Separation of timescales in a two-layered network

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

1 Citation (Scopus)


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 publication2012 24th International Teletraffic Congress (ITC 24)
Number of pages8
Publication statusPublished - 2012
Externally publishedYes
Event24th International Teletraffic Congress, ITC 2012 - Krakow, Poland
Duration: 4 Sept 20127 Sept 2012
Conference number: 24


Conference24th International Teletraffic Congress, ITC 2012
Abbreviated titleITC 2012


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