Separation of timescales in a two-layered network

M. Vlasiou, J. Zhang, B. Zwart, R.D. Mei, van der

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Abstract

We investigate a computer network consisting of two layers occurring in, for example, application servers. The ¿rst layer incorporates the arrival of jobs at a network of multi-server nodes, which we model as a many-server Jackson network. At the second layer, active servers at these nodes act now as customers who are served by a common CPU. Our main result shows a separation of time scales in heavy traf¿c: the main source of randomness occurs at the (aggregate) CPU layer; the interactions between different types of nodes at the other layer is shown to converge to a ¿xed point at a faster time scale; this also yields a state-space collapse property. Apart from these fundamental insights, we also obtain an explicit approximation for the joint law of the number of jobs in the system, which is provably accurate for heavily loaded systems and performs numerically well for moderately loaded systems. The obtained results for the model under consideration can be applied to thread-pool dimensioning in application servers, while the technique seems applicable to other layered systems too.
Original languageEnglish
Title of host publicationProceedings of the 24th International Teletraffic Congress (ITC 2012, Krakow, Poland, September 4-7, 2012)
Pages185-192
Publication statusPublished - 2012
Event24th International Teletraffic Congress (ITC24), 4-9 September 2012, Kraków, Poland - Kraków, Poland
Duration: 4 Sep 20127 Sep 2012

Conference

Conference24th International Teletraffic Congress (ITC24), 4-9 September 2012, Kraków, Poland
Abbreviated titleITC 24
CountryPoland
CityKraków
Period4/09/127/09/12
Other24th International Teletraffic Congress

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Cite this

Vlasiou, M., Zhang, J., Zwart, B., & Mei, van der, R. D. (2012). Separation of timescales in a two-layered network. In Proceedings of the 24th International Teletraffic Congress (ITC 2012, Krakow, Poland, September 4-7, 2012) (pp. 185-192)