Likelihood-based traffic modeling with Markov-modulated Poisson processes

Sofia Andersson

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1404-028X
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 long-range dependence and self-similarity. 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 Markov-modulated 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.