Unreliable server M G 1 queueing system with Bernoulli feedback, repeated attempts, modified vacation, phase repair and discouragement

الملخص EN

This paper deals with unreliable M / G / 1 queueing system with modified vacation, repeated attempts and K-phase repair.

The jobs arrive in Poisson fashion.

On finding the server busy, under setup, under repair or on vacation, the jobs either join to the orbit or balk from the system.

The jobs in the orbit repeat their request for service after some random time.

The inter retrial time of each job is general distributed.

The jobs are served according to FCFS discipline.

After receiving the unsuccessful service, the job may immediately join the tail of the original queue with some probability p or may depart from the system with probability q( = 1-p).

Accidental (operational) breakdown of the server is also considered.

There is a provision of kphase repairs to restore the server to the state as before failure.

First phase repair is essential whereas other (K-1) phases are optional.

The repairman, who restores the server, requires some time to start the first phase of repair ; this time is called as setup time.

The service time, setup time and repair time of each phase are independent and general distributed.

On finding the orbit empty, the server goes on at most J vacations repeatedly until at least one job is recorded in the orbit.

The probability generating function of steady state queue size at random epoch is obtained using supplementary variable technique.

Various models studied earlier are discussed as special cases of our model, by appropriate choice of parameter values.

Some queueing as well as reliability indices to predict the behaviour of the system are also derived.

The effects of various system parameters on the system performance indices are also examined numerically.