M[X]/G/1 Retrial Queueing System with Second Optional Service , Random Break down ,Set Up Time and Bernoulli Vacation

Abstract

In this paper, we investigate a single server batch arrival non-Markovian retrial queueing model with random break down and Bernoulli vacation. Customers arrive in batches accordingly Poisson process with arrival rate λ but are served one by one with first come first served basis. All customers demand the first essential service, whereas only some of them demand the second optional service. The server is assumed to be unreliable so that it may encounter break down at any time. As the server has to be repaired, the repair process start immediately. The customer, who finds the server busy upon arrival, can either join the orbit with probability p or he/she can leave the system with probability 1-p. Upon completion of a service the server may go for a vacation with probability θ or stay back in the system to serve a next customer with probability 1 − θ, if any. After finishing a vacation, the server could not provide service as the it should go for a setup time. Assuming that, the retrial time, the service time, the repair time, the vacation completion time and the set up time of the server are all arbitrarily distributed. We obtain the transient solution and

Efficacy of the Single Server Markovian Two-Phase Symmetric Queue with Encouraged Stationary-Queue-Size Analysis

“…working vacation and interruption of M/G/1 vacation queue investigated in [21]. The k phases service, Bernoulli's feedback T-policies for M/G/1 line model investigated in [22][23]. M [X] /G/1 queuing model with time-dependent solution instead of Bernoulli k vacation and balking consumers was examined in [23].…”

“…The k phases service, Bernoulli's feedback T-policies for M/G/1 line model investigated in [22][23]. M [X] /G/1 queuing model with time-dependent solution instead of Bernoulli k vacation and balking consumers was examined in [23]. [24] Studied the expected delay of the M/ G/1 cyclic system service line using Bernoulli scheduling.…”