| Issue |
RAIRO-Oper. Res.
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|
|
|---|---|---|
| Page(s) | S2795 - S2810 | |
| DOI | https://doi.org/10.1051/ro/2020119 | |
| Published online | 02 March 2021 | |
Transient analysis of a single server queueing system with infinite buffer
Department of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R. China
* Corresponding author: xuhoubao@bit.edu.cn
Received:
8
June
2020
Accepted:
13
October
2020
As a typical single server queueing system, computer integrated manufacturing system (CIMS) has been widely used in the field of intelligent manufacturing. However, how to derive its instantaneous index is still an important issue. This paper investigates the transient behavior of the CIMS with spectral method. By constructing an asymptotic system and analyzing the spectral distribution, we derive the explicit transient solution of the asymptotic system. Trotter–Kato theorem is used to prove that the transient solution of the CIMS is just the limitation of explicit transient solution of the asymptotic system. At the end of the paper, numerical examples are shown to illustrate the effectiveness of the proposed approximation.
Mathematics Subject Classification: 90B22 / 60K25
Key words: CIMS / asymptotic system / spectral distribution / Trotter–Kato theorem / transient behavior
© EDP Sciences, ROADEF, SMAI 2021
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