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Queue and Stochastic Models for Operations Research, 3rd Edition
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Queue and Stochastic Models for Operations Research, 3rd 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: 15 October 2025 | Viewed by 2476

Special Issue Editor

Dr. Tuan Phung-Duc

E-Mail Website
Guest Editor
Department of Policy and Planning Sciences, Institute of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba 305-8573, Ibaraki, Japan
Interests: operations research; stochastic models; queues; performance analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We would like to invite you to submit your research to this Special Issue, entitled “Queue and Stochastic Models for Operations Research, 3rd Edition”. This publication is seeking high-quality contributions on the topics of queues and related stochastic models arising from operations research.

Dr. Tuan Phung-Duc
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. 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

  • stochastic models
  • matrix analytic methods
  • asymptotic analysis of queueing models
  • game theoretic analysis of queues
  • fluid and diffusion limits, large deviation analysis of queues
  • stochastic analysis of risk models
  • matching queues
  • multidimensional Markov chains
  • novel queueing models in applications
  • stochastic analysis of machine learning systems

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Related Special Issue

Published Papers (4 papers)

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Research

14 pages, 519 KiB  
Article
Computing the Matrix G of Multi-Dimensional Markov Chains of M/G/1 Type
by Valeriy Naumov and Konstantin Samouylov
Mathematics 2025, 13(8), 1223; https://doi.org/10.3390/math13081223 - 8 Apr 2025
Viewed by 157
Abstract
We consider Md-M/G/1 processes, which are irreducible discrete-time Markov chains consisting of two components. The first component is a nonnegative integer vector, while the second component indicates the state (or phase) of the external environment. The level of a state is defined [...] Read more.
We consider Md-M/G/1 processes, which are irreducible discrete-time Markov chains consisting of two components. The first component is a nonnegative integer vector, while the second component indicates the state (or phase) of the external environment. The level of a state is defined by the minimum value in its first component. The matrix G of the process represents the conditional probabilities that, starting from a given state of a certain level, the Markov chain will first reach a lower level in a specific state. This study aims to develop an effective algorithm for computing matrices G for Md-M/G/1 processes. Full article
(This article belongs to the Special Issue Queue and Stochastic Models for Operations Research, 3rd Edition)
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18 pages, 610 KiB  
Article
Analysis of Dynamic Transaction Fee Blockchain Using Queueing Theory
by Koki Inami and Tuan Phung-Duc
Mathematics 2025, 13(6), 1010; https://doi.org/10.3390/math13061010 - 20 Mar 2025
Viewed by 319
Abstract
In recent years, blockchains have been attracting attention because they are decentralized networks with transparency and trustworthiness. Generally, transactions on blockchain networks with higher transaction fees are processed preferentially compared to others. The processing fee varies significantly depending on other transactions; it is [...] Read more.
In recent years, blockchains have been attracting attention because they are decentralized networks with transparency and trustworthiness. Generally, transactions on blockchain networks with higher transaction fees are processed preferentially compared to others. The processing fee varies significantly depending on other transactions; it is difficult to predict the fee, and it may be significantly high. These are major barriers to blockchain utilization. Although several consensus algorithms have been proposed to solve these problems, their performance has not been fully evaluated. In this study, we model a blockchain system with a base fee, such as in Ethereum, via a priority queueing model. To assess the model’s performance, we derive the stability condition, stationary probability, average number of customers, and average waiting time for each type of customer. In deriving the stability conditions, we propose a method that uses the theoretical values of the partial models. These theoretical values match well with those obtained from Monte Carlo simulations, confirming the validity of the analysis. Full article
(This article belongs to the Special Issue Queue and Stochastic Models for Operations Research, 3rd Edition)
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21 pages, 1583 KiB  
Article
Accurate Approximation for Resource Queuing Systems with Losses and Signals
by Alexander Maslov, Eduard Sopin and Konstantin Samouylov
Mathematics 2025, 13(4), 619; https://doi.org/10.3390/math13040619 - 13 Feb 2025
Viewed by 613
Abstract
We consider a queuing system with a finite number of servers and a finite pool of resources, where an arriving customer requires a server and random number of resources. During the service, each customer is associated with a Poisson flow of “signals”, where [...] Read more.
We consider a queuing system with a finite number of servers and a finite pool of resources, where an arriving customer requires a server and random number of resources. During the service, each customer is associated with a Poisson flow of “signals”, where upon a signal arrival, the currently allocated resources for a customer are released, and an attempt is made to allocate a new random amount of resources. Recently, such systems have received significant attention for their use in the analysis of 5G/6G cellular systems with non-elastic traffic demands and blockage impairments. Such queuing systems do not allow closed-form analytical solutions, and are conventionally solved using numerical methods. These methods are sensitive to the dimensions of the state space and can lead to inaccuracies. In this paper, we propose a new method for the approximate analysis of performance metrics in resource systems with signals using analytical solutions for similar systems without signals. Our detailed comparison with simulations shows that the relative error is limited to 5–10% over a wide range of system and load parameters. Full article
(This article belongs to the Special Issue Queue and Stochastic Models for Operations Research, 3rd Edition)
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14 pages, 302 KiB  
Article
Multi-Dimensional Markov Chains of M/G/1 Type
by Valeriy Naumov and Konstantin Samouylov
Mathematics 2025, 13(2), 209; https://doi.org/10.3390/math13020209 - 9 Jan 2025
Cited by 1 | Viewed by 609
Abstract
We consider an irreducible discrete-time Markov process with states represented as (k, i) where k is an M-dimensional vector with non-negative integer entries, and i indicates the state (phase) of the external environment. The number n of phases may [...] Read more.
We consider an irreducible discrete-time Markov process with states represented as (k, i) where k is an M-dimensional vector with non-negative integer entries, and i indicates the state (phase) of the external environment. The number n of phases may be either finite or infinite. One-step transitions of the process from a state (k, i) are limited to states (n, j) such that n ≥ k−1, where 1 represents the vector of all 1s. We assume that for a vector k ≥ 1, the one-step transition probability from a state (k, i) to a state (n, j) may depend on i, j, and n − k, but not on the specific values of k and n. This process can be classified as a Markov chain of M/G/1 type, where the minimum entry of the vector n defines the level of a state (n, j). It is shown that the first passage distribution matrix of such a process, also known as the matrix G, can be expressed through a family of nonnegative square matrices of order n, which is a solution to a system of nonlinear matrix equations. Full article
(This article belongs to the Special Issue Queue and Stochastic Models for Operations Research, 3rd Edition)
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