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  • Article
  • Open Access
1 Citations
2,510 Views
13 Pages

Entropy Analysis of a Flexible Markovian Queue with Server Breakdowns

  • Messaoud Bounkhel,
  • Lotfi Tadj and
  • Ramdane Hedjar

3 September 2020

In this paper, a versatile Markovian queueing system is considered. Given a fixed threshold level c, the server serves customers one a time when the queue length is less than c, and in batches of fixed size c when the queue length is greater than or...

  • Feature Paper
  • Article
  • Open Access
1 Citations
870 Views
19 Pages

6 November 2025

This paper analyzes a finite-capacity Markovian queueing system with two customer types, each assigned to a separate buffer, and a single alternating server whose service priority is dynamically controlled by a queue-length-based threshold policy. Th...

  • Article
  • Open Access
5 Citations
5,257 Views
11 Pages

A New Method for Markovian Adaptation of the Non-Markovian Queueing System Using the Hidden Markov Model

  • Ilija Tanackov,
  • Olegas Prentkovskis,
  • Žarko Jevtić,
  • Gordan Stojić and
  • Pamela Ercegovac

28 June 2019

This manuscript starts with a detailed analysis of the current solution for the queueing system M/Er/1/∞. In the existing solution, Erlang’s service is caused by Poisson’s arrival process of groups, but not individual clients. The s...

  • Article
  • Open Access
10 Citations
3,979 Views
12 Pages

7 March 2019

A flexible single-server queueing system is considered in this paper. The server adapts to the system size by using a strategy where the service provided can be either single or bulk depending on some threshold level c. If the number of customers in...

  • Article
  • Open Access
6 Citations
4,532 Views
22 Pages

Markovian Demands on Two Commodity Inventory System with Queue-Dependent Services and an Optional Retrial Facility

  • K. Jeganathan,
  • M. Abdul Reiyas,
  • S. Selvakumar,
  • N. Anbazhagan,
  • S. Amutha,
  • Gyanendra Prasad Joshi,
  • Duckjoong Jeon and
  • Changho Seo

13 June 2022

The use of a Markovian inventory system is a critical part of inventory management. The purpose of this study is to examine the demand for two commodities in a Markovian inventory system, one of which is designated as a major item (Commodity-I) and t...

  • Article
  • Open Access
464 Views
28 Pages

Analysis of a Crowdsourcing Markovian Queue with Phase-Type and Imperfect Service, Working Vacations, Breakdown, and Repair

  • N. Arulmozhi,
  • Aliakbar Montazer Haghighi,
  • G. Ayyappan and
  • G. Archana @ Gurulakshmi

23 November 2025

Analysis of a crowdsourcing Markovian queue with phase-type service is considered in this paper. In this model, a customer not only receives service but also assists in delivery. In other words, in a retail environment, while some customers shop in-s...

  • Article
  • Open Access
5 Citations
1,210 Views
16 Pages

Transient GI/MSP/1/N Queue

  • Andrzej Chydzinski

22 September 2024

A non-zero correlation between service times can be encountered in many real queueing systems. An attractive model for correlated service times is the Markovian service process, because it offers powerful fitting capabilities combined with analytical...

  • Article
  • Open Access
8 Citations
2,772 Views
15 Pages

On Probability Characteristics for a Class of Queueing Models with Impatient Customers

  • Yacov Satin,
  • Alexander Zeifman,
  • Alexander Sipin,
  • Sherif I. Ammar and
  • Janos Sztrik

15 April 2020

In this paper, a class of queueing models with impatient customers is considered. It deals with the probability characteristics of an individual customer in a non-stationary Markovian queue with impatient customers, the stationary analogue of which w...

  • Article
  • Open Access
14 Citations
3,069 Views
27 Pages

Performance Evaluation of the Priority Multi-Server System MMAP/PH/M/N Using Machine Learning Methods

  • Vladimir Vishnevsky,
  • Valentina Klimenok,
  • Alexander Sokolov and
  • Andrey Larionov

14 December 2021

In this paper, we present the results of a study of a priority multi-server queuing system with heterogeneous customers arriving according to a marked Markovian arrival process (MMAP), phase-type service times (PH), and a queue with finite capacity....

  • Article
  • Open Access
18 Citations
7,154 Views
18 Pages

14 June 2018

In this paper, we discuss a non-Markovian batch arrival general bulk service single-server queueing system with server breakdown and repair, a stand-by server, multiple vacation and re-service. The main server’s regular service time, re-service...

  • Feature Paper
  • Article
  • Open Access
12 Citations
2,905 Views
30 Pages

30 September 2022

Queueing models have proven to be very useful in real-life applications to enable the practitioners to optimize the limited resources to conduct their businesses as well as offer services efficiently. In general, we can group such applications into t...

