Transient Solution of an M[X]/G/1 Queueing Model with Bernoulli Feed Back, Random Breakdowns, Bernoulli Schedule Server Vacation and Restricted Admissibility

This paper analyze an M[X]/G/1 queue with Bernoulli feed back random server breakdowns, Bernoulli schedule server vacation and restricted admissibility policy. Customers arrive in batches following compound Poisson process and are served one by one according to first come first served basis. The service time follows general (arbitrary) distribution. The customer feedback to the tail of original queue for repeating the service until the service be successful with probability p or the customer departs the system if service be successful with probability 1-p. After completion of a service the server may go for a vacation with probability θ or continue staying in the system, to serve a next customer, if any with probability 1−θ. Unlike the usual batch arrival queueing model, there is a restriction over the admissibility of batch arrivals in which not all the arriving batches are allowed to join the system at all times. This restriction admissibility policy is different for different states of the system. The system may breakdown at random in accordance with Poisson process, while the repair time follows exponential distribution. We obtain the time dependent probability generating function in terms of their Laplace transforms and the corresponding steady state results explicitly. Also we derive the system performance measures like average number of customers in the queue and the average waiting time in closed form.