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Journal ArticleDOI

A Single Server Queue with Immediate Feedback, Working Vacation and Server Breakdown

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

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Citations
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Journal ArticleDOI
01 Mar 2019-Opsearch
TL;DR: In this investigation, a single server M/M/1/N feedback queueing system with vacation, balking, reneging and retention of reneged customers is analyzed and the steady state probabilities of the number of customers in the system are derived.
Abstract: In this investigation, a single server M/M/1/N feedback queueing system with vacation, balking, reneging and retention of reneged customers is analyzed. By considering the mathematical modeling, we derive the steady state probabilities of the number of customers in the system. We obtain important measures of effectiveness of the model by using the stationary distribution, and develop a cost model of the queueing system. Further, a numerical study and a cost profit analysis are carried out.

23 citations

Journal ArticleDOI
TL;DR: The cost optimisation analysis of a discrete-time finite-capacity multiserver queueing system with Bernoulli feedback, synchronous multiple and single working vacations, balking, and reneging during both busy and working vacation periods is concerned.
Abstract: This paper concerns the cost optimisation analysis of a discrete-time finite-capacity multiserver queueing system with Bernoulli feedback, synchronous multiple and single working vacations, balking, and reneging during both busy and working vacation periods. A reneged customer can be retained in the system by employing certain persuasive mechanism for completion of service. Using recursive method, the explicit expressions for the stationary state probabilities are obtained. Various system performance measures are presented. Further, a cost model is formulated. Then, the optimization of the model is carried out using quadratic fit search method (QFSM). Finally, the impact of various system parameters on the performance measures of the queueing system is shown numerically.

4 citations


Cites background from "A Single Server Queue with Immediat..."

  • ...Since then, queueing models with feedback have attracted a significant attention of many researchers, see for instance [22, 11, 24] and references therein....

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Journal ArticleDOI
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


Cites background from "A Single Server Queue with Immediat..."

  • ...[33], Bouchentouf and Messabihi [7], Bouchentouf et al....

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Journal ArticleDOI

Cites background from "A Single Server Queue with Immediat..."

  • ...For conceivable uses, the history and contributions of researchers on queueing systems with balking and feedback, one may see articles by Santhakumaran & Thangaraj (2000), Choudhury & Paul (2005), Kumar et al. (2013), Varalakshmi et al. (2018), Bouchentouf et al. (2019)....

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Journal ArticleDOI
TL;DR: In this paper , the authors considered a preemptive priority queueing system with vacation, where the single server may break down with imperfect coverage and derived the stationary probability distribution by using the probability generating function approach.
Abstract: This work considers a preemptive priority queueing system with vacation, where the single server may break down with imperfect coverage. Various combinations of server vacation priority queueing models have been studied by many scholars. A common assumption in these models is that the server will only resume its normal service rate after the vacation is over. However, such speculation is more limited in real-world situations. Hence, in this study, the vacation will be interrupted if a customer waits for service in the system at the moment of completion of service during vacation. The stationary probability distribution is derived by using the probability generating function approach. We also develop varieties of performance measures and provide a simple numerical example to illustrate these measures. Optimization analysis is finally carried out, including cost optimization and tri-object optimization.
References
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Journal ArticleDOI
TL;DR: The classical single server vacation model is generalized to consider a server which works at a different rate rather than completely stops during the vacation period, which approximates a multi-queue system whose service rate is one of the two speeds for which the fast speed mode cyclically moves from queue to queue with an exhaustive schedule.

388 citations


"A Single Server Queue with Immediat..." refers methods in this paper

  • ...M/M/1 working vacation queue has been introduced by Servi and Finn [6]....

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  • ...[6] Servi LD & Finn SG (2002), M/M/1 queues with working vacations (M/M/1/WV)....

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Journal ArticleDOI
TL;DR: In this paper, the distribution of the queue size as well as the Laplace-Stieltjes transform and the first two moments of the distribution function of the total time spent in the system by a customer are determined for a stationary process.
Abstract: Let us suppose that customers arrive at a counter in accordance with a Poisson process of density λ. The customers are served by a single server in order of arrival. The service times are identically distributed, mutually independent, positive random variables with distribution function H(x). Suppose that after being served each customer either immediately joins the queue again with probability p or departs permanently with probability q (p + q =1). In this paper we shell determine for a stationary process the distribution of the queue size as well as the Laplace-Stieltjes transform and the first two moments of the distribution function of the total time spent in the system by a customer.

247 citations


"A Single Server Queue with Immediat..." refers background in this paper

  • ...For further details on queues with feedback and server down refer Takacs [7], Krishnakumar et al....

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  • ...[7] Takacs L (1963), A Single Server Queue with Feedback....

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  • ...For further details on queues with feedback and server down refer Takacs [7], Krishnakumar et al. [3], Choudhury and Paul [1], Rajadurai et al. [[4], [5]], Varalakshmi et al. [[9], [10]]....

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Journal ArticleDOI
TL;DR: It is shown that the general stochastic decomposition law for M/G/1 vacation models holds for the present system also and some special cases are also studied.
Abstract: This paper is concerned with the analysis of a single-server queue with Bernoulli vacation schedules and general retrial times. We assume that the customers who find the server busy are queued in the orbit in accordance with an FCFS (first-come-first-served) discipline and only the customer at the head of the queue is allowed access to the server. We first present the necessary and sufficient condition for the system to be stable and derive analytical results for the queue length distribution, as well as some performance measures of the system under steady-state condition. We show that the general stochastic decomposition law for M/G/1 vacation models holds for the present system also. Some special cases are also studied.

91 citations


"A Single Server Queue with Immediat..." refers background in this paper

  • ...[3], Choudhury and Paul [1], Rajadurai et al....

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Journal Article
TL;DR: The queue size distribution at random epoch and at a service completion epoch is derived and the distribution of response time and busy period is derived.
Abstract: This paper deals with an M/G/1 queue with two phases of heterogeneous services and Bernoulli feedback system, where the server provides first phase of regular service to all the customers. As soon as the first phase of service of a customer is completed, it may leave the system or may immediately go for second phase of optional service in one additional service channel. However, after receiving the first phase or second phase of unsuccessful service by an unit, then it may immediately join the tail of the original queue as feedback customer to have another regular service. In this paper, first we derive the queue size distribution at random epoch and at a service completion epoch. Secondly, we derive the distribution of response time and busy period. Finally, we present some numerical results for mean response time.

43 citations


"A Single Server Queue with Immediat..." refers background in this paper

  • ...[3], Choudhury and Paul [1], Rajadurai et al....

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  • ...References [1] Choudhury G & Paul, M (2005), A two phase queueing system with Bernoulli feedback....

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  • ...For further details on queues with feedback and server down refer Takacs [7], Krishnakumar et al. [3], Choudhury and Paul [1], Rajadurai et al. [[4], [5]], Varalakshmi et al. [[9], [10]]....

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Journal ArticleDOI
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


"A Single Server Queue with Immediat..." refers result in this paper

  • ...[11] Zhang M & Hou Z (2012), M/G/1 queue with single working vaca- tion....

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  • ...The result coincides with Zhang and Hou [11]....

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