Modeling and analysis of two unreliable batch machines with a finite buffer in between

This article considers two unreliable batch machines with a finite buffer in between. Batch machines process a set of parts simultaneously; the maximum number in the set is the size of the machine. The purpose of this article is threefold: (i) to present a model of these systems and its exact analysis; (ii) to present new qualitative insights and interpretations of system behavior; and (iii) to present the comparison between full-batch and partial-batch policies. We demonstrate new generalized conservation of flow and flow-rate-idle-time relationships. Various performance measures of interest such as production rate, mean size of batches served in each machine, machine efficiencies, probabilities of blocking and starvation, and expected in-process inventory are presented. A reversibility property is demonstrated and deadlock behavior is described. The effect of the size of machines on performance measures is examined, new phenomena and insights are observed, and possible interpretations are presented.