Minimizing Delays in M/M/1/K/N Orbiting Queue through Server Vacations and Adjustable Arrival Rates

Analytical performance evaluation and delay optimisation

Résumé

This paper examines a finite capacity single server orbiting queueing model in which the server takes vacations during inactive periods. The model integrates adjustable arrival rates, developing a realistic representation of real-world systems and considering the mutual dependence of service and arrival processes. The steady-state probability equations are solved recursively and explicit iterative formulas are obtained. Customer arrive according to Poisson process with tunable arrival rates, classified as faster or slower, while blocked customers enter an orbit and attempt service again. The effectiveness of the measures for the systems and specific instances of the model are discussed.  Numerical findings have been produced and presented in the form of tables. The results demonstrate that vacations and adjustable arrivals may be proactively managed to reduce delays and improve cost-effective service for both customers and servers.