Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.0
2.3
Journals
Mathematics
Special Issues
Queueing Systems Models and Their Applications
share announcement

Queueing Systems Models and Their Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 31 July 2025 | Viewed by 6766

Special Issue Editors

Prof. Dr. Oleg Tikhonenko

E-Mail Website
Guest Editor
Faculty of Designing, University of Social Science and Humanities—USWPS, ul. Chodakowska 19/31, 03-815 Warsaw, Poland
Interests: queueing theory; stochastic processes; simulation methods; probability and statistics
Dr. Marcin Ziółkowski

E-Mail Website
Guest Editor
Institute of Information Technology, Warsaw University of Life Sciences - SGGW, Ul. Nowoursynowska 159, 02-787 Warsaw, Poland
Interests: queueing theory; applications of computer algebra systems; theory of programming; theory of teaching mathematics

Special Issue Information

Dear Colleagues,

Queueing system models have various different applications in many areas. The headway made in engineering systems, the economy, and computer science in the past few years has caused these systems to often be used, especially in the process of designing computer networks or retail systems. Compared to classical queueing models (started in the 20th century by Erlang), the current models are becoming more and more complex, taking into account new assumptions related to the character of arrival flows, the non-homogeneity of customers or non-identical servers, and possible limitations in their functioning. Investigations of such models require knowledge from many different fields of mathematics: probability theory,  stochastic processes, mathematical analysis, differential equations, discrete mathematics, and numerical methods. For obtaining results, we also use simulations constructed with the use of high-level programming languages or symbolic calculations with the help of computer algebra systems. This allows the cooperation of researchers from various scientific areas. Results of the research are additionally very practical as they allow us to calculate, in real systems, the necessary sizes of queues, the number of servers, memory buffer sizes, and expected loss probabilities. The impact of these is likely to grow dynamically in the future.

The aim of this Special Issue is to report recent research results on queueing systems and their applications in different fields, encourage interaction among the researchers investigating such models, discuss important research problems and new directions, and promote the use of different analysis methods in various research areas. We would like to invite researchers to submit their new findings on the areas mentioned above or related ones.

Topics to be covered:

  • Classical queueing systems and their modifications;
  • Queueing networks;
  • Queueing systems with non-homogeneous customers;
  • Queueing systems with non-identical servers;
  • Queueing systems with vacations;
  • Queueing systems with sectorized memory; 
  • The use of matrix methods in the analysis of complicated queueing models;
  • Numerical, algorithmic, approximation, and simulation methods in queueing systems analysis;
  • Applications of queueing systems in real engineering or computer systems. 

Prof. Dr. Oleg Tikhonenko
Dr. Marcin Ziółkowski
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

  • queueing model
  • Markov chain
  • loss probability
  • Laplace transform
  • non-homogeneous customers
  • non-identical servers
  • priority queue
  • queues with vacations
  • summary volume
  • simulation methods

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (4 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

22 pages, 4833 KiB  
Article
An M/G/1 Queue with Repeated Orbit While in Service
by Gabi Hanukov, Yonit Barron and Uri Yechiali
Mathematics 2024, 12(23), 3722; https://doi.org/10.3390/math12233722 - 27 Nov 2024
Cited by 1 | Viewed by 652
Abstract
Orbit and retrial queues have been studied extensively in the literature. A key assumption in most of these works is that customers “go to orbit” when they are blocked upon arrival. However, real-life situations exist in which customers opt to go to orbit [...] Read more.
Orbit and retrial queues have been studied extensively in the literature. A key assumption in most of these works is that customers “go to orbit” when they are blocked upon arrival. However, real-life situations exist in which customers opt to go to orbit to efficiently use their orbit time rather than residing dormant at the service station while waiting for their service to be completed. This paper studies such a system, extending the scope of traditional orbit and retrial queues. We consider an M/G/1 queue where customers repeatedly go to orbit while their service remains in progress. That is, if a customer’s service is not completed by within a specified “patience time”, the customer goes to orbit for a random “orbit time”. When the customer orbits, the server continues rendering her/his service. If, on return, the service is already completed, the customer leaves the system. Otherwise, s/he waits for another patience time. This policy is repeated until service completion. We analyze such an intricate system by applying the supplementary variable technique and using Laplace–Stieltjes transforms. Performance measures are derived, and a comparison analysis is provided between various service time distributions. Full article
(This article belongs to the Special Issue Queueing Systems Models and Their Applications)
►▼ Show Figures

