Transient solution for a finite capacity M/G a,b /1 queueing system with vacations to the server

A Review of Vacation Queueing Models in Different Framework

“…They derived the decompositions of the queue length distributions and provided relevant interpretations. Jacob and Madhusoodanan [50] dealt with the transient solution for a finite capacity M/G a,b /1 queue with server vacations. Dshalalow [32] analyzed the queueing process in stochastic systems with bulk input, batch state dependent service, server vacations and three post vacation disciples: waiting, or leaving on multiple vacation trips with or without emergency.…”

Transient Analysis of Batch Service Queue with Second Optional Service and Reneging

“…A time dependent solution of a single server queueing system with a Poisson input process has been considered by [19,20]. The transient behaviour of the infinite capacity / /1 modelwith batch arrivals and server vacations has been discussed by [21]. The transient behaviour analysis of an / /1/ queue with working breakdowns and server vacations has been studied by [22].…”

On functionals of a marked Poisson process observed by a renewal process

“…The renewal process observing the Poisson process can represent multiple vacations rendered by a server [2,3,12,13,14,15,16,17,19]. In other words, when the server leaves the system, it generates a sequence of vacation (or maintenance) segments each of which ends up with the server returning to the system and checking on its status.…”

“…In other words, when the server leaves the system, it generates a sequence of vacation (or maintenance) segments each of which ends up with the server returning to the system and checking on its status. The whole vacation period is suspended (until its next occurrence, when the queue is exhausted or, in a quorum option [4,9,10,13], drops below some specific level) whenever the system accumulates to some fixed number of units or more and this prompts the server to resume his work [1,4,9,10,11,18]. When using semiregenerative analysis it is imperative to know the status of the system on the period prior to the completion of the first service.…”