Performance and economic analysis of Markovian Bernoulli feedback queueing system with vacations, waiting server and impatient customers

Abstract

This paper concerns the analysis of a Markovian queueing system with Bernoulli feedback, single vacation, waiting server and impatient customers. We suppose that whenever the system is empty the sever waits for a random amount of time before he leaves for a vacation. Moreover, the customer’s impatience timer depends on the states of the server. If the customer’s service has not been completed before the impatience timer expires, the customer leaves the system, and via certain mechanism, impatient customer may be retained in the system. We obtain explicit expressions for the steady-state probabilities of the queueing model, using the probability generating function (PGF). Further, we obtain some important performance measures of the system and formulate a cost model. Finally, an extensive numerical study is illustrated.

The Markovian Bernoulli queues with operational server vacation, Bernoulli's weak and strong disasters, and linear impatient customers

“…In fact, since the paper of Altman and Yechiali [1], various aspects of server vacations with impatient customers for single server queuing systems have interested several authors for instance; Yue et al [12] analyzed a queuing system with impatient customers and working vacations; Yue et al [8] studied customer impatience in a single server queuing system with working vacations; Yue et al [9] analyzed an M/M/1 queue with vacations and impatience timers which depend on the server's states; Bouchentouf et al [2] were interested by the study of the economic analysis of Markovian Bernoulli feedback queuing system with waiting server, vacations and impatient arrivals.…”

Variant vacation queueing system with Bernoulli feedback, balking and server's states-dependent reneging

“…Despite the rapid growth of the literature about customers's impatience in vacation queueing models, there is very limited literature to deal with the customers' impatience during both vacation and busy periods. The authors can refer to Yue et al [39] and Bouchentouf and Guendouzi [11,12], and Cherfaoui et al et al [13].…”

Single Server Batch Arrival Bernoulli Feedback Queueing System with Waiting Server, K-Variant Vacations and Impatient Customers

“…Such queueing models have attracted the attention of many researchers (cf. Padmavathy et al [20], Ammar [21], Deepa and Kalidass [22], Bouchentouf et al [23], and Bouchentouf and Guendouzi [24]).…”