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Retrial queue

About: Retrial queue is a research topic. Over the lifetime, 784 publications have been published within this topic receiving 12354 citations.


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TL;DR: This paper considers a service station consisting of s identical, independent exponential servers and m buffers, and an efficient algorithm is developed to evaluate system steady-state probabilities, and formulas for certain system performance measures are derived in terms of the steady- state probabilities
Abstract: This paper considers a service station consisting of s identical, independent exponential servers and m buffers. Customers arrive according to a Coxian process with a stages. Blocked customers may either leave the system forever or return, after an exponentially distributed amount of time, to the service station to retry for services. An efficient algorithm is developed to evaluate system steady-state probabilities, and formulas for certain system performance measures are derived in terms of the steady-state probabilities. The computational complexity of the algorithm is shown to be O(4N), where N is the total number of state probabilities evaluated. The influence of the form of interarrival time distributions on system performance measures is examined through numerical results. Issues concerning numerical stability of the algorithm are also discussed. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

4 citations

Journal ArticleDOI
TL;DR: The existence of a unique symmetric Nash equilibrium policy is established and it is shown that its structure is characterized by a set of threshold-type strategies; the relevance of this concept in the context of a dynamic learning scenario is discussed.
Abstract: Customers arrive sequentially to a service system where the arrival times form a Poisson process of rate l. The system offers a choice between a private channel and a public set of channels. The transmission rate at each of the public channels is faster than that of the private one; however, if all of the public channels are occupied, then a customer who commits itself to using one of them attempts to connect after exponential periods of time with mean m−1. Once connection to a public channel has been made, service is completed after an exponential period of time, with mean n−1. Each customer chooses one of the two service options, basing its decision on the number of busy channels and reapplying customers, with the aim of minimizing its own expected sojourn time. The best action for an individual customer depends on the actions taken by subsequent arriving customers. We establish the existence of a unique symmetric Nash equilibrium policy and show that its structure is characterized by a set of threshold-type strategies; we discuss the relevance of this concept in the context of a dynamic learning scenario.

4 citations

Journal ArticleDOI
TL;DR: A comparative analysis between the approximate results and the established exact results for waiting time distribution have been presented and the sensitivity analysis is carried out to demonstrate the tractability of the analytical results.
Abstract: SYNOPTIC ABSTRACTThis work studies the steady state behavior of an Mx/G/1 retrial queue with k-phases of heterogeneous service under different vacation policies. If the server is busy or on vacation, an arriving batch of calls either becomes impatient and balks (leaves) the system with some probability or enters in the virtual pool of blocked calls called “orbit.” The server provides service in k-phases to all the calls. After completing the kth phase of essential service of a call, the server has an option to go for lth (l = 1,2,…,M) type of vacation with probability ηl (l = 1,2,…,M) or to continue to serve the next call (if any) with probability η0where . The explicit expressions for the expected number of calls and expected waiting time of the calls in the retrial group are obtained using supplementary variable and generating function techniques. The maximum entropy principle is also employed to derive various system performance characteristics. A comparative analysis between the approximate results an...

4 citations

Journal ArticleDOI
TL;DR: This paper presents an integrated computer simulation model for optimisation of total cost in an M/G/C retrial queue system with geometric loss, feedback and linear retrial policy, and a case study provided in which incoming calls of a clinic are modelled and analysed.
Abstract: This paper presents an integrated computer simulation model for optimisation of total cost in an M/G/C retrial queue system with geometric loss, feedback and linear retrial policy. First, the computer simulation model is used to verify and validate an M/G/C retrial queue system. Second, certain important performance measures are obtained under steady–state condition. Finally, the simulation model is used to identify the preferred alternatives to optimise the current system. Significantly, it should be noted that there is no mathematical model to analyse an M/G/C retrial queue system. In this study, an integrated approach is used to develop the simulation model of the M/G/C retrial queue system. The objective of simulation model is to minimise the total cost and find the optimum solution. Also, a case study provided in which incoming calls of a clinic are modelled and analysed, because the most obvious retrial queue application lies in phone calls. This is the first study that utilises an integrated simulation approach for optimisation of total cost in an M/G/C queuing system with geometric loss and linear retrial policy.

4 citations

Journal ArticleDOI
TL;DR: In this article, an M 1,M 2 /G 1,G 2 /1 priority retrial queue with pre-emptive resume policy is considered and the problem of ergodicity and partial generating functions of the steady state system state distribution is discussed.
Abstract: Priority mechanism is an invaluable scheduling method that allows customers to receive different quality of service. Service priority is clearly today a main feature of the operation of any manufacturing system. We are interested by an M 1 ,M 2 /G 1 ,G 2 /1 priority retrial queue with pre-emptive resume policy. For model in question, we discuss the problem of ergodicity and, by using the method of supplementary variables, find the partial generating functions of the steady state system state distribution. Moreover, some pertinent performance measures are obtained and numerical study is also performed.

4 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202326
202259
202135
202056
201947
201844