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Digital
Library of the European Council for Modelling and Simulation |
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Title: |
Simulation Of Large-Scale
Queueing Systems |
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Authors: |
Sergey
A. Vasilyev, Galina Tsareva |
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Published in:
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(2018). ECMS 2018
Proceedings Edited by: Lars Nolle, Alexandra
Burger, Christoph Tholen,
Jens Werner, Jens Wellhausen European Council for
Modeling and Simulation. doi:
10.7148/2018-0005 ISSN:
2522-2422 (ONLINE) ISSN:
2522-2414 (PRINT) ISSN:
2522-2430 (CD-ROM) 32nd European Conference on Modelling and Simulation, Wilhelmshaven, Germany, May 22nd
– May 265h, 2018 |
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Citation
format: |
Sergey
A. Vasilyev, Galina Tsareva
(2018). Simulation
Of Large-Scale Queueing Systems, ECMS 2018 Proceedings Edited by: Lars Nolle, Alexandra Burger, Christoph
Tholen, Jens Werner, Jens Wellhausen
European Council for Modeling and Simulation. doi: 10.7148/2018-0485 |
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DOI: |
https://doi.org/10.7148/2018-0485 |
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Abstract: |
In this paper we consider the dynamics of
large-scale queueing systems with an infinite number of servers. We assume that a Poisson input
flow of requests with intensity Nλ. We suppose that
each incoming request selects two any servers randomly and a next step of an
algorithm includes sending this request to the server with the shorter queue
instantly. A share uk(t) of the servers that have the queues lengths with not
less than k can be described using an system of ordinary differ-ential equations of
infinite order. We investigate this system of
ordinary differential
equations of infinite or-der
with a small real parameter. A small real parameter allows us to describe the
processes of rapid changes in large-scale queueing
systems. We use the simulation methods for this large-scale queueing systems analysis. |
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