Asymptotic Analysis of Retrial Queueing System M/M/1 with Impatient Customers, Collisions and Unreliable Server

Danilyuk, Elena; Moiseeva, Svetlana; Sztrik, János; Данилюк, Елена Ю.; Стрик, Янош

doi:10.17516/1997-1397-2020-13-2-218-230

Cited by 10 publications

(3 citation statements)

References 18 publications

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“…But, if the normality of steady state probabilities can be assumed, the limiting probability distribution of the sojourn time/waiting time of the customer in the orbit can be obtained by asymptotic methods. See in [7,17]. That's why is it important to find domains of parameters, where the steady-state system (or orbit) probabilities have normal or asymptotic normal distribution.…”

Section: Figure 2: Different Modelsmentioning

confidence: 99%

Numerical analysis of finite source Markov retrial system with non-reliable server, collision, and impatient customers

Kuki¹,

Bérczes²,

Tóth³

et al. 2020

AMI

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A retrial queuing system with a single server is investigated in this paper. The server is subject to random breakdowns. The number of customers is finite and collision may take place. A collision occurs when a customer arrives to the busy server. In case of a collision both customers involved in the collision are sent back to the orbit. From the orbit the customers retry their requests after a random waiting time. The server can be down due to a failure. During the failed period the arriving customers are sent to the orbit, as well. The novelty of this analysis is the impatient behaviour of the customers. A customer waiting in the orbit may leave it after a random waiting time. The requests of these customers will not be served. All the random variables included in the model construction are assumed to be exponentially distributed and independent from each other.The impatient property makes the model more complex, so the derivation of a direct algorithmic solution (which was provided for the non-impatient case) is difficult. For numerical calculations the MOSEL-2 tool can be used. This tool solves the Kolmogorov system equations, and from the resulting steady-state probabilities various system characteristics and performance measures can be calculated, i.e. mean response time, mean waiting time in the orbit, utilization of the server, probability of the unserved impatient requests. Principally the effect of the impatient property is investigated in

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Section: Figure 2: Different Modelsmentioning

confidence: 99%

Numerical analysis of finite source Markov retrial system with non-reliable server, collision, and impatient customers

Kuki¹,

Bérczes²,

Tóth³

et al. 2020

AMI

View full text Add to dashboard Cite

show abstract

“…Impatience of the customers is a natural phenomenon and an interesting topic in queueing theory. The process of reneging and balking is extensively studied by many researchers, for example in [1][2][3][4][5][6][7][8][9][10]13,14,20,24]. Whenever an arriving customer decides not to enter the system, which is called balking while in reneging a customer in the system after waiting for some time leaves the system without being served.…”

Section: Introductionmentioning

confidence: 99%

Some Special Features of Finite-Source Retrial Queues with Collisions, an Unreliable Server and Impatient Customers in the Orbit

Sztrik

Tóth

2021

Information Technologies and Mathematical Modelling. Queueing Theory and Applications

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The goal of the paper is to study a finite-source retrial queuing system with collisions and customers' impatience behavior in the orbit. The situation when an incoming customer from the orbit or from the source finds the server busy causes a collision and both requests are directed toward the orbit. It is assumed that every request in the source is eligible to generate customers whenever the server is failed but these requests immediately go into orbit. A customer after some waiting in the orbit can depart without fulfilling its service requirement these are the socalled impatient/reneging/abandoned customers. In that case it returns to the source. A customer who is under service when the server fails is also sent to the orbit. The source, service, retrial, impatience, operation and repair times are supposed to be independent of each other. The novelty of the investigation is to carry out a sensitivity analysis comparing various distributions of impatience time of customers on the performance measures such as mean number of customers in the orbit, mean waiting time of an arbitrary, successfully served and reneging customers, probability of abandonment, server utilization, etc.

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“…In that, an asymptotic analysis method is used to define the stationary distribution of the number of customers in the orbit. We investigate the same model as in [2], but the results are gathered by our simulation program package. With this approach, it is possible to calculate performance measures that can not be determined or almost impossible to give exact formulas using numerical or asymptotic analysis.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Retrial Queueing System M/G/1 with Impatient Customers, Collisions and Unreliable Server Using Simulation

Sztrik

Tóth

Danilyuk

et al. 2021

Information Technologies and Mathematical Modelling. Queueing Theory and Applications

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In this paper, we consider a retrial queueing system of M/G/1 type with an unreliable server, collisions, and impatient customers. The novelty of our work is to carry out a sensitivity analysis applying different distributions of service time of customers on significant performance measures for example on the probability of abandonment, the mean waiting time of an arbitrary, successfully served, impatient customer, etc. A customer is able to depart from the system in the orbit if it does not get its appropriate service after a definite random waiting time so these will be the so-called impatient customers. In the case of server failure, requests are allowed to enter the system but these will be forwarded immediately towards the orbit. The service, retrial, impatience, operation, and repair times are supposed to be independent of each other. Several graphical illustrations demonstrate the comparisons of the investigated distributions and the interesting phenomena which are obtained by our self-developed simulation program. The achieved results are compared to the results of the [2] to check how the system characteristics changes if we use other distributions of service time and to present the advantages of performing simulations in certain scenarios.

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Asymptotic Analysis of Retrial Queueing System M/M/1 with Impatient Customers, Collisions and Unreliable Server

Cited by 10 publications

References 18 publications

Numerical analysis of finite source Markov retrial system with non-reliable server, collision, and impatient customers

Numerical analysis of finite source Markov retrial system with non-reliable server, collision, and impatient customers

Some Special Features of Finite-Source Retrial Queues with Collisions, an Unreliable Server and Impatient Customers in the Orbit

Analysis of Retrial Queueing System M/G/1 with Impatient Customers, Collisions and Unreliable Server Using Simulation

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