ANALYSIS OF A MULTI TYPE SERVICE OF A NON-MARKOVIAN QUEUE WITH BREAKDOWN, DELAY TIME AND OPTIONAL VACATION

We consider an M /G /1 queuing system with k-types of service, random breakdowns, delay times for repairs to start and a second optional vacation. All arriving customers may choose k either of type j services with probability p(j) where Sigma(k)(j=1) p(j) = 1, j is an element of {1, 2, 3, ... , k}. When the system becomes empty, the server goes for regular vacation and at the end of the first vacation the server may take a second optional vacation with pro (1 - theta). bability theta, otherwise he remains in the system with probability. The system may breakdown at random, its repairs do not start immediately and there is a delay time. The delay times and the repair times follow a general distribution. Using supplementary variable technique, we derive the probability generating function for the number of customers in the system, the average number of customers in the system and the average waiting time of customers in the system. Particular case is deduced to check the validity of the present model with already existing models. Numerical examples are also provided.