On the M/G/1 retrial queue subjected to breakdowns

Abstract

Retrial queueing systems are characterized by the requirement that customers finding the service area busy must join the retrial group and reapply for service at random intervals. This paper deals with the M/G/1 retrial queue subjected to breakdowns. We use its stochastic decomposition property to approximate the model performance in the case of general retrial times.

AN M/G/1 RETRIAL QUEUE WITH UNRELIABLE SERVER FOR STREAMING MULTIMEDIA APPLICATIONS

“…All models considering retrial queues with server breakdowns assume an M/G/1/1 loss system with the exception of [6] and [21]. [2,3,7,16,20,23,24,27]) force these customers into the orbit, whereas others [4][5][6]11,15,26] provide the option of joining the orbit or departing the system. For retrial models with no waiting room and server breakdowns, customers arriving to find the server unavailable (busy or failed) join the orbit.…”

“…For retrial models with no waiting room and server breakdowns, customers arriving to find the server unavailable (busy or failed) join the orbit. A variety of failure types are considered in the literature, including starting failures [16,20,27], vacations [7,23], active breakdowns [6,24,26], and, like our model, both active and idle breakdowns [2][3][4][5]11,15]. [2,3,7,16,20,23,24,27]) force these customers into the orbit, whereas others [4][5][6]11,15,26] provide the option of joining the orbit or departing the system.…”

“…Some models (cf. [2,3,7,16,20,23,24,27]) force these customers into the orbit, whereas others [4][5][6]11,15,26] provide the option of joining the orbit or departing the system. With the exception of two cases ( [3,24]), these models also either force or provide the option for in-service customers interrupted by a server failure to join the orbit.…”

“…Our model differs from these in that arriving customers who find the server busy or failed join the normal queue, whereas interrupted customers always join the orbit and attempt to reaccess the server at random intervals. A variety of failure types are considered in the literature, including starting failures [16,20,27], vacations [7,23], active breakdowns [6,24,26], and, like our model, both active and idle breakdowns [2][3][4][5]11,15]. Most orbits are assumed to behave as infinite-server queues with identical exponential service times; however, some models (cf.…”

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

“…Gautam Choudhury [14] discussed batch arrival with above mentioned models. Djellab [17] discussed M/G/1 retial queue with breakdowns. Krishnakumar et al [26] discussed two phase retrial queue under preemptive resume.…”