Transient analysis of a single server queueing system with infinite buffer

Huo, Huixia; Xu, Houbao; Chen, Zhuoqian; Win, Thet Thet

doi:10.1051/ro/2020119

Huo, Huixia ; Xu, Houbao ; Chen, Zhuoqian ; Win, Thet Thet

RAIRO. Operations Research, Tome 55 (2021), pp. S2795-S2810

Résumé

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.

MR

DOI : 10.1051/ro/2020119

Classification : 90B22, 60K25
Keywords: CIMS, asymptotic system, spectral distribution, Trotter–Kato theorem, transient behavior

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     author = {Huo, Huixia and Xu, Houbao and Chen, Zhuoqian and Win, Thet Thet},
     title = {Transient analysis of a single server queueing system with infinite buffer},
     journal = {RAIRO. Operations Research},
     pages = {S2795--S2810},
     year = {2021},
     publisher = {EDP-Sciences},
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     doi = {10.1051/ro/2020119},
     mrnumber = {4223203},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ro/2020119/}
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Huo, Huixia; Xu, Houbao; Chen, Zhuoqian; Win, Thet Thet. Transient analysis of a single server queueing system with infinite buffer. RAIRO. Operations Research, Tome 55 (2021), pp. S2795-S2810. doi: 10.1051/ro/2020119

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