Single server retrial queues with two way communication
Jesús R. Artalejo,Tuan Phung-Duc +1 more
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The main aim of this paper is to study the steady state behavior of an M/G/1-type retrial queue in which there are two flows of arrivals namely ingoing calls made by regular customers and outgoing calls making by the server when it is idle.About:
This article is published in Applied Mathematical Modelling.The article was published on 2013-02-15 and is currently open access. It has received 74 citations till now. The article focuses on the topics: Retrial queue & Markovian arrival process.read more
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A survey of retrial queueing systems
Jeongsim Kim,Bara Kim +1 more
TL;DR: The main focus of this survey is to show analytic results for queue length distributions, waiting time distribution, and tail asymptotics for the queue length and waiting time distributions.
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Two-way communication retrial queues with multiple types of outgoing calls
Hiroyuki Sakurai,Tuan Phung-Duc +1 more
TL;DR: In this paper, the authors considered a single server Markovian retrial queue with multiple types of outgoing calls and obtained explicit expressions for the joint stationary distribution of the number of calls in the orbit and the state of the server via the generating function approach.
Journal ArticleDOI
Stability analysis of a multiclass retrial system with classical retrial policy
Evsey Morozov,Tuan Phung-Duc +1 more
TL;DR: The regenerative structure of the (non-Markovian) queue-size process (total number of customers in the primary system and in orbits) is exploited to develop the stability analysis and it is shown that these conditions are sufficient for stability as well.
Posted Content
Retrial Queueing Models: A Survey on Theory and Applications.
TL;DR: This paper investigates the state of the art of the theoretical researches including exact solutions, stability, asymptotic analyses and multidimensional models on retrial models arising from real world applications.
Journal ArticleDOI
Scaling limits for single server retrial queues with two-way communication
Hiroyuki Sakurai,Tuan Phung-Duc +1 more
TL;DR: A decomposition property is obtained where it is proved that the queue length is decomposed into the sum of three independent random variables with clear physical meaning.
References
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Poisson Arrivals See Time Averages
TL;DR: This paper presents a proof of this result under one basic assumption: the process being observed cannot anticipate the future jumps of the Poisson process.
Journal ArticleDOI
Singularity analysis of generating functions
Philippe Flajolet,Andrew Odlyzko +1 more
TL;DR: This work presents a class of methods by which one can translate, on a term-by-term basis, an asymptotic expansion of a function around a dominant singularity into a corresponding asymPTotic expansion for the Taylor coefficients of the function.
Book
Retrial Queueing Systems: A Computational Approach
TL;DR: This book is intended for an audience ranging from advanced undergraduates to researchers interested in queueing theory, but also in applied probability, stochastic models of the operations research, and engineering.