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Queueing Systems
Published in: Queueing Systems 3-4/2022

30-03-2022

Stability condition of a cascade system with a general number of stations

Authors: Masakiyo Miyazawa, Evsey Morozov

Published in: Queueing Systems | Issue 3-4/2022

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Excerpt

For \(k \ge 2\), we consider a k-station cascade system in which exogenously arriving customers at single server station i are called class-i for \(i \in {\mathscr {K}} \equiv \{1,2,\ldots ,k\}\), and they or one of waiting class-i customers moves to the station \(i+1\) as class-\(i|(i+1)\) for \(i \le k-1\) if station \(i+1\) is empty and if the queue size of class-i customers including arriving one is greater than a given threshold level \(C_{i} \ge 1\). If not, exogenously arriving class-i customers simply enter station i. For \(i \le k-1\), the service of class-\(i|(i+1)\) customer is preempted by class-\((i+1)\) customer and resumed when there is no class-\((i+1)\) customer, while, for \(i \in {\mathscr {K}}\), class-i customers are served in the first-come-first-served manner. All customers who once completed their service immediately leave the system. …
previous article The Wei–Norman method for the infinite-server queue with phase-type arrivals
next article Characterisation of multivariate phase type distributions

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Literature
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Miyazawa, M., Morozov, E.: Stability of a cascade system with a general number of stations. Under preparation, (2022)
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Morozov, E., Steyaert, B.: Stability analysis of a two-station cascade queueing network. Ann. Oper. Res. 202, 135–160 (2013)CrossRef
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Tezcan, T.: Stability analysis of N-model systems under a static priority rule. Queu. Syst. 73, 235–259 (2013)CrossRef
Metadata
Title
Stability condition of a cascade system with a general number of stations
Authors
Masakiyo Miyazawa
Evsey Morozov
Publication date
30-03-2022
Publisher
Springer US
Published in
Queueing Systems / Issue 3-4/2022
Print ISSN: 0257-0130
Electronic ISSN: 1572-9443
DOI
https://doi.org/10.1007/s11134-022-09768-5

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