Tid: 4 december 2006 kl 15.15-17.00
Plats : Seminarierummet 3733, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7. Karta!
Föredragshållare: Professor Thomas Mikosch, Laboratory of Actuarial Mathematics, University of Copenhagen.
Titel: Scaling limits for workload processes.
Sammanfattning: We study different scaling behaviour of a very general telecommunications workload process. The activities of a telecommunication system are described by a marked point process ((Tn,Zn))n∈ Z, where Tn is the arrival time of a packet brought to the system or the starting time of the activity of an individual source and the mark Zn is the amount of work brought to the system at time Tn. This model includes the popular ON/OFF process and the infinite source Poisson model. In addition to the latter models, one can flexibly model dependence of the inter-arrival times Tn-Tn-1, clustering behaviour due to the arrival of an impulse generating a flow of activities but also dependence between the arrival process (Tn) and the marks (Zn). Similarly to the ON/OFF and infinite source Poisson model, we can derive a multitude of scaling limits for the workload process of one source or for the superposition of an increasing number of such sources. The memory in the workload depends on a variety of factors such as the tails of the inter-arrival times or the tails of the distribution of activities initiated at an arrival Tn or the number of activities starting at Tn. It turns out that, as in standard results on the scaling behaviour of workload processes in telecommunications, fractional Brownian motion or infinite variance stable Lévy motion can occur in the scaling limit. However, fractional Brownian motion is a much more robust limit than the stable motion, and many other limits may occur as well.
The talk is based on joint work with Gennady Samorodnitsky, Cornell University.