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Modelling and Performance Analysis of Telecommunication Queuing Systems Using Continuous-Time Markov Chains: A Condensed Review
Subject area: Science,Engineering and Technology · Area of research: Continuous-Time Markov Chains
DOI: 10.64388/IREV10I4-1723674
Abstract
This paper presents a comprehensive modelling and performance analysis of telecommunication queuing systems using Continuous-Time Markov Chains (CTMCs). The research addresses the stochastic nature of packet arrivals and service processes by developing mathematical representations for classic queuing models: M/M/1, M/M/c, and M/M/1/K. Steady-state probability distributions are derived through the construction of transition rate matrices and the solution of global balance equations. Key performance metrics—system utilization, mean queue length, waiting time, and blocking probability—are analytically evaluated. The study investigates the impact of traffic intensity on system stability and demonstrates the efficacy of CTMC-based analysis in capacity planning and resource allocation. Extensive numerical results show that multiserver systems offer significant performance improvements through statistical multiplexing, while finite buffer systems provide stability at the cost of blocking probability. The paper also analyses advanced topics such as priority queues, guard channels in cellular networks, the impact of service time variability, and overflow traffic peakedness. The findings provide foundational tools for network engineers to optimize resource allocation and enhance Quality of Service (QoS) in dynamic telecommunication environments.
Keywords
Continuous-Time Markov Chains, Queuing Theory, Telecommunications, Erlang Formulas, Performance Modeling, Stochastic Processes, Network Design.
References
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[2] R. B. Cooper, Introduction to Queueing Theory, 2nd ed. North-Holland, 1981.
[3] A. K. Erlang, “The theory of probabilities and telephone conversations,” Nyt Tidsskrift for Matematik B, vol. 20, pp. 33–39, 1909.
[4] A. K. Erlang, “Solution of some problems in the theory of probabilities of significance in automatic telephone exchanges,” Elektroteknikeren, vol. 13, 1917.
[5] Gross, J. F. Shortle, J. M. Thompson, and C. M. Harris, Fundamentals of Queueing Theory, 4th ed. John Wiley & Sons, 2008.
[6] M. Harchol-Balter, Performance Modeling and Design of Computer Systems: Queueing Theory in Action. Cambridge University Press, 2013.
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[10] L. Kleinrock, Queueing Systems, Volume I: Theory. John Wiley & Sons, 1975.
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[12] M. F. Neuts, Matrix-Geometric Solutions in Stochastic to Stochastic-Process Limits and Their Application to Models: An Algorithmic Approach. Johns Hopkins University Press, Springer, 2002.
[13] S. M. Ross, Introduction to Probability Models, 11th ed. and arXiv preprint. Academic Press, 2014.
[14] W. Whitt, Stochastic-Process Limits: An Introduction
[15] M. Zukerman, “Introduction to Queueing Theory and Stochastic Teletraffic Models,” arXiv:1307.2968, 2013. arXiv
How to cite this paper
@article{1723674,
author = {Owoade Praise Oluwapelumi, Ini Adinya, Folorunso Tobi Emmanuel},
title = {Modelling and Performance Analysis of Telecommunication Queuing Systems Using Continuous-Time Markov Chains: A Condensed Review},
journal = {Iconic Research And Engineering Journals},
year = {2026},
volume = {10},
number = {4},
pages = {371-382},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1723674.pdf},
abstract = {This paper presents a comprehensive modelling and performance analysis of telecommunication queuing systems using Continuous-Time Markov Chains (CTMCs). The research addresses the stochastic nature of packet arrivals and service processes by developing mathematical representations for classic queuing models: M/M/1, M/M/c, and M/M/1/K. Steady-state probability distributions are derived through the construction of transition rate matrices and the solution of global balance equations. Key performance metrics—system utilization, mean queue length, waiting time, and blocking probability—are analytically evaluated. The study investigates the impact of traffic intensity on system stability and demonstrates the efficacy of CTMC-based analysis in capacity planning and resource allocation. Extensive numerical results show that multiserver systems offer significant performance improvements through statistical multiplexing, while finite buffer systems provide stability at the cost of blocking probability. The paper also analyses advanced topics such as priority queues, guard channels in cellular networks, the impact of service time variability, and overflow traffic peakedness. The findings provide foundational tools for network engineers to optimize resource allocation and enhance Quality of Service (QoS) in dynamic telecommunication environments.},
keywords = {Continuous-Time Markov Chains, Queuing Theory, Telecommunications, Erlang Formulas, Performance Modeling, Stochastic Processes, Network Design.},
month = {October},
doi = {https://doi.org/10.64388/IREV10I4-1723674}
}