A Markov chain description of a workstation with infinite capacity

Abstract

We present a discrete-time model for a workstation with infinite operating capacity at which one job arrives at every time instant and starts being processed. The jobs stay in the system for a possibly truncated geometrically distributed time period. We introduce and analyze a Markov chain which gives at any time a complete description of the state of the work on all jobs. Its positively recurrent states are the dyadic numbers in (0, 1]; we give its stationary distribution explicitly. For the busy period analysis of the workstation we study first-entrance problems of this Markov chain.