Topic
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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15 May 2013TL;DR: A multi-server retrial queueing system with the Batch Markovian Arrival Process and phase type service time distribution and description of several independent Markov processes in parallel that allows to compute the stationary distribution of the system for large number of servers is considered.
Abstract: We consider a multi-server retrial queueing system with the Batch Markovian Arrival Process and phase type service time distribution. Such a quite general queueing system suits for modeling, e.g., modern wireless communication networks. We assume that arriving customers, which do not succeed to start the service immediately upon arrival due to the lack of available servers, may leave the system forever (balk) or join the orbit for further retrials. Customers in the orbit are impatient (they may leave the system forever after exponentially distributed duration of the stay in the orbit) and non-persistent (they may leave the system forever after any unsuccessful attempt to reach the service). Approach by V. Ramaswami and D. Lucantoni for description of several independent Markov processes in parallel that allows to compute the stationary distribution of the system for large number of servers is used along with the results for multi-dimensional asymptotically quasi-Toeplitz Markov chains for computation of steady state distribution of the system states and some its performance measures.
9 citations
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TL;DR: An approximation is provided for GI/G/c retrial queue with general retrial time by approximating the general distribution with phase type distribution and some numerical results are presented.
Abstract: We consider the PH/PH/c retrial queues with PH-retrial time. Approximation formulae for the distribution of the number of customers in service facility, sojourn time distribution and the mean number of customers in orbit are presented. We provide an approximation for GI/G/c retrial queue with general retrial time by approximating the general distribution with phase type distribution. Some numerical results are presented.
9 citations
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TL;DR: It is shown that the number of customers in orbit and in the system as a whole are monotonically changed if the retrial rates in one system are bounded by the rates in second one.
Abstract: We consider several multi-server retrial queueing models with exponential retrial times that arise in the literature of retrial queues. The effect of retrial rates on the behavior of the queue length process is investigated via sample path approach. We show that the number of customers in orbit and in the system as a whole are monotonically changed if the retrial rates in one system are bounded by the rates in second one. The monotonicity results are applied to show the convergence of generalized truncated systems that have been widely used for approximating the stationary queue length distribution in retrial queues.
9 citations
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21 Jun 2017TL;DR: Queueing system with limited processor sharing, which operates in the Markovian random environment, is considered and numerical example illustrates possibility of optimal adjustment of the server capacity to the state of the random environment.
Abstract: Queueing system with limited processor sharing, which operates in the Markovian random environment, is considered. Parameters of the system (pattern of the arrival rate, capacity of the server, i.e., the number of customers than can share the server simultaneously, the service intensity, the impatience rate, etc.) depend on the state of the random environment. Customers arriving when the server capacity is exhausted join orbit and retry for service later. The stationary distribution of the system states (including the number of customers in orbit and in service) is computed and expressions for the key performance measures of the system are derived. Numerical example illustrates possibility of optimal adjustment of the server capacity to the state of the random environment.
9 citations
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25 Sep 2017TL;DR: A simulation program is built to investigate finite-source retrial queuing system with collision of the customers where the server is subject to random breakdowns and repairs depending on whether it is idle or busy.
Abstract: The aim of the present paper is to build a simulation program to investigate finite-source retrial queuing system with collision of the customers where the server is subject to random breakdowns and repairs depending on whether it is idle or busy. All the random variables involved in the model construction are assumed to be independent and generally distributed. The novelty of the investigation is to carry sensitivity analysis of the performance measures using various distributions. Several figures show the effect of different distributions on the performance measures such as mean and variance of number of customers in the system, mean and variance of response time, mean and variance of time a customer spent in service, mean and variance of sojourn time in the orbit.
9 citations