Modelling and Performance Analysis of Telecommunication Queuing Systems Using Continuous-Time Markov Chains: A Condensed Review

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.