1. Péter Hága Eötvös Loránd University, Hungary European Conference on Complex Systems 2008 Jerusalem, Israel

2.  Internet is a complex system ◦ topology ◦ traffic  Goal: determine the ◦ physical properties of the network ◦ properties of the traffic  Tool to collect measurement data: „active measurements” 16th September 2008.ECCS '082

3. Passive methods  continuous monitoring  For a given node or link  Not disturbs the traffic  Requires administrative rights 16th September 2008.ECCS '083 Active methods  Artificial probe traffic  Measures a whole path between the sender and receiver  Disturbs traffic and system  Not requires special rights Traffic is organized: in packets Important properties:  Source and destination  Packet size  Timestamp of sending and receiving C1C1 FIFO queue

4. 16th September 2008.ECCS '08 Goal : determine important parameters of the physical network and the traffic Typical questions : background traffic, available bandwidth, physical capacity, network topology, packet loss rate, propagation delay, queuing delay, background traffic arriving process background traffic 4 senderreceiver Sending timestamps: Receiving timestamps:

5. the measurements are based on self-induced congestion, so we look for the signs of congestion as the function of the load of caused by the probe traffic 16th September 2008.ECCS '08 time  input spacing at the sender ’’ output spacing at the receiver 5

6. 16th September 2008.ECCS '086 ??? General packet pair model

7. 16th September 2008.ECCS '087 Single-hop, fluid traffic ??? General packet pair model

8. 16th September 2008.ECCS '088 B background traffic probe traffic C Physical capacity: background traffic: Fluid approximation of the Internet traffic: assuming infinitely small background packets, instead of real sizes

9. 16th September 2008.ECCS '089  parameters of the dispersion curve in fluid approximation: p - size of probe packets B – amount of the background traffic C - physical capacity of the network  Correct asymptotic behavior for single-hop network  Deviation in the transitional region

10. 16th September 2008.ECCS '0810 Single-hop, fluid traffic Single-hop, granular traffic ??? General packet pair model

11.  Liu et al., Haga et al.  Based on transient queuing theory  Background traffic assumption: Poisson arrival process and finite packet size (NOT fluid)!  Old fluid parameters: ◦ p - size of probe packets ◦ B – amount of the background traffic ◦ C - physical capacity of the network  Extending with a new parameter: ◦ P g - granularity  only a single-hop model 11 P.Haga et al.: Granular model of packet-pair separation, INFOCOM 2006 & Computer Networks 2007

12. 16th September 2008.ECCS '0812 Single-hop, fluid traffic Single-hop, granular traffic Multi-hop, fluid traffic ??? General packet pair model

13. Physical capacity: 16th September 2008.ECCS '0813 B 11 background traffic B 33 background traffic probe traffic B 23 background traffic C1C1 C2C2 C3C3 background traffic: i: hop ID where the traffic enters j: hop ID where the traffic leaves

14. 16th September 2008.ECCS '0814 B 11 background traffic B 33 background traffic B 22 background traffic probe traffic C1C1 C2C2 C3C3

15. 16th September 2008.ECCS '0815 Physical capacity:background traffic: B 11 background traffic B 33 background traffic B 12 background traffic probe traffic B 23 background traffic C1C1 C2C2 C3C3

16. B 11 background traffic B 22 background traffic B 33 background traffic B 12 background traffic probe traffic B 23 background traffic C1C1 C2C2 C3C3 B 13 background traffic 16th September 2008.ECCS '0816 The actual separation of the probe packets: Introducing the effective size of the probe packet: Initial conditions: The final dispersion curve: The way of determining the dispersion curve is iterating the two key quantities:

17. 17 Iteration of packet spacing: Iteration of effective size of probe packet: The final dispersion curve:

18.  Problem is to determine the traffic parameters  Active measurements techniques  Single-hop, fluid traffic  Single-hop, granular traffic  The dispersion curve for a multi-hop path  Fluid approximation for multi-hop path  Traffic matrix  Iterative formula for general multi-hop cases 16th September 2008.ECCS '0818 Single-hop, fluid traffic Single-hop, granular traffic Multi-hop, fluid traffic ??? General packet pair model

19. 16th September 2008.ECCS '0819

20. 16th September 2008.ECCS '08 ’’ outgoing spacing at the receiver node background traffic stochastic process artificial probe packets with pre-defined time separation  input spacing at the sender node 20

21. 16th September 2008.ECCS '0821 B 11 background traffic B 22 background traffic probe traffic C1C1 C2C2 The „2 hop” dispersion curve:

22. 16th September 2008.ECCS '0822 B 11 background traffic B 22 background traffic B 12 background traffic probe traffic C1C1 C2C2 The dispersion curve can not calculated in the way of: since some background traffic is jammed between the probe packets!

23. 16th September 2008.ECCS '0823 The dispersion curve in closed form. After long thinking...

24. 16th September 2008.ECCS '0824 probe traffic no background traffic B 11 background traffic B 33 background traffic B 22 background traffic probe traffic C1C1 C2C2 C3C3 C1C1 C2C2 C3C3 B 11 background traffic B 22 background traffic B 33 background traffic B 12 background traffic probe traffic B 23 background traffic C1C1 C2C2 C3C3 B 13 background traffic