Single server retrial queues with two way communication

Artalejo, Jesús R.; Phung-Duc, Tuan

doi:10.1016/j.apm.2012.04.022

Cited by 77 publications

(33 citation statements)

References 29 publications

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“…We expanded the denominator in the second step and kept the first two terms, while we kept the dominating terms of the expansion of the resulting product in the third step. 3. R * exists and is equal to R h : this is a boundary case of the other two cases.…”

Section: Asymptotic Inversion Of Q(z)mentioning

confidence: 96%

“…This case is therefore of the critical type (R f 3 = f 2 (R f 2 )). According to [8], section VI.9, p. 411, the singularity type is then a mix of the types of both functions f 2 and f 3 VII.1,p. 446), while f 3 (z) is of exponential type.…”

Section: Asymptotic Inversion Of Q(z)mentioning

confidence: 99%

“…In [3], tail asymptotics for the queue length are obtained for the M/G/1 retrial queue with two-way communication where the server makes outgoing calls in its idle time. In [3], the service time distributions of incoming calls and outgoing calls follow an arbitrary distribution.…”

Section: Introductionmentioning

confidence: 99%

“…We can extend this to a ∆-domain to any complex number ζ by the mapping z → ζ z 3. Also known as Vivanti's theorem or the Vivanti-Pringsheim theorem.…”

mentioning

confidence: 99%

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Asymptotics of queue length distributions in priority retrial queues

Walraevens

Claeys

Phung-Duc

2018

Performance Evaluation

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We calculate asymptotics of the distribution of the number of customers in orbit in a two-class priority retrial M/G/1-type queueing model. In this model, priority customers wait in line while non-priority customers join an orbit and retry later. Although the generating function and moments of the number of customers in orbit has been analyzed before, asymptotics of the distribution have not been thoroughly investigated. We use singularity analysis of the probability generating function to do just that. Our results show that different regimes exist for these asymptotics in case of lighttailed service times: in what we call the 'priority regime', the tail asymptotics have the same decay (∼ cn −3/2 R −n ) as in the priority non-retrial queue and the retrial rate only influences the constant c. In the 'retrial regime', the retrial rate also influences the sub-exponential factor of the asymptotics. In this regime, asymptotics are very similar to asymptotics in retrial queues without (priority) waiting line. Finally, we also analyze the case that the service time distribution is power law (with or without exponential cut-off) using the same technique.

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Section: Asymptotic Inversion Of Q(z)mentioning

confidence: 96%

Section: Asymptotic Inversion Of Q(z)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…We can extend this to a ∆-domain to any complex number ζ by the mapping z → ζ z 3. Also known as Vivanti's theorem or the Vivanti-Pringsheim theorem.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Asymptotics of queue length distributions in priority retrial queues

Walraevens

Claeys

Phung-Duc

2018

Performance Evaluation

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show abstract

“…They derived explicit expressions for the generating functions as well as the joint stationary distribution of the number of calls in the orbit and the state of the server. Artalejo and Phung-Duc [4] extended their analysis to an M/G/1 retrial queue with two-way communication, which turns out to have a close relation with retrial queues and priority (see, Falin et al [17]) where an infinite buffer is available for outgoing calls. In all the previous works, there is at most one flow of outgoing calls.…”

Section: Introductionmentioning

confidence: 99%

Bounds of the stationary distribution in M/G/1 retrial queue with two-way communication and n types of outgoing calls

2019

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In this article we analyze the M/G/1 retrial queue with two-way communication and n types of outgoing calls from a stochastic comparison viewpoint. The main idea is that given a complex Markov chain that cannot be analyzed numerically, we propose to bound it by a new Markov chain, which is easier to solve by using a stochastic comparison approach. Particularly, we study the monotonicity of the transition operator of the embedded Markov chain relative to the stochastic and convex orderings. Bounds are also obtained for the stationary distribution of the embedded Markov chain at departure epochs. Additionally, the performance measures of the considered system can be estimated by those of an M/M/1 retrial queue with two-way communication and n types of outgoing calls when the service time distribution is NBUE (respectively, NWUE). Finally, we test numerically the accuracy of the proposed bounds.

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A Coupling-Based Analysis of a Multiclass Retrial System with State-Dependent Retrial Rates

Morozov

Morozova

2019

Queueing Theory and Network Applications

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Single server retrial queues with two way communication

Cited by 77 publications

References 29 publications

Asymptotics of queue length distributions in priority retrial queues

Asymptotics of queue length distributions in priority retrial queues

Bounds of the stationary distribution in M/G/1 retrial queue with two-way communication and n types of outgoing calls

A Coupling-Based Analysis of a Multiclass Retrial System with State-Dependent Retrial Rates

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