Abstract
In this paper we study the transient behavior of the MGEL/MGEM/1 queueing system, where MGE is the class of mixed generalized Erlang distributions which can approximate an arbitrary distribution. We use the method of stages combined with the separation of variables and root finding techniques together with linear and tensor algebra. We find simple closed form expressions for the Laplace transforms of the queue length distribution and the waiting time distribution under FCFS when the system is initially empty and the busy period distribution. We report computational results by inverting these expressions numerically in the time domain. Because of the simplicity of the expressions derived our algorithm is very fast and robust.
| Original language | English |
|---|---|
| Pages (from-to) | 153-184 |
| Number of pages | 32 |
| Journal | Queueing Systems |
| Volume | 10 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1992 Sep |
| Externally published | Yes |
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Keywords
- busy period
- linear algebra
- transform methods
- Transient analysis
ASJC Scopus subject areas
- Management Science and Operations Research
- Computer Science Applications
- Computational Theory and Mathematics
Cite this
Transient and busy period analysis of the GI/G/1 queue : The method of stages. / Bertsimas, Dimitris J.; Nakazato, Daisuke.
In: Queueing Systems, Vol. 10, No. 3, 09.1992, p. 153-184.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Transient and busy period analysis of the GI/G/1 queue
T2 - The method of stages
AU - Bertsimas, Dimitris J.
AU - Nakazato, Daisuke
PY - 1992/9
Y1 - 1992/9
N2 - In this paper we study the transient behavior of the MGEL/MGEM/1 queueing system, where MGE is the class of mixed generalized Erlang distributions which can approximate an arbitrary distribution. We use the method of stages combined with the separation of variables and root finding techniques together with linear and tensor algebra. We find simple closed form expressions for the Laplace transforms of the queue length distribution and the waiting time distribution under FCFS when the system is initially empty and the busy period distribution. We report computational results by inverting these expressions numerically in the time domain. Because of the simplicity of the expressions derived our algorithm is very fast and robust.
AB - In this paper we study the transient behavior of the MGEL/MGEM/1 queueing system, where MGE is the class of mixed generalized Erlang distributions which can approximate an arbitrary distribution. We use the method of stages combined with the separation of variables and root finding techniques together with linear and tensor algebra. We find simple closed form expressions for the Laplace transforms of the queue length distribution and the waiting time distribution under FCFS when the system is initially empty and the busy period distribution. We report computational results by inverting these expressions numerically in the time domain. Because of the simplicity of the expressions derived our algorithm is very fast and robust.
KW - busy period
KW - linear algebra
KW - transform methods
KW - Transient analysis
UR - http://www.scopus.com/inward/record.url?scp=0042907872&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0042907872&partnerID=8YFLogxK
U2 - 10.1007/BF01159205
DO - 10.1007/BF01159205
M3 - Article
AN - SCOPUS:0042907872
VL - 10
SP - 153
EP - 184
JO - Queueing Systems
JF - Queueing Systems
SN - 0257-0130
IS - 3
ER -