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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: In this article, the authors deal with the maximum entropy principle (MEP) to explore the steady state behavior of the bulk arrival retrial queuing system and derive various system performance measures.
Abstract: This paper deals with the maximum entropy principle (MEP) to explore the steady state behaviour of the bulk arrival retrial queuing system. The concepts of Bernoulli vacation schedule and second optional service are taken into consideration. After the completion of first essential service (second optional service), the server has an option to go for vacation with probability p(q) or may continue to serve the next customer, if any with complementary probability. During vacation, the server is allowed to do some secondary work and is called on working vacation. By introducing supplementary variables and using generating function technique, we obtain the expected number of the customers and expected waiting time of the customers in the retrial group. By employing the maximum entropy approach, we derive various system performance measures. By taking the numerical illustrations we perform a comparative study between the exact waiting time and the approximate waiting time based on MEP analysis. The sensitivity analysis is also carried out to validate the analytical results.
2 citations
2 citations
TL;DR: In this paper, the authors considered an M/G/1 retrial queue with finite capacity of the retrial group and derived the Laplace transform of the busy period using the catastrophe method.
Abstract: We consider an M/G/1 retrial queue with finite capacity of the retrial group. We derive the Laplace transform of the busy period using the catastrophe method. This is the key point for the numerical inversion of the density function and the computation of moments. Our results can be used to approach the corresponding descriptors of the M/G/1 queue with infinite retrial group, for which direct analysis seems intractable.
2 citations
TL;DR: By using the characteristic method for partial differential equations, the steady-state distributions of the server state and the number of customers in the orbit are obtained along with various performance measures and the reliability of the system is analyzed detailed.
Abstract: We consider an \begin{document}$ M^X/G/1 $\end{document} retrial queue with impatient customers subject to disastrous failures at which times all customers in the system are lost. When the server finishes serving a customer and finds the orbit empty, the server becomes dormant until \begin{document}$ N $\end{document} or more customers accumulate. If a coming batch of customers finds the server idle, one of the arriving customers begins his service immediately and the rest join the orbit to repeat their request later. Otherwise, if the server is dormant or busy or down, all customers of the coming batch enter the orbit. When the server is under repair, customers in the orbit can become impatient after waiting a random amount of time and leave the system. By using the characteristic method for partial differential equations, the steady-state distributions of the server state and the number of customers in the orbit are obtained along with various performance measures. In addition, the reliability of the system is analyzed detailed. Finally, an application to telecommunication networks is provided and the effects of various parameters on the system performance are demonstrated numerically.
2 citations
TL;DR: In this paper, the time invariant joint distribution of number of customers in the orbit as well as stock level in a stochastic queuing environment is presented by applying Neuts Matrix Geometric Method.
Abstract: This paper mainly deals with the customers whose arrivals depend upon the existing stock level and base stock ordering policy in a stochastic queuing environment. The time between any successive primary as well as retrial arrivals and lead time are following independent exponential distributions. By applying Neuts Matrix Geometric Method, we present the time invariant joint distribution of number of customers in the orbit as well as stock level. Adequate numerical results are explored according to different characteristics of the system performance measures. Further we discuss the advantages between stock depending and non-depending arrivals about the expected total cost and parameter analysis. Also we explore the model with a different class of stock dependent arrivals under the various cost structure and replenishment time. Managerial insights of this model helps to make the decision for an appropriate base stock ordering policy under certain random conditions with a stock dependent demand rate and a limited holding capacity for ordered items.
2 citations