M/M/1 Non-preemptive Priority Queuing System with Multiple Vacations and Vacation Interruptions

Non-preemptive priority queue system is a type of where customers with higher priorities cannot interrupt low one while being served. High consumers will still be at the head queue. This article discusses non-preemptive multiple working vacations, vacation can interrupted. Customers are classified into two classes, namely class I (non-preemptive customers) and II, exponentially distributed service rates. receive services slower rate than during normal busy periods when they enter it on vacation. Suppose other waiting in after completing In that case, interrupted, switch to period rate. The model's performance measurements obtained using complementary variable method analyzing state change equation following birth death processes find probability generating function for both classes. results numerical solution show expected value number time reduced times (θ) (μ_0 ) increase.