Internet: Announcement

Leader	Stilian Stoev (Boston University), sstoev@bu.edu
Meeting	Thursday 2:00 - 3:00 pm, room 203
Members	Robert Buche (North Carolina State University), rtbuche@unity.ncsu.edu Arka Ghosh (University of North Carolina, Chapel Hill), apghosh@email.unc.edu Krishanu Maulik (EURANDOM, The Netherlands), maulik@eurandom.tue.nl George Michailidis (University of Michigan), gmichail@umich.edu Cheolwoo Park (SAMSI), cwpark@email.unc.edu David Rolls (SAMSI), rollsd@uncw.edu Robert Wolpert (Duke University), wolpert@stat.duke.edu
Outline Objectives	The fractional Brownian motion (FBM) has been a very successful model for the traffic in modern telecommunication networks such as Ethernet-LAN and more generally, the Internet. FBM captures two major characteristic features of the network traffic: {\it time scale invariance} (statistical self-similarity) and {\it long-range dependence} (LRD). A Gaussian stochastic process $X={X(t)}, t>0$ is said to be FBM if it has mean zero, stationary increments and is self-similar, that is, for all a>0, the processes {X(at)}, t>0 and a^H X(t), t>0, have equal finite-dimensional distributions. The parameter H belongs to the range (0,1) and is called the self-similarity parameter of the FBM process X. H is also the Hurst parameter of fractional Gaussian noise time series Y(k):=X(k)-X(k-1), k=1,2,... The FBM process can be also regarded as a physical traffic model. It appears in the limit of the superposition of independent ON/OFF sources with heavy-tailed ON and OFF periods, which mimic the flows in a busy network link. FBM is also the limit process of a physical infinite Poisson source model with heavy-tailed sources. Current extensive studies of real traffic data, however, indicate that FBM alone cannot be used to explain the traffic burstiness (see http://www-dirt.cs.unc.edu/net_lrd/). Traffic burstiness appears to be a serious non-stationary effect in data, that cannot be contributed to seasonality or periodicity. Our goal in this group will be to study, whether and how can the FBM model be augmented to account for non-stationarity effects (burstiness) in real data. We plan to focus on the so-called multifractional Brownian motion (MBM) model. The MBM processes Y={Y(t)}, t>0 extend the class of FBM processes by allowing the self-similarity parameter H to change with time, that is, H=H(t). More precisely, Y(t) is defined by replacing the parameter H in an integral representation of the FBM procsess by a function of time H(t), t>0. The resulting MBM process is Gaussian and locally self-similar, that is, Y(t) behaves, locally, like a self-similar process with self-similarity parameter H(t). We plan to investigate, whether these type of processes are relevant models for network traffic. More precisely, we will first focus on the following themes: * Extend existing physical models (e.g. the infinite Poisson source model or the ON/OFF model) by obtaining the MBM as a stochastic-process limit. * Explore the connections between the infinite Poisson source model and the ON/OFF model. * Validation of the models under consideration, by: (a) developing techniques to estimate H(t), locally, by using novel exploratory tools such as Dependent SiZer and wavelet analysis. (b) Estimating the parameters in the physical model from traffic data; experimenting with synthetic traffic data over a real network. We look forward to actively collaborating with other workgroups on the above mentioned themes. The above listed topics are quite broad and preliminary, so any new related ideas and directions of research are very welcome. Please contact Stilian Stoev sstoev@samsi.info if you want to take part in this workgroup or any suggestions.
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