A Study on M/G/1 Queueing System with Extended Vacation, Random Breakdowns and General Repair

Abstract

This Paper study about a Non Markovian queueing model with general vacation, Random breakdown followed by a repair process .An additional aspect of Extended vacation is considered here. After a service completion, the server takes a vacation. The server has the option to take an extended vacation after general vacation or the server may continue to stay in the system to serve the customers. It is assumed that customers arrive at the system one by one. Vacation time, extended vacation time and repair time follows general distribution.Steady state results in explicit and closed form in terms of the probability generating functions for the number of customers in the queue, average number of customers, and the average waiting time in the queue are derived.