| Abstract: | Typically the availability, steady-state queue length distribution, and mean queue length of Markov queueing systems subject to random breakdowns are computed by generating function or matrix geometric numerical methods. In this paper we point out that, for single server systems, a simple partition balance approach is easier. We illustrate this observation by deriving expressions for the availability, steady-state queue length distribution, mean queue length, and server utilization of a single server system subject to multi-mode, bi-level, Poisson distributed breakdowns of exponentially distributed duration. A numerical example illustrating some of the relations between these measures is also given. Our setup provides a simple, computationally tractable, Markov model for systems in which breakdowns of different types occur and are repaired at rates dependent on the type and severity of the breakdown. |
