An M|Ph|1 queueing system subject to breakdowns with non-homogeneous interarrival, service, life and repair times

In this paper, an MIPhll queueing system with server breakdowns is studied for both the finite and infinite buffer case. Jobs arrive at the server according to a non-homogeneous Poisson process with a non-homogeneous service time distribution which is of phase type. The life-times of the server are non-homogeneously exponentially distributed and the repair times of the server are non-homogeneously phase type distributed. The non-homogeneity of these distributions is due to the dependence of their parameters on the number of jobs in the system as well as the interdependence of these parameters. For these models, an explicit recursive matrix representation of the stationary queue length distribution is obtained