  • Article
  • Open Access
1,989 Views
11 Pages

This paper studies a Markovian queue with multiple working vacations and controlled vacation interruption. If there are at least N customers waiting upon completion of a service at a lower rate, the vacation is interrupted and the server returns to t...

  • Article
  • Open Access
12 Citations
3,112 Views
26 Pages

MMAP/(PH,PH)/1 Queue with Priority Loss through Feedback

  • Divya Velayudhan Nair,
  • Achyutha Krishnamoorthy,
  • Agassi Melikov and
  • Sevinj Aliyeva

29 July 2021

In this paper, we consider two single server queueing systems to which customers of two distinct priorities (P1 and P2) arrive according to a Marked Markovian arrival process (MMAP). They are served according to two distinct phase type distributions....

  • Article
  • Open Access
25 Citations
4,970 Views
16 Pages

Priority Multi-Server Queueing System with Heterogeneous Customers

  • Valentina Klimenok,
  • Alexander Dudin and
  • Vladimir Vishnevsky

4 September 2020

In this paper, we analyze a multi-server queueing system with heterogeneous customers that arrive according to a marked Markovian arrival process. Customers of two types differ in priorities and parameters of phase type distribution of their service...

  • Article
  • Open Access
394 Views
22 Pages

9 January 2026

This study focuses on forecasting and optimizing the performance of a real-world object modelled by a multi-server queueing system that processes two types of users: primary (new) users and repeating users. The repeating users are those who succeeded...

  • Article
  • Open Access
7 Citations
2,367 Views
21 Pages

Retrial BMAP/PH/N Queueing System with a Threshold-Dependent Inter-Retrial Time Distribution

  • Valentina I. Klimenok,
  • Alexander N. Dudin,
  • Vladimir M. Vishnevsky and
  • Olga V. Semenova

16 January 2022

In this paper, we study a multi-server queueing system with retrials and an infinite orbit. The arrival of primary customers is described by a batch Markovian arrival process (BMAP), and the service times have a phase-type (PH) distribution. Previous...

  • Article
  • Open Access
3 Citations
3,161 Views
17 Pages

6 September 2019

We consider a queueing network with a finite number of nodes and servers moving between the nodes as a model of car sharing. The arrival process of customers to various nodes is defined by a marked Markovian arrival process. The customer that arrives...

  • Article
  • Open Access
5 Citations
4,079 Views
20 Pages

30 January 2021

The imbalanced distribution of shared bikes in the dockless bike-sharing system (a typical example of the resource-sharing system), which may lead to potential customer churn and lost profit, gradually becomes a vital problem for bike-sharing firms a...

  • Feature Paper
  • Article
  • Open Access
8 Citations
3,097 Views
16 Pages

Steady State Analysis of Impulse Customers and Cancellation Policy in Queueing-Inventory System

  • V. Vinitha,
  • N. Anbazhagan,
  • S. Amutha,
  • K. Jeganathan,
  • Gyanendra Prasad Joshi,
  • Woong Cho and
  • Suseok Seo

28 November 2021

This article discusses the queueing-inventory model with a cancellation policy and two classes of customers. The two classes of customers are named ordinary and impulse customers. A customer who does not plan to buy the product when entering the syst...

  • Article
  • Open Access
836 Views
22 Pages

Transient Analysis of a Continuous-Service Markovian Queueing Model with Offline and Online Customers

  • Ramupillai Sudhesh,
  • Paulsamy Balakrishnan and
  • Ratchaga Dass Sebasthi Priya

9 July 2025

This study examines a single-server Markovian queueing system featuring continuous service and an infinite number of customers at both ends—namely, offline and online clients. Offline customers are conventional clients who arrive at the system...

  • Feature Paper
  • Article
  • Open Access
3 Citations
1,465 Views
15 Pages

22 April 2023

We consider a non-standard class of Markovian time: varying infinite capacity queues with possibly heterogeneous servers and impatience. We assume that during service time, a customer may switch to the faster server (with no delay), when such a serve...

  • Article
  • Open Access
12 Citations
2,519 Views
16 Pages

This work considers a preemptive priority queueing system with vacation, where the single server may break down with imperfect coverage. Various combinations of server vacation priority queueing models have been studied by many scholars. A common ass...

  • Article
  • Open Access
12 Citations
3,153 Views
11 Pages

30 July 2019

Consideration is given to the nonstationary analogue of M / M / 1 queueing model in which the service happens only in batches of size 2, with the arrival rate λ ( t ) and the service rate μ ( t ) . One proposes a new...

