2010;Atencia, 2014;2016). There are also a number of recent publications closely related to queueing systems with disasters.…”