Likelihoodbased traffic modeling with Markovmodulated Poisson processes
Sofia Andersson
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2000
ISSN 1404028X

Abstract:

Traffic characterization and modeling are of great importance in the analysis
and dimensioning of today's increasingly complex communication systems. Customers
entering a queue must be offered a reasonable quality of service, for example
in terms of waiting times and small fractions of lost packets due to buffer
overflow. During the late 80's and early 90's new features of network
traffic were revealed, such as longrange dependence and selfsimilarity.
The traditional Poisson process cannot possibly catch these characteristics
and thus new approaches have been taken to characterize network traffic.

In paper A of this thesis a Markovmodulated Poisson process (MMPP) built
up as a superposition of ON/OFF sources is used to model data traffic. The
main idea is to let each of the sources work on different time scales and
in this way try to catch dependence over several time scales. The parameters
of our model are estimated using maximum likelihood. To derive the likelihood
estimates we need initial values for the algorithms used. We here use moment
estimates fitting the second order properties of the process of counts. The
moment estimates are also used

for a comparative purpose and the likelihood estimates proves to supply superior
estimates. Part of the explanation to this could be that while the fit of
the process of counts is deteriorated, the likelihood estimates give a better
fit of the second order properties of the interarrival times.


In paper B we investigate the microdynamics of some sets of data traffic.
The approach used is poissonification, which is a way of transforming a point
process into a Poisson process locally. Poissonification can be used when
modeling a doubly stochastic process, such as the MMPP in paper A, to find
the time scale where we no longer have the doubly stochastic behavior. To
measure the influence of poissonification, the poissonified traffic is fed
into a queue. Results show that provided the poissonification is carried
out at a sufficiently small time scale the performance characteristics are
not decisively changed and this gives a guide to how to choose the time

scale where to start modeling.
