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Recent Research in Queuing Theory and Stochastic Models, 2nd Edition
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Recent Research in Queuing Theory and Stochastic Models, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 31 July 2025 | Viewed by 3242

Special Issue Editors

Dr. Ivan Atencia

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Guest Editor
Department of Applied Mathematics, University of Malaga, 29071 Málaga, Spain
Interests: applied mathematics; operations research; queueing systems; performance analysis; home automation systems
Special Issues, Collections and Topics in MDPI journals
Dr. José Luis Galán-García

E-Mail Website
Guest Editor
Departamento de Matemática Aplicada, Escuela de Ingenierías Industriales, University of Málaga, 29071 Málaga, Spain
Interests: mathematics education; modeling and simulation; mathematical programming; applications of computer algebra systems (CAS); applied mathematics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The purpose of this Special Issue is to contribute novel papers to the study of queueing theory and stochastic models. Queueing models are among the best-known theories of stochastic modeling, and their progress and development have been increasing exponentially since A.K. Erlang (1917) and T.O. Engset (1918) first studied communications networks and their congestion problems. A server, waiting line and arriving flow of customers constitute the basis of any queueing model. The way in which these items are considered and the various disciplines to which they are attached open a wide range of possibilities in terms of handling situations that arise in real-life problems.

In contemporary research, concepts such as sojourn times and busy periods have become quite relevant due to their importance in traffic engineering, telecommunications, and computer systems.

As for the temporal concept in queueing systems, it should be noted that these systems have been traditionally considered in a context of continuous time, but that the last two decades has seen an increasing interest in the study of discrete-time queueing systems since they are more suitable than their continuous counterpart for computer modeling and telecommunication systems.

Any relevant papers related to the queueing systems and stochastic models are welcome.

Dr. Ivan Atencia
Dr. José Luis Galán-García
Guest Editors

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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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.

Keywords

  • Markov chains
  • stochastic process
  • sojourn times
  • busy periods
  • heavy traffic regime
  • multichannel stochastic network

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Related Special Issue

Published Papers (3 papers)

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Research

36 pages, 2377 KiB  
Article
Use Cases of Machine Learning in Queueing Theory Based on a GI/G/K System
by Dmitry Efrosinin, Vladimir Vishnevsky, Natalia Stepanova and Janos Sztrik
Mathematics 2025, 13(5), 776; https://doi.org/10.3390/math13050776 - 26 Feb 2025
Viewed by 940
Abstract
Machine learning (ML) in queueing theory combines the predictive and optimization capabilities of ML with the analytical frameworks of queueing models to improve performance in systems such as telecommunications, manufacturing, and service industries. In this paper we give an overview of how ML [...] Read more.
Machine learning (ML) in queueing theory combines the predictive and optimization capabilities of ML with the analytical frameworks of queueing models to improve performance in systems such as telecommunications, manufacturing, and service industries. In this paper we give an overview of how ML is applied in queueing theory, highlighting its use cases, benefits, and challenges. We consider a classical GI/G/K-type queueing system, which is at the same time rather complex for obtaining analytical results, consisting of K homogeneous servers with an arbitrary distribution of time between incoming customers and equally distributed service times, also with an arbitrary distribution. Different simulation techniques are used to obtain the training and test samples needed to apply the supervised ML algorithms to problems of regression and classification, and some results of the approximation analysis of such a system will be needed to verify the results. ML algorithms are used also to solve both parametric and dynamic optimization problems. The latter is achieved by means of a reinforcement learning approach. It is shown that the application of ML in queueing theory is a promising technique to handle the complexity and stochastic nature of such systems. Full article
(This article belongs to the Special Issue Recent Research in Queuing Theory and Stochastic Models, 2nd Edition)
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19 pages, 502 KiB  
Article
A Dual Tandem Queue as a Model of a Pick-Up Point with Batch Receipt and Issue of Parcels
by Alexander N. Dudin, Olga S. Dudina, Sergei A. Dudin and Agassi Melikov
Mathematics 2025, 13(3), 488; https://doi.org/10.3390/math13030488 - 31 Jan 2025
Viewed by 699
Abstract
Parcel delivery networks have grown rapidly during the last few years due to the intensive evolution of online marketplaces. We address the issue of managing the operation of a network’s pick-up point, including the selection of the warehouse’s capacity and the policy for [...] Read more.
Parcel delivery networks have grown rapidly during the last few years due to the intensive evolution of online marketplaces. We address the issue of managing the operation of a network’s pick-up point, including the selection of the warehouse’s capacity and the policy for accepting orders for delivery. The existence of the time lag between order placing and delivery to the pick-up point is accounted for via modeling the order’s processing as the service in the dual tandem queueing system. Distinguishing features of this tandem queue are the account of possible irregularity in order generation via consideration of the versatile Markov arrival process and the possibilities of batch transfer of the orders to the pick-up point, group withdrawal of orders there, and client no-show. To reduce the probability of an order rejection at the pick-up point due to the overflow of the warehouse, a threshold strategy of order admission at the first stage on a tandem is proposed. Under the fixed value of the threshold, tandem operation is described by the continuous-time multidimensional Markov chain with a block lower Hessenberg structure for the generator. Stationary performance measures of the tandem system are calculated. Numerical results highlight the dependence of these measures on the capacity of the warehouse and the admission threshold. The possibility of the use of the results for managerial goals is demonstrated. In particular, the results can be used for the optimal selection of the capacity of a warehouse and the policy of suspending order admission. Full article
(This article belongs to the Special Issue Recent Research in Queuing Theory and Stochastic Models, 2nd Edition)
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24 pages, 333 KiB  
Article
Discrete-Time Retrial Queuing Systems with Last-Come-First-Served (LCFS) and First-Come-First-Served (FCFS) Disciplines: Negative Customer Impact and Stochastic Analysis
by Iván Atencia-Mckillop, Sixto Sánchez-Merino, Inmaculada Fortes-Ruiz and José Luis Galán-García
Mathematics 2025, 13(1), 107; https://doi.org/10.3390/math13010107 - 30 Dec 2024
Viewed by 519
Abstract
This paper examines a discrete-time retrial queuing system that incorporates negative customers, system breakdowns, and repairs. In this model, an arriving customer has the option to go directly to the server, pushing the currently served customer, if any, to the front of the [...] Read more.
This paper examines a discrete-time retrial queuing system that incorporates negative customers, system breakdowns, and repairs. In this model, an arriving customer has the option to go directly to the server, pushing the currently served customer, if any, to the front of the orbit queue, or to join the orbit based on a First-Come-First-Served (FCFS) discipline. The study also considers negative customers who not only remove the customer currently being served but also cause a server breakdown. An in-depth analysis of the model is conducted using a generating function approach, leading to the determination of the distribution and expected values of the number of customers in the orbit and the entire system. The paper explores the stochastic decomposition law and provides bounds for the difference between the steady-state distribution of this system and a comparable standard system. Recursive formulas for the steady-state distributions of the orbit and the system are developed. Additionally, it is shown that the studied discrete-time system can approximate the M/G/1 continuous-time version of the model. The research includes a detailed examination of the customer’s sojourn time distribution in the orbit and the system, utilizing the busy period of an auxiliary system. The paper concludes with numerical examples that highlight how different system parameters affect various performance characteristics, and a section summarizing the key research contributions. Full article
(This article belongs to the Special Issue Recent Research in Queuing Theory and Stochastic Models, 2nd Edition)
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