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

Björn LandfeldtSchool of Information Technologies

Investigating a theoretical model

Bjorn Landfeldt

University of Sydney


We’ll look at:

• We have a theory and a model

• How do we check the accuracy of our model?

• Methodology

• Things to consider


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


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?


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.


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.


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


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


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?


Initial investigation

• Numerical analysis

• We vary Hurst parameter (traffic intensity)

• Delay follows reasonable pattern and right order of magnitude.


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!


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)


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 :)


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


So, when use what?

• Depends really!

• MAIN point:

• No matter what you use, THINK before you start

• Errors possible in ALL approaches


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


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.


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.


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?


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


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


Error propagation

€

V = πr2 × h = 3.14 × 52 ×10 = 785cm2

€

δV = δr + δh =Δr

r+

Δh

hΔV = δV (V )

Δr

r=

0.05

5;Δh

h=

0.01

10;δV = 0.01+ 0.001 = 0.011

ΔV = 0.011× 785 = 8.642


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.

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

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