Asymptotic Diffusion Analysis of Multi-Server Retrial Queue with Hyper-Exponential Service

Moiseev, Alexander; Nazarov, Anatoly; Paul, Svetlana

doi:10.3390/math8040531

Cited by 12 publications

(4 citation statements)

References 20 publications

(39 reference statements)

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“…Zhang et al [3] investigated a retrial queue with varying service provision rates based on the server status and proposes an optimal model for the same. Moiseev et al [4] presented an asymptotic diffusion for a retrial queue with multiple servers, where the service time followed a hyperexponential distribution, providing a valuable tool for analysing and optimizing such systems. Fiems [5] reviewed retrial queueing models with varying retry durations, using mathematical and probabilistic techniques to understand their performance and behaviour in practical applications.…”

Section: Introductionmentioning

confidence: 99%

Unreliable Multi Server Retrial Queueing System with Reneging and Diverse Outgoing Services

Vadivel,

Venugopal,

Pakkirisamy

2024

MMEP

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This article explores a M/M/m unreliable retrial queue with reneging and diverse outgoing services. Incoming calls that arrive and discover all servers occupied join the orbit. The buffering incomings from the orbit retry their request after a while or leave the system without receiving service. When the orbit becomes empty, the idle server provides outgoing services. It is assumed that there are two categories of outgoing services. Due to unexpected circumstances, the server may breakdown. When a server undergoes breakdown, immediate repair process begins. Post-server breakdown, incoming calls go into orbit and retry service randomly, whereas the two variants of outgoing calls leave the system. The study utilizes a quasi-birth-death (QBD) process to analyse the stationary system size distribution. The steady state probabilities and the rate matrix are obtained through the matrix geometric method (MGM). Various performance metrics are evaluated for the proposed model. The study examines the impact of various system-based parameters on efficiency metrics with the help of numerical results.

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Section: Introductionmentioning

confidence: 99%

Unreliable Multi Server Retrial Queueing System with Reneging and Diverse Outgoing Services

Vadivel,

Venugopal,

Pakkirisamy

2024

MMEP

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“…For example, in [6], a stationary probability distribution of the number of customers in orbit was obtained under conditions of a large delay of customers in orbit. To perform more detailed and accurate analysis of the model a method of asymptotic diffusion analysis is applied [7].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic diffusion analysis of the retrial queuing system with feedback and batch Poisson arrival

Nazarov,

Rozhkova,

Titarenko

2023

Discrete and Continuous Models

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The mathematical model of the retrial queuing system \(M^{[n]}/M/1\) with feedback and batch Poisson arrival is constructed. Customers arrive in groups. If the server is free, one of the arriving customers starts his service, the rest join the orbit. The retrial and service times are exponentially distributed. The customer whose service is completed leaves the system, or reservice, or goes to the orbit. The method of asymptotic diffusion analysis is proposed for finding the probability distribution of the number of customers in orbit. The asymptotic condition is growing average waiting time in orbit. The accuracy of the diffusion approximation is obtained.

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“…The methods applied in queueing theory are used to analyze the model, which is described by a queueing system (QS) with a buffer and its retrial group [2,6,8,12]. We assume that if there is free resource, the elastic session will be established upon arrival, otherwise it will await in the buffer, from where it can depart for buffer' retrial group [3,8,14,15,17] and return after a moment.…”

Section: Introductionmentioning

confidence: 99%

Methods for Analyzing Slicing Technology in 5G Wireless Network Described as Queueing System with Unlimited Buffer and Retrial Group

Adou

Markova

2021

Information Technologies and Mathematical Modelling. Queueing Theory and Applications

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Fourth generation wireless network was very soon about to not be able to support or withstand the exponential growth of traffic in modern wireless telecommunication networks. In addition, the inflexibility of mobile networks until now is making the situation even more complicated. In response, the fifth generation (5G) wireless telecommunication network was developed, allowing flexible and quick deployment of applications and services to accommodate specific requirements of users in very diverse fields. The cornerstone of 5G is called slicing technology: a mechanism making possible the creation and configuration of multiple network services on top of the same infrastructure with help of its defined network slices. The international telecommunication union (ITU) has defined three categories of use which have been brought into conformity with the 3GPP standards. These categories are specified by three generic slices of 5G: enhanced mobile broadband (eMBB), ultra-reliable low latency communications (uRLLc) and massive machine type communications (mMTC). We consider queueing system with queue and its retrial group for modeling slicing technology in 5G wireless network.

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Asymptotic Diffusion Analysis of Multi-Server Retrial Queue with Hyper-Exponential Service

Cited by 12 publications

References 20 publications

Unreliable Multi Server Retrial Queueing System with Reneging and Diverse Outgoing Services

Unreliable Multi Server Retrial Queueing System with Reneging and Diverse Outgoing Services

Asymptotic diffusion analysis of the retrial queuing system with feedback and batch Poisson arrival

Methods for Analyzing Slicing Technology in 5G Wireless Network Described as Queueing System with Unlimited Buffer and Retrial Group

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