1. Björn Landfeldt School of Information Technologies Investigating a theoretical model Bjorn Landfeldt University of Sydney

2. Björn Landfeldt School of Information Technologies We’ll look at: We have a theory and a model How do we check the accuracy of our model? Methodology Things to consider

3. Björn Landfeldt School of Information Technologies Background This paper is rather mathematical, we won’t go through the models in detail (unless you really want a Laplace question in quiz). We’ll focus on experiments

4. Björn Landfeldt School of Information Technologies Background Telecommunication traffic –interarrival times Poisson distributed –makes modeling very easy Internet traffic, no such luck –Many different applications –Capture effects, etc. What does it look like?

5. Björn Landfeldt School of Information Technologies So what? System engineering –Save costs (dimension correctly) –Provide guarantees to customers –SLAs possible only with tight bounds Assuming Poisson we don’t know what will happen just that it will not be very accurate.

6. Björn Landfeldt School of Information Technologies So what does traffic look like? Many studies show, Internet traffic exhibits –Self similar patterns (similar characteristics over different time scales) –Heavy tailed distributions Several models have been proposed.

7. Björn Landfeldt School of Information Technologies In this paper: We investigate queuing delay through a router using priority queuing Devise first closed form expressions for such a system Our traffic model –Simple (few parameters) –Flexible (can model large range of traffic) Developed by Mine Caglar

8. Björn Landfeldt School of Information Technologies Without going into details: We present a model for how to calculate queuing delay through a single router We the want to investigate if our model is correct

9. Björn Landfeldt School of Information Technologies What tools can we use? Numerical analysis –Get numerical results from closed form expression –Do they make sense? Simulations –Get numerical results –Do they make sense? Experimental measurements –What do we get in reality?

10. Björn Landfeldt School of Information Technologies Initial investigation Numerical analysis We vary Hurst parameter (traffic intensity) Delay follows reasonable pattern and right order of magnitude.

11. Björn Landfeldt School of Information Technologies Next step We implement a simulator and run simulations. Compare our results with numerical results Output very similar, good However, our own code, have we introduced bias? Experiment time!

12. Björn Landfeldt School of Information Technologies Experiments We purchase a CISCO router and a couple of PCs to use as source and sink Configure router with 2 queues PQ Implement traffic generator and run on source trough router to sink Synchronise clocks and measure time through router (packet sniffer)

13. Björn Landfeldt School of Information Technologies Results Experiments larger delay than simulation and numerical when H increases why? Two reasons really –Input queue packets waiting (looks like longer delay in router) –NTP (timing protocol for synchronisation) uses low priority queue through router gets delayed when H increases, sync skewed Paper not updated to show this correctly yet :)

14. Björn Landfeldt School of Information Technologies What conclusions do we draw The model matches both simulations and experiments well (when errors taken into account) Our mathematical model is accurate –That does not mean we know how to set H for all traffic though!!! –We can determine queuing delay if we know H

15. Björn Landfeldt School of Information Technologies So, when use what? Depends really! MAIN point: No matter what you use, THINK before you start Errors possible in ALL approaches

16. Björn Landfeldt School of Information Technologies So, when use what? If your model is complete (no simplifications), analytical model accurate and provable If you make any simplifications/assumptions remember this when drawing conclusions

17. Björn Landfeldt School of Information Technologies So, when use what? Simulations Good, when you need quick indications of what will happen r want to investigate something of low complexity Investigations of scale. Can you experiment with the Gnutella network? No choice.

18. Björn Landfeldt School of Information Technologies So, when use what? Experiments –Used to get exact results, very good. –However, setup prone to errors –Results validity, only for exact experiment. Can conclusions be generalised? Think before determining that.

19. Björn Landfeldt School of Information Technologies Before experimenting Ask yourself –What are my sources of error? –How big are those errors? –How can they affect my results? –If I change experimental setup, will the above points change?

20. Björn Landfeldt School of Information Technologies Make a habit of Estimating the errors in your results. Use: –Gaussian approximation –Logarithmic transformation etc. Understanding that the results of a single run may not show anything

21. Björn Landfeldt School of Information Technologies Error propagation Addition and subtraction –eA = bB + cC; e = b+c easy but, Multiplication and division? What is error of volume of cylinder –Radius 5 cm +- 0.05 cm, hight 10 cm +- 0.01 cm

22. Björn Landfeldt School of Information Technologies Error propagation

23. Björn Landfeldt School of Information Technologies Conclusion You have choices use correct method for the job Always think before starting the investigations Be critical and aware of errors in your work Don’t generalise your results and conclusions without considering if you can.