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

Abstract

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.

[Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following supplementary resources: datasets, additional tables, detailed proofs]

Keywords:

• Markov model
• batch machines
• production lines
• a finite buffer
• ergodicity
• conservation of flow
• control policies
• deadlock
• production control

Acknowledgements

The authors wish to thank the department editor, anonymous reviewers, and the editor-in-chief for their valuable comments and suggestions. The authors are grateful to Deborah Goodman and Anita Chambers, who proofread the article. This research was partially supported by Start-up Grant under Grant No. SUG3/06 and Academic Research Funding Tier 1 by Ministry of Education in Singapore under Grant No. RG12/07.