Steady state analysis of an Mx/G/1 queue with two phase service and Bernoulli vacation schedule under multiple vacation policy

Abstract

This paper examines the steady state behaviour of a batch arrival queue with two phases of heterogeneous service along and Bernoulli schedule vacation under multiple vacation policy, where after two successive phases service or first vacation the server may go for further vacations until it finds a new batch of customer in the system. We carry out an extensive stationary analysis of the system, including existence of stationary regime, queue size distribution of idle period process, embedded Markov chain steady state distribution of stationary queue size, busy period distribution along with some system characteristics.

A Two Stage Batch Arrival Queue with Reneging during Vacation and Breakdown Periods

“…In recent years, extensive amount of work has been done on batch arrival queues with vacations and breakdowns. We mention a few recent papers by Kumar and Arumuganathan [16], Choudhury, Tadj and Paul [17], Maraghi, Madan and Darby-Dowman [18], Khalaf, Madan and Lukas [19].…”

Algorithmic analysis of the multi-server system with a modified Bernoulli vacation schedule

“…This overhauling can be utilized as a vacation in the presented model. Another application of such model based on Choudhury et al [17] may well be found in some transportation systems in which a ferry driver or locomotive driver may have a vacation after every round of trip.…”

“…A numbers of papers [13][14][15][16] have recently appeared in queueing literature in which the server provides to each heterogeneous service with Bernoulli schedule vacation (BSV). The so-called BSV means that when the service of a unit is completed, the server may leave for a vacation of random length with probability p or may continue to serve the next unit, if any with probability 1 À p (see Choudhury et al [17]). For the multiple server vacation models, there are only a limited number of studies due 0307-904X/$ -see front matter Ó 2010 Elsevier Inc. All rights reserved.…”

A batch arrival unreliable Bernoulli vacation model with two phases of service and general retrial times

“…Otherwise, the server waits for the first customer to arrive. Recently, there has been considerable attention paid to the study of M/G/1-type queuing systems with two phases of service under Bernoulli vacation schedule and different vacation policies, see Choudhury et al (2007), and Madan (2005, 2004), in which after two successive phases of service, the server may go for Bernoulli vacation. Further, Haridass and Arumuganathan (2011) investigated a bulk service queueing system with variant threshold policy for secondary jobs, which is related to our two phase queueing system.…”