Abstract
This paper considers an m-station cascade system with renewal arrival processes and general service time distributions. Miyazawa and Morozov (Queueing Syst 100:225–227, 2022a; Stability of a cascade system with two stations and its extension for multiple stations, 2022b. arXiv:2203.14294v1) formulated a conjecture on the stability of this cascade system. In this paper, we show that this conjecture is not true for m≥ 3. We also show that when m≥ 3 , the stability condition is not determined solely by the moments of the interarrival and service times, but also depends on their distributions. In addition, we provide the necessary and sufficient condition for the stability of this cascade system by modifying a result of Miyazawa and Morozov (2022).
Original language | English |
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Pages (from-to) | 53-64 |
Number of pages | 12 |
Journal | Queueing Systems |
Volume | 104 |
Issue number | 1-2 |
DOIs | |
Publication status | Published - 2023 Jun |
Bibliographical note
Funding Information:We are grateful to the reviewers for their valuable comments and suggestions. B. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A2B5B01001864). J. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1A01065568).
Funding Information:
We are grateful to the reviewers for their valuable comments and suggestions. B. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A2B5B01001864). J. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1A01065568).
Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Keywords
- Cascade system
- Positive Harris recurrence
- Stability
ASJC Scopus subject areas
- Statistics and Probability
- Computer Science Applications
- Management Science and Operations Research
- Computational Theory and Mathematics