##
**The exponentialization approach to flexible manufacturing system models with general processing times.**
*(English)*
Zbl 0601.90070

Recently flexible manufacturing systems (FMSs) have been modelled as closed networks of queues. In this paper we develop an exponentialization approach to the modeling of FMS networks with general processing times. The idea of the approach is to transform the network into an (approximately) equivalent exponential network, where each station has exponential processing times with state-dependent rates. The approach is formulated as a fixed-point problem. Numerical examples have indicated excellent accuracies of the approach. This approach can also be readily adapted to accommodate limited local buffers and dynamic parts routing.

### MSC:

90B30 | Production models |

90B22 | Queues and service in operations research |

60K20 | Applications of Markov renewal processes (reliability, queueing networks, etc.) |

60K25 | Queueing theory (aspects of probability theory) |

90B10 | Deterministic network models in operations research |

### Keywords:

general service-time distribution; flexible manufacturing systems; closed networks of queues; exponentialization approach; limited local buffers; dynamic parts routing
PDF
BibTeX
XML
Cite

\textit{D. D. Yao} and \textit{J. A. Buzacott}, Eur. J. Oper. Res. 24, 410--416 (1986; Zbl 0601.90070)

Full Text:
DOI

### References:

[1] | Bruell, S. C.; Balbo, G., Computational Algorithms for Closed Queueing Networks (1980), North-Holland: North-Holland New York · Zbl 0452.68044 |

[2] | Cavaille, J. B.; Dubois, D., Heuristic methods based on mean value analysis for flexible manufacturing system performance evaluation, (Proceedings of the 21st IEEE Conference on Decision and Control. Proceedings of the 21st IEEE Conference on Decision and Control, Orlando, Fl. (1982)) · Zbl 0545.90053 |

[3] | Chandy, K. M.; Herzog, U.; Woo, L. S., Approximate analysis of general queueing networks, IBM Journal of Research & Development, 19, 43-49 (1975) · Zbl 0293.90021 |

[4] | Dallery, Y.; David, R., A new approach based on operational analysis for flexible manufacturing systems performance evaluation, (Proceedings of the 22nd IEEE Conference on Decision and Control. Proceedings of the 22nd IEEE Conference on Decision and Control, San Antonio, TX (1983)) |

[5] | Denning, P. J.; Buzen, J. P., The operational analysis of queueing network models, Computer Survey, 10, 3, 225-261 (1978) · Zbl 0385.68038 |

[6] | Gordon, W. J.; Newell, G. F., Closed queueing networks with exponential servers, Operations Research, 15, 252-267 (1967) · Zbl 0168.16603 |

[7] | Marie, R. A., An approximate analytical method for general queueing networks, IEEE Transaction on Software Engineering, 5, 530-538 (1979) · Zbl 0422.90037 |

[8] | Reiser, M., A queueing network analysis of computer communication networks with window flow control, IEEE Transactions on Communication, 27, 1199-1209 (1979) · Zbl 0429.68042 |

[9] | Reiser, M., Mean-value analysis and convolution method for queue-dependent servers in closed queueing networks, Performance Evaluation, 1, 7-18 (1981) · Zbl 0457.60064 |

[10] | Sauer, C. H.; Chandy, K. M., Approximate analysis of central server models, IBM Journal of Research & Development, 19, 301-313 (1975) · Zbl 0302.68080 |

[11] | Shanthikumar, J. G.; Gocmen, M., Heuristic analysis of closed queueing networks, International Journal of Production Research, 21, 675-690 (1983) · Zbl 0542.90039 |

[12] | Shum, A.; Buzen, J. P., The EPF technique: A method for obtaining approximate solution to closed queueing networks with general service times, (Beilner, H.; Gelenbe, E., Measuring, Modeling and Evaluating Computer Systems (1977), North-Holland: North-Holland Amsterdam) |

[13] | Solberg, J. J., A mathematical model of computerized manufacturing systems, (Proceedings of the 4th Internatial Conference on Production Research. Proceedings of the 4th Internatial Conference on Production Research, Tokyo, Japan (1977)) · Zbl 0591.90046 |

[14] | Suri, R., Robustness of queueing network formulas, Journal of the Association for Computer Machinery, 30, 564-594 (1983) · Zbl 0628.68036 |

[15] | Whitt, W., The queueing network analyzer, Bell Systems Technical Journal, 62, 2779-2815 (1983) |

[16] | Whitt, W., Open and closed models for networks of queues, Bell systems Technical Journal, 63, 1911-1979 (1984) · Zbl 0594.90032 |

[17] | Yao, D. D., Modeling a class of state-dependent routing in flexible manufacturing systems, (Proceedings of the 1st ORSA/TIMS Conference on Flexible Manufacturing Systems (1984), University of Michigan: University of Michigan Ann Arbor, MI) |

[18] | Yao, D. D.; Buzacott, J. A., Queueing models for a flexible machining station, Part II: the method of Coxian phases, European Journal of Operational Research, 19, 2, 233-240 (1984) |

[19] | Yao, D. D.; Buzacott, J. A., Modelling the performance of flexible manufacturing systems, International Journal of Production Research (1985), to appear · Zbl 0569.90030 |

[20] | Zangwill, W. I.; Garcia, C. B., Pathways to Solutions, Fixed Points, and Equilibria (1981), Prentice-Hall: Prentice-Hall Englewood Cliff, NJ · Zbl 0512.90070 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.