Approximations of retrial queue with limited number of retrials

Shin, Yang Woo; Moon, Dug Hee

doi:10.1016/j.cor.2009.03.025

Cited by 10 publications

(6 citation statements)

References 13 publications

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“…, m depends on the number of sources of repeated calls is the system. The similar process with λ j1,...,j k ,...,jm = λ = const was analyzed in [7,8,13] using numerical methods.…”

Section: Steady State Analysis Of Systems With Limited Number Of Retrmentioning

confidence: 99%

On Multiserver State-Dependent Retrial Queues Operating in Stationary Regime

Lebedev

Ponomarov

Pryshchepa

2021

Information Technologies and Mathematical Modelling. Queueing Theory and Applications

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In this paper, we consider Markov models for two types of multiserver retrial queues with an input flow rate that depends on a number of calls in an orbit: classical state-dependent models and statedependent queues with limited number of retrials. For both systems, the conditions for the existence of the stationary regime are defined and formulas for steady-state probabilities are presented. The investigative technique is based on approximation of the input system by the system with truncated state space.

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“…, m depends on the number of sources of repeated calls is the system. The similar process with λ j1,...,j k ,...,jm = λ = const was analyzed in [7,8,13] using numerical methods.…”

Section: Steady State Analysis Of Systems With Limited Number Of Retrmentioning

confidence: 99%

On Multiserver State-Dependent Retrial Queues Operating in Stationary Regime

Lebedev

Ponomarov

Pryshchepa

2021

Information Technologies and Mathematical Modelling. Queueing Theory and Applications

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“…The method has been also introduced as a method of reducing dimension [66], an approximation with the help of a loss model [19,Section 2.8.1] and Fredericks and Reisner approximation [5,Section 3.4.4]. However, the method has not been attracted a lot of attention until Shin and Moon [52] used it for an approximation of M/M/c retrial queue with phase type distribution of retrial time. Here, we denote the Fredericks and Reisner's approach by dimension reduction method.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Shin and Moon present approximation results of the performance characteristics indicated in [17] for the complex systems by using the dimension reduction method in a series of papers [52,53,56,58,59,60]. The objective this paper is to exposit the dimension reduction method and show the usefulness of the method by presenting the recent results of the authors.…”

Section: Introductionmentioning

confidence: 99%

Dimension Reduction for Approximation of Advanced Retrial Queues : Tutorial and Review

Shin¹

2017

Journal of applied mathematics & informatics

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Retrial queues have been widely used to model the many practical situations arising from telephone systems, telecommunication networks and call centers. An approximation method for a simple Markovian retrial queue by reducing the two dimensional problem to one dimensional problem was presented by Fredericks and Reisner in 1979. The method seems to be a promising approach to approximate the retrial queues with complex structure, but the method has not been attracted a lot of attention for about thirty years. In this paper, we exposit the method in detail and show the usefulness of the method by presenting the recent results for approximating the retrial queues with complex structure such as multiserver retrial queues with phase type distribution of retrial time, impatient customers with general persistent function and/or multiclass customers, etc.

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“…Motivated by CSMA/CD-like systems, this paper focuses on a retrial queue with limited heterogeneous retrials like in [6,5], but we assume arrivals come from a finite population. In contrast to previous work which investigates decomposition methods, we here consider the light-traffic approximation.…”

Section: Introductionmentioning

confidence: 99%

“…Shin and Moon [6,5] consider a similar multiserver retrial queue with Poisson arrivals. Customers that are blocked for the first time either abandon the system or join the first orbit.…”

Section: Introductionmentioning

confidence: 99%

Light-traffic analysis of queues with limited heterogenous retrials

Fiems

Phung-Duc

2016

Proceedings of the 11th International Conference on Queueing Theory and Network Applications

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We consider a Markovian single-server retrial queueing system. Customers in orbit retry after an exponentially distributed amount of time, the retrial rate depending on the number of times the customer has retried before. Moreover, the number of retrials by a single customer is bounded by K, customers abandoning after the kth retrial with probability p k . As this queueing system is not amenable for exact analysis, we focus on its performance in light traffic. In particular, we describe a fast algorithm for calculating the terms in the Maclaurin series expansion of various performance measures, the arrival rate being the independent parameter of the expansion. We illustrate our approach by various numerical examples and verify the accuracy of the light traffic approximation by means of simulation.

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Approximations of retrial queue with limited number of retrials

Cited by 10 publications

References 13 publications

On Multiserver State-Dependent Retrial Queues Operating in Stationary Regime

On Multiserver State-Dependent Retrial Queues Operating in Stationary Regime

Dimension Reduction for Approximation of Advanced Retrial Queues : Tutorial and Review

Light-traffic analysis of queues with limited heterogenous retrials

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