Analysis of a synchronization station for the performance evaluation of a kanban system with a general arrival process of demands

The kanban system has attracted wide interest in recent years, and a lot of work has been devoted to the modeling of such systems, as well as to methods to evaluate their performance. Especially, in a previous work, we proposed an analytical method to evaluate the performance of a kanban system producing a single part type; we assumed that demands for the finished product arrive in single unit, according to a Poisson process. The present paper proposes an extension of this method to the case where the demands arrive according to a general process. We are more particularly interested in the analysis in isolation of the synchronization station between the finished parts of the system and the external demands. This leads to the resolution of a quasi-birth-and-death process with an infinite number of states and with a very regular structure. We thus propose a matrix-geometric solution of this problem.