Retrial Queues

Falin, G.; Templeton, J. G. C.

doi:10.1007/978-1-4899-2977-8

Cited by 652 publications

(472 citation statements)

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“…An overview is given in [1,2]. Characteristic of retrial queues is the fact that calls (or, in general, customers) that cannot be served upon arrival enter an orbit and request for a retrial after some random time.…”

Section: Introductionmentioning

confidence: 99%

Two Way Communication Retrial Queues with Balanced Call Blending

Phung-Duc

Rogiest

2012

Analytical and Stochastic Modeling Techniques and Applications

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Abstract. In call centers, call blending consists in the mixing of incoming and outgoing call activity. Artalejo and Phung-Duc recently provided an apt model for such a setting, with a two way communication retrial queue. However, by assuming a classical (proportional) retrial rate for the incoming calls, the outgoing call activity is largely blocked when many incoming calls are in orbit, which may be unwanted, especially when outgoing calls are vital to the service offered.In this paper, we assume a balanced way of call blending, through a retrial queue with constant retrial rate for incoming calls. For the single server case (one operator), a generating functions approach enables deriving explicit formulas for the joint stationary distribution of the number of incoming calls and the system state, and also for the factorial moments. This is complemented with a stability analysis, expressions for performance measures, and also recursive formulas, allowing reliable numerical calculation. For the multiserver case (multiple operators), we provide a quasi-birth-and-death process formulation, enabling deriving a sufficient and necessary condition for stability in this case, as well as a numerical recipe to obtain the stationary distribution.

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Section: Introductionmentioning

confidence: 99%

Two Way Communication Retrial Queues with Balanced Call Blending

Phung-Duc

Rogiest

2012

Analytical and Stochastic Modeling Techniques and Applications

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“…. , N, is fully determined by (11). Now, since G n (z) is analytic within −1 ≤ z ≤ 1, if there is a rootẑ in that interval such that |A(ẑ)| = 0, then the same root applies to A n (z) so that |A n (ẑ)| = 0 as well.…”

Section: Generating Functionsmentioning

confidence: 99%

“…Tandem queues with finite buffers and blocking, causing retrials, have recently been studied and applied to Internet data traffic (see, for eaxample, [6,7]). There is also a vast literature on retrial queues (e.g., [3,9,11,30] and references therein). Queues with impatient customers and abandonments have also been studied; see, for example, [1,31].…”

Section: Introductionmentioning

confidence: 99%

Queues in tandem with customer deadlines and retrials

Reed

Yechiali

2012

Queueing Syst

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We study queues in tandem with customer deadlines and retrials. We first consider a 2-queue Markovian system with blocking at the second queue, analyze it, and derive its stability condition. We then study a non-Markovian setting and derive the stability condition for an approximating diffusion, showing its similarity to the former condition. In the Markovian setting, we use probability generating functions and matrix analytic techniques. In the diffusion setting, we consider expectations of the first hitting times of compact sets.

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“…Queueing systems with repeated attempts are found suitable for modelling the processes in telephone switching systems, digital cellular mobile networks, packet switching networks, local area networks, stock and flow etc. Review of retrial queueing literature can be found in the bibliographies of Artalejo (1999aArtalejo ( , 1999b and the books by Falin and Templeton (1997) and Artalejo and Gomez Corral (2008). The applications of retrial queues in science and engineering are given in Kulkarni and Liang (1997).…”

Section: Introductionmentioning

confidence: 99%

An M[X]/G/1 Retrial G-Queue with Server Breakdown

A.Divya¹

2015

IJIRSET

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Batch arrival retrial queue with positive and negative customers is considered. If the server is idle upon the arrival of a batch, one of the customers in the batch receives service immediately and others join the orbit. If the server is busy, all the customers join the orbit. The arrival of negative customer brings the server down and removes the customer in service from the system. The server is subject to random breakdown while it is working. Using supplementary variable technique, expected number of customers in the orbit and expected number of customers in the system are derived. Stochastic decomposition property is established. Some special cases are discussed and numerical results are presented.

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Retrial Queues

Cited by 652 publications

References 0 publications

Two Way Communication Retrial Queues with Balanced Call Blending

Two Way Communication Retrial Queues with Balanced Call Blending

Queues in tandem with customer deadlines and retrials

An M[X]/G/1 Retrial G-Queue with Server Breakdown

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