Two Way Communication Retrial Queues with Balanced Call Blending

Phung-Duc, Tuan; Rogiest, Wouter

doi:10.1007/978-3-642-30782-9_2

Cited by 14 publications

(5 citation statements)

References 13 publications

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“…If we set b = 1, then the ergodicity condition is consistent with Equation ( 15) in Phung-Duc and Rogiest [24].…”

Section: Ergodicitysupporting

confidence: 53%

Multiserver Retrial Queue with Two-Way Communication and Synchronous Working Vacation

Liu,

Chiou,

Chen

et al. 2024

Mathematics

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This work investigates a two-way communication retrial queue with synchronous working vacation and a constant retrial policy. During the idle time, a server makes an outgoing call after a random length. The service time of the incoming call and outgoing call obeys exponential distribution with different rates. If the incoming call finds all servers to be unavailable, it may or may not enter orbit. All servers immediately go on vacation simultaneously as soon as they find an empty system after the service finishes. During vacation, the servers can provide a service to those incoming calls, but this is at a lower-speed rate. The stationary probability distribution and the ergodic condition are obtained utilizing the matrix geometric technique. Some system characteristics are developed. Using MATLAB software, the variation in average orbit length, idle ratio, and the average number of servers in different server states is plotted for different values of the incoming/outgoing call rate and retrial rate. We further propose a multi-objective optimization model from which the optimal rate of outgoing calls and optimal vacation rate are explicitly obtained.

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“…If we set b = 1, then the ergodicity condition is consistent with Equation ( 15) in Phung-Duc and Rogiest [24].…”

Section: Ergodicitysupporting

confidence: 53%

Multiserver Retrial Queue with Two-Way Communication and Synchronous Working Vacation

Liu,

Chiou,

Chen

et al. 2024

Mathematics

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“…Approximation methods are essential to deal with the complexity of communication protocols especially in a call center context, where the server not only serves incoming calls, but in idle time it makes outgoing calls to the outside. This type of systems with both incoming and outgoing calls is referred to as a two-way communication retrial queueing model [21,22]. Many researchers undertook to examine such a model in the literature of queues.…”

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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“…One of the first paper on the retrial queueing system with two-way communication was presented by Falin [11]. So far several authors have investigated this type of models [7,8,[15][16][17]19,20].…”

Section: Introductionmentioning

confidence: 99%

Modeling of a Two-Way Communication System with a Special Searching for Customers

Kuki

Bérczes

Sztrik

et al. 2019

Communications in Computer and Information Science

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In this paper a special system with two-way communication is modelled by a finite and an infinite sources queueing system with retrial. The system is unreliable, the server may subject to random breakdowns. Customers from the finite source are the first order or regular customers, while the customers from the infinite source are the second order or the invited customers. The novelty of this paper is to investigate and model this unreliable system with different idle and busy breakdown intensity and different service rates for first and second order customers. In case of a busy server for first order customers, they can retry their requests. In case of an idle server, the second order customers are called for service. The effect of the breakdown and repair intensities are also investigated. The system balance equations are formulated, and the steady state probabilities can be obtained. Here the MOSEL-2 tool is used for these calculations. By the help of these probabilities the common performance measures are calculated and displayed.

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Two Way Communication Retrial Queues with Balanced Call Blending

Cited by 14 publications

References 13 publications

Multiserver Retrial Queue with Two-Way Communication and Synchronous Working Vacation

Multiserver Retrial Queue with Two-Way Communication and Synchronous Working Vacation

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

Modeling of a Two-Way Communication System with a Special Searching for Customers

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