  • Feature Paper
  • Review
  • Open Access
25 Citations
4,276 Views
25 Pages

14 February 2020

This paper is largely a review. It considers two main methods used to study stability and to obtain appropriate quantitative estimates of perturbations of (inhomogeneous) Markov chains with continuous time and a finite or countable state space. An ap...

  • Article
  • Open Access
17 Citations
3,274 Views
17 Pages

Analysis of MAP/PH/1 Queueing System with Degrading Service Rate and Phase Type Vacation

  • Alka Choudhary,
  • Srinivas R. Chakravarthy and
  • Dinesh C. Sharma

25 September 2021

Degradation of services arises in practice due to a variety of reasons including wear-and-tear of machinery and fatigue. In this paper, we look at MAP/PH/1-type queueing models in which degradation is introduced. There are several ways to incorporate...

  • Article
  • Open Access
10 Citations
2,860 Views
11 Pages

A Multi-Type Queueing Inventory System—A Model for Selection and Allocation of Spectra

  • Thulaseedharan Salini Sinu Lal,
  • Varghese Chaukayil Joshua,
  • Vladimir Vishnevsky,
  • Dmitry Kozyrev and
  • Achyutha Krishnamoorthy

24 February 2022

The model discussed in this paper provides an efficient mechanism for the selection and allocation of available limited spectra for transmission of heterogeneous data in a network. The data packets (customers), belonging to different classes, arrive...

  • Article
  • Open Access
19 Citations
3,237 Views
20 Pages

27 December 2020

The problem considered is the computation of the (limiting) time-dependent performance characteristics of one-dimensional continuous-time Markov chains with discrete state space and time varying intensities. Numerical solution techniques can benefit...

  • Article
  • Open Access
1 Citations
2,616 Views
12 Pages

On Two Interacting Markovian Queueing Systems

  • Valeriy A. Naumov,
  • Yuliya V. Gaidamaka and
  • Konstantin E. Samouylov

1 September 2019

In this paper, we study a Markovian queuing system consisting of two subsystems of an arbitrary structure. Each subsystem generates a multi-class Markovian arrival process of customers arriving to the other subsystem. We derive the necessary and suff...

  • Article
  • Open Access
2 Citations
7,528 Views
23 Pages

30 April 2024

In non-Markovian tandem queueing networks the output process of one site, which is the input process to the next site, is not renewal. Consequently, the correlation analysis of that output processes is essential when studying such networks. A correla...

  • Article
  • Open Access
24 Citations
3,446 Views
18 Pages

22 August 2022

In this research, we look at the work associated with the encouraged arrival line with feedback, balking and maintaining reneged clients. We analyse the quality control policy for the Markovian model using an iterative method to the nth customer in t...

  • Article
  • Open Access
9 Citations
3,107 Views
18 Pages

24 June 2023

This paper investigates the concept of a Markovian queueing model with heterogeneous, intermittently available servers with feedback under a hybrid vacation policy. Both the asymmetric transition representation and the hybrid vacation policy are addr...

  • Article
  • Open Access
7 Citations
2,448 Views
24 Pages

Queueing System with Potential for Recruiting Secondary Servers

  • Srinivas R. Chakravarthy,
  • Alexander N. Dudin,
  • Sergey A. Dudin and
  • Olga S. Dudina

26 January 2023

In this paper, we consider a single server queueing system in which the arrivals occur according to a Markovian arrival process (MAP). The served customers may be recruited (or opted from those customers’ point of view) to act as secondary servers to...

  • Feature Paper
  • Article
  • Open Access
11 Citations
3,778 Views
22 Pages

Analysis of a Discrete-Time Queueing Model with Disasters

  • Mustafa Demircioglu,
  • Herwig Bruneel and
  • Sabine Wittevrongel

17 December 2021

Queueing models with disasters can be used to evaluate the impact of a breakdown or a system reset in a service facility. In this paper, we consider a discrete-time single-server queueing system with general independent arrivals and general independe...

  • Article
  • Open Access
2 Citations
1,793 Views
18 Pages

Modeling and Estimation of Traffic Intensity in M/M/1 Queueing System with Balking: Classical and Bayesian Approaches

  • Bhaskar Kushvaha,
  • Dhruba Das,
  • Asmita Tamuli,
  • Dibyajyoti Bora,
  • Mrinal Deka and
  • Amit Choudhury

This article focuses on both classical and Bayesian inference of traffic intensity in a single-server Markovian queueing model considering balking. To reflect real-world situations, the article introduces the concept of balking, where customers opt n...

