Single server queue with server breakdown including priority and varying rates

الملخص EN

A single server queueing system with service interruption due to failure of the major/minor service unit has been studied.

The job’s inter-arrival time as well as the failure time and the repair time of the major/minor service unit are assumed to be exponentially distributed.

The arrival of the jobs to the service facility consisting of major and minor units depends upon the state of the server which may be either operational (partially operational) mode with both units (only major unit) functioning well or in breakdown mode due to failure of the major unit or both units.

The failure of service units may occur individually or due to some common cause.

The repair rate of the major service unit is also affected with the state of the minor service unit.

The repair of the major unit is given pre-emptive priority over the repair of the minor unit.

The steady state queue size distribution for various states has been obtained by using generating function method.

The average number of jobs in various states, server availability etc.

have been derived explicitly.