An Unreliable Optional Stage M X ∕ G ∕1 Retrial Queue with Immediate Feedbacks and at most J Vacations
01 Jan 2018-pp 437-445
TL;DR: A repeated attempt queue with multistages of service and almost J vacations is investigated, and steady results are deduced using supplementary variable technique.
Abstract: A repeated attempt queue with multistages of service and almost J vacations is investigated. Balking (or reneging) is applicable for customers. If the orbit is empty at service accomplishment time, the server takes at most J vacations. Busy server may fail for a short interval of time. Using supplementary variable technique, the steady results are deduced.
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TL;DR: An overview and literature survey on the performance modeling and analysis of single server, general service queueing system with service interruption using supplementary variable technique and factors causing service interruption such as unreliable server and server vacation are presented.
Abstract: In most of the queueing models, service is considered to be complete without any interruption. But in reality, queueing systems are subject to interruptions due to failure of server or any other cause. In the present article, we present an overview and literature survey on the performance modeling and analysis of single server, general service queueing system with service interruption using supplementary variable technique. The factors causing service interruption such as unreliable server and server vacation are elaborated. The brief of supplementary variable technique to establish the queue size distribution is explained for single server non-Markovian queueing models by incorporating the features of service interruption. The basic concepts and review of literature on the queues with server breakdown and/or vacationing server are described. The research works done during last 10 years (2010–2019) on queues with service interruption involving many other key concepts namely Bernoulli vacation, multiple vacation, bulk arrival, discouragement, etc. and queueing scenarios of service interruption are reported. Some specific applications are also highlighted.
16 citations
References
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TL;DR: This paper deals with the steady-state behavior of an M^X/G/1 retrial queue with an additional second phase of optional service and service interruption where breakdowns occur randomly at any instant while the server is serving the customers.
Abstract: This paper deals with the steady-state behavior of an M^X/G/1 retrial queue with an additional second phase of optional service and service interruption where breakdowns occur randomly at any instant while the server is serving the customers. Further, the concept of delay time is also introduced in the model. This model generalizes both the classical M^X/G/1 retrial queue with service interruption as well as the M^X/G/1 queue with second optional service and service interruption. We carry out an extensive analysis of this model.
40 citations
01 Jan 2009
TL;DR: An M / G / 1 retrial queue with a first-come-first-served (FCFS) orbit, general retrial time, two-phase service and server breakdown is investigated and the authors obtain the steady-state solutions for both queueing and reliability measures of interest.
Abstract: Received: 24 November 2005 / Revised: 1 April 2008c 2009 Springer Science + Business Media, LLCAbstract An M/G/1 retrial queue with a first-come-first-served (FCFS) orbit, general retrial time,two-phase service and server breakdown is investigated in this paper. Customers are allowed to balkand renege at particular times. Assume that the customers who find the server busy are queued inthe orbit in accordance with an FCFS discipline. All customers demand the first “essential” service,whereas only some of them demand the second “optional” service, and the second service is multi-optional. During the service, the server is subject to breakdown and repair. Assume that the retrialtime, the service time, and the repair time of the server are all arbitrarily distributed. By using thesupplementary variables method, the authors obtain the steady-state solutions for both queueing andreliability measures of interest.Key words Balking, breakdowns, retrial queue, two-phase service.
21 citations
TL;DR: In this article, an M/G/1 retrial queue with a first-come-first-served (FCFS) orbit, general retrial time, two-phase service and server breakdown is investigated.
Abstract: An M / G / 1 retrial queue with a first-come-first-served (FCFS) orbit, general retrial time, two-phase service and server breakdown is investigated in this paper. Customers are allowed to balk and renege at particular times. Assume that the customers who find the server busy are queued in the orbit in accordance with an FCFS discipline. All customers demand the first “essential” service, whereas only some of them demand the second “optional” service, and the second service is multioptional. During the service, the server is subject to breakdown and repair. Assume that the retrial time, the service time, and the repair time of the server are all arbitrarily distributed. By using the supplementary variables method, the authors obtain the steady-state solutions for both queueing and reliability measures of interest.
21 citations
TL;DR: The mathematical model is constructed and the probability generating functions of number of customers in the system when it is idle, busy, on vacation and under repair are derived.
Abstract: This paper investigates the steady state behaviour of an M[x]/G/1 retrial queue with two phases of service under Bernoulli vacation schedule and breakdown. Any arriving batch finding the server busy, breakdown or on vacation enters an orbit. Otherwise one customer from the arriving batch enters the service immediately while the rest join the orbit. After completion of each two phases of service, the server either goes for a vacation with probability p or may wait for serving the next customer with probability (1-p). While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. We construct the mathematical model and derive the probability generating functions of number of customers in the system when it is idle, busy, on vacation and under repair. Some system performances are obtained.
17 citations
09 Jul 2010
TL;DR: The embedded Markov chain underlying the considered queueing system and its stable condition is studied and some analytical results for the system size distribution as well as some other performance measures of the system are derived.
Abstract: A retrial queue with general retrial times, a modified vacation policy and server breakdowns is investigated in this paper. We study the embedded Markov chain underlying the considered queueing system and its stable condition. By applying the supplementary variable technique, some analytical results for the system size distribution as well as some other performance measures of the system are derived. The effects of various parameters on the system performance are analyzed numerically.
9 citations