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

Abstract

We consider a single server Markovian feedback queue with variant of multiple vacation policy, balking, server's states-dependent reneging, and retention of reneged customers. We obtain the steady-state solution of the considered queue based on the use of probability generating functions. Then, the closed-form expressions of different system characteristics are derived. Finally, we present some numerical results in order to show the impact of the parameters of impatience timers on the performance measures of the system.

Analysis of bulk service queuing system with rework, unreliable server, resuming service and two kinds of multiple vacation

“…Recently, the mathematicians, Binay Kumar [13], Zirem et al [14], Charan Jeet Singh et al [15], Sethi [16], Chakravarthyet al [17], Vijaya Laxmi Pikkala et al [18], Kerobyan et al [19] are discussed the unreliable queuing systems. Ayyappan et al [20], Bouchentouf,et al ([21,22,23,24], Nithya et al [25], Kempa et al [26], Joshi et al [27], Sadhna Singh et al [28] have analysed a queuing system incorporated with multiple vacation.…”

Analysis of single server finite buffer queue under discouraged arrival and retention of reneging

“…In a similar line retention of impatient customers with optimal service and working vacations has been analysed by VijayaLaxmi et al [18] without considering the aspect of balking and buffer size. A single server Markovian queueing system with Bernoulli feedback, balking, server's states-dependent reneging, and retention of reneged customers under variant multiple vacation policy was analysed by Bouchentouf et al [19]. A heterogeneous queuing system with reverse balking and reneging was discussed by Som and Kumar [20].…”

“…In another work Bouchentouf et al [21] presented the mathematical modelling of a multi-server Markovian queue with Bernoulli feedback under variant of multiple vacation policy in the absence of retention strategy. In these papers [15][16][17][18][19] authors did not assume the concept of discouraged arrival. Rasheed and Manoharan [22] studied a Markovian queueing system in the absence of customers' impatience.…”

“…Though this model has been analyzed by many researchers, however, to the best of our knowledge, the added restrictions of discouraged arrival, reneging, retention of reneged customers and balking has not been dealt with in the literature. Only a restricted version considering the single and multi-server queuing model assuming impatient customers is available in [3,4,10,[15][16][17][18][19]. In this paper, we try to address these gaps in the literature.…”