Journal of Computations & Modelling

M[X] / G / 1 with Bernoulli Schedule Server Vacation Random Break Down and second optional Repair

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• Abstract

  We present a single server subject to random breakdowns followed by a repair and Bernoulli scheduled server vacation. The customers arrive in batches and whose service being provided one by one according to first come first served discipline. Upon completion of a service, the server will go for vacation with probability p or remain staying back in the system for providing the service to the next customer with probability 1-p, if any. Both service time and vacation time follow general (arbitrary) distribution. The system may experience breakdown at random time and the breakdowns occur according to Poisson stream. Once the server breakdown, it must be send to repair process immediately. The most realistic aspect in modeling of a unreliable server, multi optional repair may be required. If the server could not be repaired or restored with the first essential repair, subsequent repairs are needed for the restoration of the server. Both essential and optional repair times follow exponential distribution. We obtain the time dependent probability generating functions in terms of their Laplace transforms and the corresponding steady state results explicitly. Also we derive the average number of customers in the queue and the average waiting time in closed form.