1. Detecting the Long-Range Dependence in the Internet Traffic with Packet Trains Péter Hága, Gábor Vattay Department Of Physics of Complex Systems Eötvös University

2. ECCS 2006 - Oxford, UK - 25/09/2006 active probing in communication networks packet pair and packet train methods dispersion curves for pairs and trains the dispersion curve for different background traffic arrival processes relative stretch, phase transition! power laws in the average stretch relation between the power laws and the cross traffic arrival process Motivation & Overview modeling communication networks like the Internet importance of the background traffic arrival process difficulties in determining different statistical properties

3. ECCS 2006 - Oxford, UK - 25/09/2006 Active probing methods SenderReceiver Sender Monitor: Receiver Monitor: Goal : estimate network parameters (available bandwidth, physical bandwidth, cross traffic statistical properties, etc.) with end-to-end methods background traffic

4. ECCS 2006 - Oxford, UK - 25/09/2006 Packet pair methods ’’ output spacing, receiver node background traffic stochastic process (Poisson, Pareto, generally unknown ) probe pairs fixed inter packet delay  input spacing, sender node

5. ECCS 2006 - Oxford, UK - 25/09/2006  ’  p/C+  the curve is based on self induced congestion, since the probe pair congests the bottleneck link with a certain  inter pair spacing fluid model – correct asymptotic behavior, deviation in the transition range Dispersion curve for packet pairs  ’    p/(C-C c ) time  input spacing, sender node ’’ output spacing, receiver node

6. ECCS 2006 - Oxford, UK - 25/09/2006 Packet pairs with different arrival processes background traffic scenarios: Poisson arrival process Pareto arrival processes to model long-range dependent background traffic

7. ECCS 2006 - Oxford, UK - 25/09/2006 Packet trains ’n’n nn background traffic stochastic process (Poisson, Pareto generally unknown) probe stream fixed inter packet delay input spacing, sender node output spacing, receiver node

8. ECCS 2006 - Oxford, UK - 25/09/2006 Dispersion curve for packet trains

9. ECCS 2006 - Oxford, UK - 25/09/2006 Relative stretch phase transition and finite size effect? Relative stretch ( order parameter ):

10. ECCS 2006 - Oxford, UK - 25/09/2006 Phase transitions the phases are separated by a critical point in this critical point the convergence of the observed curve to some limit follows a power law function uncongested phase congested phase

11. ECCS 2006 - Oxford, UK - 25/09/2006 Average stretch The average of the deviation of the observed  ’ and the  fluid values at  where , for Poisson process ,for Pareto process (  infinite variance) Based on the central limit theorem it can be shown that:

12. ECCS 2006 - Oxford, UK - 25/09/2006 Average stretch at  c Average stretch  as a function of the packet train length if  c => power law behavior 

13. ECCS 2006 - Oxford, UK - 25/09/2006 -0.22-0.23 Pareto  -0.33 Pareto  -0.40-0.41 Pareto  -0.50 Pareto  -0.51-0.50Poisson fitted exponent calculated exponent for Poisson process:  for Pareto process:  Average stretch: The arrival process of the unknown traffic can be determined! Exponents for different arrival process

14. ECCS 2006 - Oxford, UK - 25/09/2006 Summary & Future work experiments in the real test laboratory to validate the method, the vision: experiments in the etomic infrastructure to investigate the spatial-temporal behavior of the network traffic new approach in the analysis of packet train experiments using packet trains to infer internal properties of the network this approach is working well in simulations to determine the arrival process of the background traffic

15. ECCS 2006 - Oxford, UK - 25/09/2006 Etomic Infrastructure etomic stations routers

16. ECCS 2006 - Oxford, UK - 25/09/2006 This work was partially supported by the National Science Foundation (OTKA T37903), the National Office for Research and Technology (NKFP 02/032/2004 and NAP 2005/ KCKHA005) and the EU IST FET Complexity EVERGROW Integrated Project. Thank you for your attention! IST Future and Emerging Technologies

17. ECCS 2006 - Oxford, UK - 25/09/2006 Relation of the average stretch and the packet train length at different  values  c =>not a power law relation  c => non trivial power law behavior -0.5<a<0  c =>   Average stretch at different  values