Performance Evaluation of M/M/1/N Queuing Systems: A Study of Capacity Constraints and Service Dynamics

The M/M/1/N queueing model is a finite-capacity system that is defined by a single server, exponential interarrival and service periods, and a restricted buffer size. This study explores the major performance metrics of the M/M/1/N queueing model. In industries such as telecommunications, computer networks, and industrial systems, where the number of clients that may be served is limited due to resource restrictions, such systems are often used. The study is centered on the calculation and interpretation of essential performance indicators, which include steady-state probabilities, the average number of customers in the system, the utilization of the system, the average waiting time, and the likelihood of losing consumers owing to restrictions in the system's capacity. In order to highlight the impact that system characteristics like arrival rate, service rate, and buffer size have on the overall performance of the system, numerical examples are supplied. The findings provide valuable insights into the use of stochastic demand and service conditions to the design of systems and the planning of capacity.