Special Issue "Queueing Theory and Network Applications"

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: 31 October 2022 | Viewed by 828

Special Issue Editor

Dr. Alexander Moiseev
E-Mail Website
Guest Editor
Institute of Applied Mathematics and Computer Science, Tomsk State University, 36 Lenin Ave., 634050 Tomsk, Russia
Interests: queueing theory; simulation; software engineering
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Special Issue Information

Dear Colleagues,

Queueing theory today plays an important role in the development of the most modern communication technologies. Devices and technologies have made very great progress, but their further advancement in many areas has reached its limit in the physical or cost sense, or close to this limit. Mathematics in general and queueing theory in particular can help solve a number of problems by analyzing, identifying bottlenecks and optimizing existing technologies and approaches.

In this Special Issue, we propose to collect articles devoted primarily to solving practical modern problems using queueing theory. These can be problems related to technology, social or economic problems, or problems in any other areas. Of course, we invite publications and papers in pure queueing theory too, because they can serve as a basis for future applied research.

Dr. Alexander Moiseev
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.


  • queueing theory
  • networks
  • telecommunications
  • control and reliability in queues
  • applied probability
  • stochastic processes
  • simulations

Published Papers (1 paper)

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Retrial Queuing-Inventory Systems with Delayed Feedback and Instantaneous Damaging of Items
Axioms 2022, 11(5), 241; https://doi.org/10.3390/axioms11050241 - 20 May 2022
Cited by 1 | Viewed by 593
This paper studies a Markov model of a queuing-inventory system with primary, retrial, and feedback customers. Primary customers form a Poisson flow, and if an inventory level is positive upon their arrival, they instantly receive the items. If the inventory level is equal [...] Read more.
This paper studies a Markov model of a queuing-inventory system with primary, retrial, and feedback customers. Primary customers form a Poisson flow, and if an inventory level is positive upon their arrival, they instantly receive the items. If the inventory level is equal to zero upon arrival of a primary customer, then this customer, according to the Bernoulli scheme, either leaves the system or goes into an infinite buffer to repeat their request in the future. The rate of retrial customers is constant, and if the inventory level is zero upon arrival of a retrial customer, then this customer, according to the Bernoulli scheme, either leaves orbit or remains in orbit to repeat its request in the future. According to the Bernoulli scheme, each served primary or retrial customer either leaves the system or feedbacks into orbit to repeat their request. Destructive customers that form a Poisson flow cause damage to items. Unlike primary, retrial, and feedback customers, destructive customers do not require items, since, upon arrival of such customers, the inventory level instantly decreases by one. The system adopted one of two replenishment policies: (s, Q) or (s, S). In both policies, the lead time is a random variable that has an exponential distribution. It is shown that the mathematical model of the system under study was a two-dimensional Markov chain with an infinite state space. Algorithms for calculating the elements of the generating matrices of the constructed chains were developed, and the ergodicity conditions for both policies were found. To calculate the steady-state probabilities, a matrix-geometric method was used. Formulas were found for calculating the main performance measures of the system. The results of the numerical experiments, including the minimization of the total cost, are demonstrated. Full article
(This article belongs to the Special Issue Queueing Theory and Network Applications)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Asymptotic Diffusion Analysis of Retrial Queueing System M/M/1 with Impatient Customers, Collisions and Unreliable Server
Authors: Danilyuk, E.; Plekhanov, A.; Moiseeva, S.; Sztrik, J.
Affiliation: Department of Informatics and Networks, Faculty of Informatics, University of Debrecen, Egyetem tér 1, 4032 Debrecen, Hungary
Abstract: In the paper the retrial queueing system of M/M/1 type with Poisson flow of arrivals, impatient customers, collisions and unreliable service device is considered. To make the problem more realistic and hence to be more complicated we include breakdowns and repairs of the service into the research. Retrial time of customers in the orbit, service time, impatience time of customers in the orbit, server's lifetime (depending on whether it is idle or busy) and server recovery time are supposed to exponentially distributed. The problem of finding the probability distribution of the number of customers in orbit by the method of asymptotic diffusion analysis is solved under the condition of a heavy load of the system and long time patience of customers in the orbit. Numerical results are presented that demonstrate the scope of the obtained theoretical conclusions, and a comparative analysis of the method of asymptotic analysis and the method of asymptotic diffusion analysis for the considered problem is given.

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