|
Digital
Library of the European Council for Modelling
and Simulation |
Title: |
Infinite-Server Queueing Tandem With MMPP Arrivals
And Random Capacity Of Customers |
Authors: |
Aleksander
Moiseev, Svetlana Moiseeva, Ekaterina Lisovskaya |
Published in: |
(2017).ECMS 2017 Proceedings
Edited by: Zita Zoltay Paprika, Péter Horák, Kata Váradi, Péter Tamás
Zwierczyk, Ágnes Vidovics-Dancs, János Péter Rádics European Council for Modeling and Simulation. doi:10.7148/2017 ISBN:
978-0-9932440-4-9/ ISBN:
978-0-9932440-5-6 (CD) 31st European Conference on Modelling and
Simulation, Budapest, Hungary, May 23rd
– May 26th, 2017 |
Citation
format: |
Aleksander
Moiseev, Svetlana Moiseeva, Ekaterina Lisovskaya (2017). Infinite-Server
Queueing Tandem With MMPP Arrivals And Random Capacity Of Customers, ECMS
2017 Proceedings Edited by: Zita Zoltay Paprika, Péter Horák, Kata Váradi,
Péter Tamás Zwierczyk, Ágnes Vidovics-Dancs, János Péter Rádics
European Council for Modeling and Simulation. doi:
10.7148/2017-0673 |
DOI: |
https://doi.org/10.7148/2017-0673 |
Abstract: |
Tandem
of two queueing systems with infinite number of servers is considered.
Customers arrive at the first stage of the tandem according to Markovian
modulated Poisson process, and after a completion of their services, they go
to the second stage. Each customer carries some data package with a random
value (capacity of the customer). Service time does not depend on the
customers’ capacities in this study, capacities are
used just to fix some additional characteristic of the system evolution. It
is shown that two-dimensional probability distribution of total capacities at
the stages of the system is two-dimensional Gaussian under the asymptotic
condition of a high rate of arrivals. Presented numerical experiments and
simulations allow to determine an applicability area
of the asymptotic result. |
Full
text: |