A study on M/G/1 retrial G - queue with two phases of service, immediate feedback and working vacations
01 Nov 2017-Vol. 263, Iss: 4, pp 042156
About: This article is published in Microelectronics Systems Education.The article was published on 2017-11-01 and is currently open access. It has received 5 citations till now. The article focuses on the topics: Service (business) & Queue.
Citations
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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
TL;DR: This paper deals with analyze of a single server queueing system with immediate feedbacks and working vacation, using supplementary variable technique the steady state results are deduced.
Abstract: This paper deals with analyze of a single server queueing system with immediate feedbacks and working vacation. Upon arrival if the customer sees the server to be busy then it joins the tail end of queue. Otherwise if server is idle, the customer gets into service. After completion of service, the customer is allowed to make an immediate feedback in finite number. Busy server may fail for a short interval of time. Using supplementary variable technique the steady state results are deduced. Some system performance measures are discussed
6 citations
TL;DR: This paper deals with customers’ impatience behaviour for single server Markovian queueing system under K-variant working vacation policy, waiting server, Bernoulli feedback, balking, reneging, and retention of reneged customers and proves the stochastic decomposition properties.
Abstract: This paper deals with customers’ impatience behaviour for single server Markovian queueing system under K-variant working vacation policy, waiting server, Bernoulli feedback, balking, reneging, and retention of reneged customers. Using the probability generating function (PGF) technique, we obtain the steady-state solution of the system. Besides, we prove the stochastic decomposition properties. Useful performance measures of the considered queueing system are derived. A cost model is developed. Then, the parameter optimisation is carried out numerically, using a quadratic fit search method (QFSM). Finally, numerical examples are provided to visualise the analytical results.
3 citations
TL;DR: In this article , a regular busy server crashes due to negative customer traffic, and holiday interruption is being considered, a working vacation (WV) server at a low service rate works, if there are clients on the computer at the end of each holiday, the server the probability that a new visitor is inactive and on vacation is p (single WV) or with probability q (multiple WVs).
Abstract: A Regular busy server crashes due to negative customer traffic, and holiday interruption is being considered. If the orbit empties at the end of a positive customer service, the server worked Going on vacation. A working vacation (WV) server at a low service rate works. If there are clients on the computer at the end of each holiday, the server the probability that a new visitor is inactive and on vacation is p (single WV) or with probability q (multiple WVs). Substantial variable technique, constant state probability for the system and its orbit we found the generating function. System performance measures, reliability measures and random decay law are discussed. Finally, Some numerical examples and cost optimization analysis provided. Alternative: Single-Server Review G- Sequence, Incredible Review G-Series, Volume Visit Review G-Series. Evaluation Preference: Working vacation, Bernoulli feedback, Random vacations, single vacation. Unreliable retrial G-queue, Batch arrival Retrial G-queue, single server iteration is taken as a G-sequence alternative and working vacations, random vacations, single vacation, and Bernoulli vacation is taken evaluation parameters. In this from analysis Fuzzy ARAS method the best solution determines the solution with the shortest distance and the longest distance from the negative-best solution, but comparison of these distances is not considered significant. As a result it seems unreliable retrial G-queue got the first rank where as is the Batch arrival Retrial G-queue is having the lowest rank.
3 citations
TL;DR: In this paper , the concept of a single server retrial queueing system with delayed repair and feedback under a working vacation policy, along with the asymmetric transition representation, is discussed.
Abstract: The concept of a single server retrial queueing system with delayed repair and feedback under a working vacation policy, along with the asymmetric transition representation, is discussed in this article. In addition, consumers are entitled to balk and renege in some situations. The steady-state probability generating function for system size and orbit size is derived by using the approach of supplementary variables. Discussions include key metrics of the system and a few significant special conditions. Moreover, the impact of system parameters is examined through the analysis of some numerical examples.
2 citations
References
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TL;DR: The general decomposition law for this retrial queueing system is established and the effects of various parameters on the system performance are analyzed numerically.
Abstract: This paper deals with a single server retrial queueing system with working vacation in which the server works with different service rates rather than completely terminating the service during its vacation period. We assume that both service times in a regular service period and in a working vacation period are generally distributed. The steady state distributions of the server state and the number of jobs in the orbit were obtained along with other performance measures. The general decomposition law for this retrial queueing system is established. The effects of various parameters on the system performance are also analyzed numerically.
32 citations
TL;DR: In this article, an M/G/1 queue with single working vacation is analyzed using the method of supplementary variable and the matrix-analytic method, obtaining the queue length distribution and service status at the arbitrary epoch under steady state conditions.
Abstract: In this paper, an M/G/1 queue with single working vacation is analyzed. Using the method of supplementary variable and the matrix-analytic method, we obtain the queue length distribution and service status at the arbitrary epoch under steady state conditions. Further, we derive expected busy period and expected busy cycle. Finally, server special cases are presented.
31 citations
TL;DR: In this paper, an M/G/1 retrial G-queue with preemptive resume priority and collisions under linear retrial policy subject to the server breakdowns and delayed repairs is considered.
Abstract: We consider an M/G/1 retrial G-queue with preemptive resume priority and collisions under linear retrial policy subject to the server breakdowns and delayed repairs. A breakdown at the busy server is represented by the arrival of a negative customer which causes the customer being in service to be lost. The stability condition of the system is derived. Using generating function technique, the steady-state distributions of the server state and the number of customers in the orbit are obtained along with some interesting and important performance measures. The stochastic decomposition property is investigated. Further, some special cases of interest are discussed. Finally, numerical illustrations are provided.
27 citations
TL;DR: This paper considers a batch arrival retrial queue with feedback under Bernoulli vacation schedule, where the busy server is subjected to breakdown due to the arrival of negative customers.
Abstract: In this paper, we consider a batch arrival retrial queue with feedback under Bernoulli vacation schedule, where the busy server is subjected to breakdown due to the arrival of negative customers. Any arriving batch of positive customers finds the server free, one of the customers from the batch enters into the service area and the rest of them join into the orbit. Arriving positive customers may balk (or renege) the system at particular times. After completion of service the unsatisfied positive customer may rejoin into the orbit to get another regular service as feedback customer. The server takes Bernoulli vacation after service completion of positive customers. After completion of service (if the server is not taking vacation), repair or vacation the server searches for the customers in the orbit or remains idle. The steady state probability generating function for the system size is obtained by using the supplementary variable method. Some system performance measures, reliability measures and stochastic decomposition law are discussed. Finally, some numerical examples and cost optimization analysis are presented.
18 citations
TL;DR: An M/G/1 G-queue with server breakdowns, working vacations and vacation interruption is analyzed using the method of supplementary variable and the matrix-analytic method and the queue length distribution and the probability of service status at the arbitrary epoch under steady state conditions are obtained.
Abstract: In this paper, an M/G/1 G-queue with server breakdowns, working vacations and vacation interruption is analyzed. A breakdown at busy server is represented by the arrival of a negative customer which causes the customer being in service to be lost. After repair the server is as good as new. Using the method of supplementary variable and the matrix-analytic method,the queue length distribution and the probability of service status at the arbitrary epoch under steady state conditions are obtained. Further, a special cases are presented. Finally, numerical illustrations are provided.
17 citations