### Abstract

This paper presents two algorithms to analytically approximate work in process (WIP)-dependent inter-departure times for tandem queues composed of a series of M/M/1 systems. The first algorithm is used for homogeneous tandem queues, the second for such with bottlenecks. Both algorithms are based on the possible combinations of distributing the WIP on the queues. For each combination the time to the next departure is estimated. A weighted average of all estimated times of each WIP level is calculated to get the expected mean inter-departure time. The generated inter-departure times are used in a simple model of the tandem queue. The inter-departure times, the average WIP and average cycle time of the tandem queue and the simple model are compared in several tandem queue parameterizations. Results show only a small error between the simple model and the tandem queue, rendering this approach applicable in many applications.

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

Pages (from-to) | 1188-1196 |

Number of pages | 9 |

Journal | Simulation |

Volume | 90 |

Issue number | 10 |

DOIs | |

State | Published - Oct 12 2014 |

### Fingerprint

### Keywords

- discrete event simulation
- simplification
- WIP-dependent inter-departure times

### ASJC Scopus subject areas

- Software
- Computer Graphics and Computer-Aided Design
- Modeling and Simulation

### Cite this

**Simplification of des models of M/M/1 tandem queues by approximating WIP-dependent inter-departure times.** / Huber, Daniel; Fowler, John; Armbruster, Hans.

Research output: Contribution to journal › Article

*Simulation*, vol. 90, no. 10, pp. 1188-1196. https://doi.org/10.1177/0037549714546665

}

TY - JOUR

T1 - Simplification of des models of M/M/1 tandem queues by approximating WIP-dependent inter-departure times

AU - Huber, Daniel

AU - Fowler, John

AU - Armbruster, Hans

PY - 2014/10/12

Y1 - 2014/10/12

N2 - This paper presents two algorithms to analytically approximate work in process (WIP)-dependent inter-departure times for tandem queues composed of a series of M/M/1 systems. The first algorithm is used for homogeneous tandem queues, the second for such with bottlenecks. Both algorithms are based on the possible combinations of distributing the WIP on the queues. For each combination the time to the next departure is estimated. A weighted average of all estimated times of each WIP level is calculated to get the expected mean inter-departure time. The generated inter-departure times are used in a simple model of the tandem queue. The inter-departure times, the average WIP and average cycle time of the tandem queue and the simple model are compared in several tandem queue parameterizations. Results show only a small error between the simple model and the tandem queue, rendering this approach applicable in many applications.

AB - This paper presents two algorithms to analytically approximate work in process (WIP)-dependent inter-departure times for tandem queues composed of a series of M/M/1 systems. The first algorithm is used for homogeneous tandem queues, the second for such with bottlenecks. Both algorithms are based on the possible combinations of distributing the WIP on the queues. For each combination the time to the next departure is estimated. A weighted average of all estimated times of each WIP level is calculated to get the expected mean inter-departure time. The generated inter-departure times are used in a simple model of the tandem queue. The inter-departure times, the average WIP and average cycle time of the tandem queue and the simple model are compared in several tandem queue parameterizations. Results show only a small error between the simple model and the tandem queue, rendering this approach applicable in many applications.

KW - discrete event simulation

KW - simplification

KW - WIP-dependent inter-departure times

UR - http://www.scopus.com/inward/record.url?scp=84910069664&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84910069664&partnerID=8YFLogxK

U2 - 10.1177/0037549714546665

DO - 10.1177/0037549714546665

M3 - Article

AN - SCOPUS:84910069664

VL - 90

SP - 1188

EP - 1196

JO - Simulation

JF - Simulation

SN - 0037-5497

IS - 10

ER -