Abstract
In this paper, we study a multiserver system in which each customer requires a random number of servers simultaneously and a random but identical service time at all occupied servers. This model describes the dynamics of modern high performance clusters. Stability criteria of this system (under exponential assumptions) have been proved earlier for the two-server system only. Using a matrix-analytic approach, we obtain stability criteria of such a system under exponential assumptions and with an arbitrary number of servers.
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Acknowledgments
The authors thank Philippe Robert for his valuable comments and attracting attention to the paper (Kipnis and Robert 1990), and Bart Steyaert for some useful suggestions. The authors are also thankful to the anonymous referees for their careful reading and useful comments which have helped us to improve the readability of the paper. This work is supported by Russian Foundation for Basic Research, projects 13-07-00008, 14-07-31007, 15-07-02341, 15-07-02354, 15-07-02360, the organising committee of the ECQT2014 and the Program of strategic development of Petrozavodsk State University.
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Rumyantsev, A., Morozov, E. Stability criterion of a multiserver model with simultaneous service. Ann Oper Res 252, 29–39 (2017). https://doi.org/10.1007/s10479-015-1917-2
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DOI: https://doi.org/10.1007/s10479-015-1917-2
Keywords
- Multi-server systems
- Simultaneous service
- Concurrent server release
- Stability conditions
- Stationary workload
- High-performance cluster
- Supercomputer