Figure 1

21 pages, 2753 KiB  
Article
Strategic Queueing Behavior of Two Groups of Patients in a Healthcare System
by Youxin Liu, Liwei Liu, Tao Jiang and Xudong Chai
Mathematics 2024, 12(10), 1579; https://doi.org/10.3390/math12101579 - 18 May 2024
Cited by 1 | Viewed by 1240
Abstract
Long waiting times and crowded services are the current medical situation in China. Especially in hierarchic healthcare systems, as high-quality medical resources are mainly concentrated in comprehensive hospitals, patients are too concentrated in these hospitals, which leads to overcrowding. This paper constructs a [...] Read more.
Long waiting times and crowded services are the current medical situation in China. Especially in hierarchic healthcare systems, as high-quality medical resources are mainly concentrated in comprehensive hospitals, patients are too concentrated in these hospitals, which leads to overcrowding. This paper constructs a game-theoretical queueing model to analyze the strategic queueing behavior of patients. In such hospitals, patients are divided into first-visit and referred patients, and the hospitals provide patients with two service phases of “diagnosis” and “treatment”. We first obtain the expected sojourn time. By defining the patience level of patients, the queueing behavior of patients in equilibrium is studied. The results suggest that as long as the patients with low patience levels join the queue, the patients with high patience levels also join the queue. As more patients arrive at the hospitals, the queueing behavior of patients with high patience levels may have a negative effect on that of patients with low patience levels. The numerical results also show that the equilibrium behavior deviates from a socially optimal solution; therefore, to reach maximal social welfare, the social planner should adopt some regulatory policies to control the arrival rates of patients. Full article
(This article belongs to the Special Issue Queueing Systems Models and Their Applications)
►▼ Show Figures

Figure 1

23 pages, 459 KiB  
Article
Analysis of a Two-Stage Tandem Queuing System with Priority and Clearing Service in the Second Stage
by Jia Xu and Liwei Liu
Mathematics 2024, 12(10), 1500; https://doi.org/10.3390/math12101500 - 11 May 2024
Viewed by 1630
Abstract
This paper considers a two-stage tandem queuing system with ordinary customers and priority customers. Upon arrival, ordinary customers are individually served in the first stage, then move to the second stage and receive clearing service. Priority customers can bypass the first stage and [...] Read more.
This paper considers a two-stage tandem queuing system with ordinary customers and priority customers. Upon arrival, ordinary customers are individually served in the first stage, then move to the second stage and receive clearing service. Priority customers can bypass the first stage and proceed directly to the second stage for clearing service. The second stage has N service seats. All customers currently in the second stage are served simultaneously (i.e., clearing service). Once there are N customers in the second stage, the first stage will be blocked, and newly arriving priority customers will balk and leave without joining. We first formulate a two-dimensional Markov chain to analyze this queuing system and derive the stability condition. Subsequently, the stationary distribution of the system is derived using the matrix-analytic method and spectral expansion technique. Furthermore, analytical expressions for the mean queue length, mean sojourn time, and other performance measures are presented. Finally, some numerical examples are provided to illustrate the effects of various parameters, offering valuable insights for designing such two-stage tandem queuing systems. Full article
(This article belongs to the Special Issue Queueing Systems Models and Their Applications)
►▼ Show Figures

Figure 1

19 pages, 726 KiB  
Article
On the Control Policy of a Queuing–Inventory System with Variable Inventory Replenishment Speed
by Jung Woo Baek
Mathematics 2024, 12(2), 194; https://doi.org/10.3390/math12020194 - 7 Jan 2024
Cited by 1 | Viewed by 1489
Abstract
This paper considers a make-to-order production–inventory system that comprises a production facility and an inventory warehouse. Customers arrive at the facility to place an order, and the orders are processed using the first-come-first-served (FCFS) discipline. The warehouse supplies inventory items (raw materials) for [...] Read more.
This paper considers a make-to-order production–inventory system that comprises a production facility and an inventory warehouse. Customers arrive at the facility to place an order, and the orders are processed using the first-come-first-served (FCFS) discipline. The warehouse supplies inventory items (raw materials) for the production process, and the warehouse inventory is replenished by internal production. The speed of internal production can be controlled through additional costs. If the inventory level drops to zero, the unmet demand waits in the facility until the inventory is replenished. During the stockout period, newly arriving demand is lost. The stationary joint probability of unmet demands and inventory items is derived, and a cost model is constructed. The optimal control policy for internal production is investigated to minimize the cost per unit time of the system. The experimental results show that such a production speed adjustment could reduce costs by up to 42% compared to the cases without the adjustment. Full article
(This article belongs to the Special Issue Queueing Systems Models and Their Applications)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-4
Back to TopTop