Virtual paths networks fast performance analysis

Pablo Belzarena,
Paola Bermolen,
Pedro Casas,
María Simon

Mobility Management and Quality-of-Service for Heterogeneous Networks (ed. Demetres D. Kouvatsos), , , , Volume 1, page 359-386- 2009

Research group(s): Analisis de Redes, Trafico y Estadisticas de Servi (art)

Department(s): Telecomunicaciones

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## Abstract

The performance analysis of a link is a well studied problem.
However, for a service provider
the most interesting issue is the end-to-end quality of serv
ice (QoS) evaluation. The focus of this work
is to go from the link to the network analysis. This can be done
in a complete but complex way or using
an approximation to speedup the calculations. We analyse an
d compare both methods.
Large Deviations Theory applications to Data Networks are m
ainly based on the many sources as-
ymptotic. This asymptotic is adequate for networks like Int
ernet backbones, where the assumption that
the network is fed by a large number of sources is reasonable.
Recently, Ozturk et al. have proposed a slightly different mo
del called many sources and small buffer
asymptotic. They give a formula to calculate the link overflo
w probability and the end-to-end Loss Ratio
of traffic streams in a virtual path feed forward network of gen
eral topology. They also define the
fictitious
network
concept. The fictitious network has the same topology than th
e real one, but each traffic stream
goes across a link on its path without being affected by the ups
tream links until that one. So, in the
fictitious network each internal link can be analysed as an ex
ternal one. Therefore, the fictitious network
usage simplifies dramatically the network performance anal
ysis.
Our main motivation to simplify this task is to allow on-line
performance analysis and traffic engi-
neering algorithms in virtual path networks as MPLS or ATM.
Ozturk et al. show that the fictitious network overestimates
the overflow probability and the end to
end Loss Ratio. Therefore, decisions based on the fictitious
network analysis are safe. However, this
overestimation leads to network resources under-utilizat
ion.
Under certain conditions the real and the fictitious network
analysis give the same results (there is
no overestimation). In this work we establish sufficient cond
itions to assure that this coincidence arises.
Those conditions are not necessary, and we give an easy way to
check if exact results may be obtained
even though sufficient conditions are not met. When the real an
d fictitious networks analysis give different
results, we find a method to bound the overestimation.
Finally, we show some numerical examples to compare the perf
ormance analysis in the real vs. the
fictitious network, and to validate our main results

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