Simulation Models of Modified Multiple Vacation Policy for Multi-Server Queuing Systems

Abstract

We consider a multi-server vacation queueing system that operates in the modified multiple vacation policy related to the number of busy servers. The condition for the transition to vacation mode at the time of the release of the server is the lack of customers in the queue and the implementation of one of the restrictions on the number of servers currently in use byand c is the number of servers. When the server returns from vacation it observes the following rule. If there is at least one customer in the queue, the server commences service and serves exhaustively before taking another vacation. If the server finds that there is no queue and the U c -condition is satisfied, then it takes another vacation. Using GPSS World simulation models, we studied the dependencies of the system performance measures on the following parameters: the load factor, coefficient of variation of the inter-arrival times, value of U c , duration of vacations, and number of servers.We tested the simulation models by comparing the results with the known ones obtained by an analytical method. The value of the simulation time, which makes it possible to obtain results