Journal ArticleDOI
On the busy period of the M/G/1 retrial queue
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In this article, the M/G/1 retrial queue with repeated attempts is considered, where a customer who finds the server busy, leaves the service area and joins a pool of unsatisfied customers.Abstract:
The M/G/1 queue with repeated attempts is considered. A customer who finds the server busy, leaves the service area and joins a pool of unsatisfied customers. Each customer in the pool repeats his demand after a random amount of time until he finds the server free. We focus on the busy period L of the M/G/1$ retrial queue. The structure of the busy period and its analysis in terms of Laplace transforms have been discussed by several authors. However, this solution has serious limitations in practice. For instance, we cannot compute the first moments of L by direct differentiation. This paper complements the existing work and provides a direct method of calculation for the second moment of L.read more
Citations
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Journal ArticleDOI
Standard and retrial queueing systems: a comparative analysis
Jesús R. Artalejo,G. I. Falin +1 more
TL;DR: The theory of retrial queues as discussed by the authors is a branch of the queueing theory, characterized by the following basic assumption: a customer who cannot get service (due to finite capacity of the system, balking, impatience, etc.) leaves the service area, but after some random delay returns to the system again.
Journal ArticleDOI
An M[X]/G/1 retrial queue with server breakdowns and constant rate of repeated attempts
TL;DR: A recursive scheme to compute the distribution of the number of served customers during the k-busy period and the ordinary busy period of the M[X]/G/1 retrial queue and the effects of several parameters on the system are analysed numerically.
Journal ArticleDOI
An M|G|1 Retrial Queue with Nonpersistent Customers and Orbital Search
TL;DR: In this article, the M|G|1 retrial queue with nonpersistent customers and orbital search is considered, and the structure of the busy period and its analysis in terms of Laplace transform is discussed.
Journal ArticleDOI
On multiserver feedback retrial queue with finite buffer
TL;DR: This paper deals with a multiserver feedback retrial queueing system with finite waiting position and constant retrial rate, analyzed as a quasi-birth-and-death process, and the necessary and sufficient condition for stability of the system is investigated.
Journal ArticleDOI
Analysis of the busy period for the M/M/c queue: an algorithmic approach
TL;DR: In this paper, the Laplace-Stieltjes transform of the busy period of a multi-server M/M/c queueing system is used to compute the moments of the length of a busy period and the number of customers served during it.
References
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Book
Numerical Recipes in C: The Art of Scientific Computing
TL;DR: Numerical Recipes: The Art of Scientific Computing as discussed by the authors is a complete text and reference book on scientific computing with over 100 new routines (now well over 300 in all), plus upgraded versions of many of the original routines, with many new topics presented at the same accessible level.
Journal ArticleDOI
A survey of retrial queues
TL;DR: A survey of the main results and methods of the theory of retrial queues, concentrating on Markovian single and multi-channel systems, as well as models with batch arrivals, multiclasses, customer impatience, double connection, control devices, two-way communication and buffer.
Journal ArticleDOI
Entropy maximisation and queueing network models
TL;DR: This paper traces the progress achieved so far towards the creation of ME and MRE product-form approximations and related algorithms for the performance analysis of general Queueing Network Models (QNMs) and indicates potential research extensions in the area.
Journal ArticleDOI
New results in the theory of repeated orders queueing systems
Qui Hoon Choo,Brian Conolly +1 more
TL;DR: The repeated orders queueing system (ROO) permits no waiting or queueing in the normal sense as discussed by the authors, instead customers who find the service (or device, to use an engineering term) busy make reapplications at random intervals and in random order until their needs are met.