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 |
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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.
In: Simulation, Vol. 90, No. 10, 12.10.2014, p. 1188-1196.Research output: Contribution to journal › Article
}
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 -