  • Article
  • Open Access
8 Citations
3,810 Views
25 Pages

10 June 2023

The problem of optimal scheduling in a system with parallel queues and a single server has been extensively studied in queueing theory. However, such systems have mostly been analysed by assuming homogeneous attributes of arrival and service processe...

  • Article
  • Open Access
8 Citations
3,329 Views
16 Pages

Performance Analysis of Hybrid MTS/MTO Systems with Stochastic Demand and Production

  • Dieter Fiems,
  • Eline De Cuypere,
  • Koen De Turck and
  • Dieter Claeys

2 November 2020

We present a comprehensive numerical approach with reasonably light complexity in terms of implementation and computation for assessing the performance of hybrid make-to-stock (MTS)/make-to-order (MTO) systems. In such hybrid systems, semi-finished p...

  • Article
  • Open Access
6 Citations
4,020 Views
21 Pages

New Analytic Solutions of Queueing System for Shared–Short Lanes at Unsignalized Intersections

  • Ilija Tanackov,
  • Darko Dragić,
  • Siniša Sremac,
  • Vuk Bogdanović,
  • Bojan Matić and
  • Milica Milojević

6 January 2019

Designing the crossroads capacity is a prerequisite for achieving a high level of service with the same sustainability in stochastic traffic flow. Also, modeling of crossroad capacity can influence on balancing (symmetry) of traffic flow. Loss of pri...

  • Article
  • Open Access
2,001 Views
10 Pages

12 April 2023

The Hawkes process, which is generally defined for the continuous-time setting, can be described as a self-exciting simple point process with a clustering effect, whose jump rate depends on its entire history. Due to past events determining future de...

  • Article
  • Open Access
1 Citations
1,306 Views
20 Pages

The mathematical framework presented in this article focuses on the controlled-transmission protocol’s asynchronous process of bandwidth allocation for the target virtual connection implemented under competition for communication resources. The...

  • Article
  • Open Access
4 Citations
2,094 Views
20 Pages

3 January 2024

Heterogeneous systems of limited capacity have general applications in manufacturing, but also in logistic or service systems due to the differences in server or workstation performance or work assignment; this is in close relationship with system fl...

  • Article
  • Open Access
3 Citations
2,452 Views
24 Pages

2 December 2023

We discuss two queueing-inventory systems with catastrophes in the warehouse. Catastrophes occur according to the Poisson process and instantly destroy all items in the inventory. The arrivals of the consumer customers follow a Markovian arrival proc...

  • Article
  • Open Access
5 Citations
3,871 Views
16 Pages

25 May 2020

This paper proposes a real-time chain and a novel embedded Markovian queueing model with variable bulk arrival (VBA) and variable bulk service (VBS) in order to establish and assure a theoretical foundation to design a blockchain-based real-time syst...

  • Article
  • Open Access
9 Citations
4,996 Views
21 Pages

17 March 2023

In this paper, we consider a queueing system consisting of two multi-server subsystems that is designed for the service of clients arriving at a system according to a Markovian arrival process (MAP). Arriving clients receive information about the num...

  • Article
  • Open Access
8 Citations
2,330 Views
12 Pages

Queueing-Inventory System for Two Commodities with Optional Demands of Customers and MAP Arrivals

  • N. Anbazhagan,
  • Gyanendra Prasad Joshi,
  • R. Suganya,
  • S. Amutha,
  • V. Vinitha and
  • Bhanu Shrestha

25 May 2022

This research analyses the performance of a perishable queueing-inventory system for two commodities with optional customers demands. We assume in the article that all customers who come to the system can only purchase the first item or the second it...

  • Article
  • Open Access
11 Citations
3,600 Views
25 Pages

Analysis of Stock-Dependent Arrival Process in a Retrial Stochastic Inventory System with Server Vacation

  • C. Sugapriya,
  • M. Nithya,
  • K. Jeganathan,
  • N. Anbazhagan,
  • Gyanendra Prasad Joshi,
  • Eunmok Yang and
  • Suseok Seo

17 January 2022

The present study deals with the stock-dependent Markovian demand of a retrial queueing system with a single server and multiple server vacation. The items are restocked under a continuous review (s,Q) ordering policy. When there is no item in the sy...

  • Article
  • Open Access
8 Citations
2,491 Views
26 Pages

Queueing-Inventory with One Essential and m Optional Items with Environment Change Process Forming Correlated Renewal Process (MEP)

  • Jaison Jacob,
  • Dhanya Shajin,
  • Achyutha Krishnamoorthy,
  • Vladimir Vishnevsky and
  • Dmitry Kozyrev

29 December 2021

We consider a queueing inventory with one essential and m optional items for sale. The system evolves in environments that change randomly. There are n environments that appear in a random fashion governed by a Marked Markovian Environment change pro...

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