A Steady state behavior of M/M/1 queue with an optional differentiated working vacations and arrival restriction
Abstract
In this paper, we aim to study the steady state behaviour of an M/M/1 queue with an optional differentiated working vacation I and II. After finishing a busy period, the server takes either an optional working vacation I or an optional working vacation II. Customer arrival is restricted when the server is either on an optional working vacation I or an optional working vacation II. The model's stable solution is derived using the probability generating function. Additionally, specific expressions are used to discuss a number of the performance measurements for the provided model. For cost optimization analysis, the Particle Swarm Optimization (PSO) method is also employed to reduce the total cost. We minimized the total cost of providing the best service by using the PSO optimization method. A few numerical examples are provided to illustrate the effects of different arrival rates, service rates, server vacation times, and customer wait times.
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