### Abstract

Queue changes associated with each step of a manufacturing system are modeled by constant vector fields (fluid model of a queueing network). Observing these vector fields at fixed events reduces them to a set of piecewise linear maps. It is proved that these maps show only periodic or eventually periodic orbits. An algorithm to determine the period of the orbits is presented. The dependence of the period on the processing rates is shown for a 3(4)-step, 2-machine problem.

Original language | English (US) |
---|---|

Pages (from-to) | 708-725 |

Number of pages | 18 |

Journal | Mathematics of Operations Research |

Volume | 25 |

Issue number | 4 |

State | Published - Nov 2000 |

### Fingerprint

### ASJC Scopus subject areas

- Management Science and Operations Research
- Mathematics(all)
- Applied Mathematics

### Cite this

*Mathematics of Operations Research*,

*25*(4), 708-725.

**Periodic orbits in a class of re-entrant manufacturing systems.** / Diaz-Rivera, Ivonne; Armbruster, Hans; Taylor, Thomas.

Research output: Contribution to journal › Article

*Mathematics of Operations Research*, vol. 25, no. 4, pp. 708-725.

}

TY - JOUR

T1 - Periodic orbits in a class of re-entrant manufacturing systems

AU - Diaz-Rivera, Ivonne

AU - Armbruster, Hans

AU - Taylor, Thomas

PY - 2000/11

Y1 - 2000/11

N2 - Queue changes associated with each step of a manufacturing system are modeled by constant vector fields (fluid model of a queueing network). Observing these vector fields at fixed events reduces them to a set of piecewise linear maps. It is proved that these maps show only periodic or eventually periodic orbits. An algorithm to determine the period of the orbits is presented. The dependence of the period on the processing rates is shown for a 3(4)-step, 2-machine problem.

AB - Queue changes associated with each step of a manufacturing system are modeled by constant vector fields (fluid model of a queueing network). Observing these vector fields at fixed events reduces them to a set of piecewise linear maps. It is proved that these maps show only periodic or eventually periodic orbits. An algorithm to determine the period of the orbits is presented. The dependence of the period on the processing rates is shown for a 3(4)-step, 2-machine problem.

UR - http://www.scopus.com/inward/record.url?scp=0034313979&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034313979&partnerID=8YFLogxK

M3 - Article

VL - 25

SP - 708

EP - 725

JO - Mathematics of Operations Research

JF - Mathematics of Operations Research

SN - 0364-765X

IS - 4

ER -