Markov Chain-Based Models in Queuing Theory: An Operations Research Perspective - Kumar, Sharad; Renuka; Kumar, Vikas (RESEARCH HUB International Multidisciplinary Research Journal, 2025)
Queuing theory is a fundamental discipline within operations research that focuses on analyzing systems characterized by congestion and waiting lines. Markov chain-based models offer a mathematically rigorous and probabilistically sound framework for modeling such systems, particularly those governed by random arrival and service processes. This paper examines key queuing configurations—including M/M/1, M/M/c, M/M/1/K, and Jackson Networks—using continuous-time Markov chains (CTMCs) to derive performance metrics such as system utilization, waiting time, queue length, and blocking probability. Analytical solutions were complemented by simulation models to validate findings under varied operational scenarios. Results reveal that Markovian models accurately predict system behavior under stable conditions and provide actionable insights for resource allocation and capacity planning. However, the study also identifies limitations in addressing non-exponential input distributions and complex system dynamics. Consequently, it advocates for hybrid approaches that combine Markov models with simulation and machine learning for enhanced scalability and adaptability. The findings reinforce the enduring relevance of Markov chain-based queuing models while pointing toward future directions for intelligent operations research.