Models of production lines as Quasi-Birth–Death processes

The aim of this work is to illustrate the suitability of quasi–birth–death processes (QBDs) for stochastic modelling of production lines. With this end in mind, first, an introduction to QBDs is made, so that the reader who may not be acquainted with this aspect of stochastic modelling may be introduced to the basics of the topic. Then, a formal definition of QBD is given and the QBDs are contrasted with the traditional birth–death processes. Later, examples of QBD models pertaining to production lines are presented. The rationale of this exposition is to show how QBDs present themselves within the context of production lines and to show the kind of work that needs to be performed to fully specify the corresponding QBDs. By compiling the aforementioned models, the strength of QBDs in modelling production lines is demonstrated.