[e2e] simulation using self-similar traffic

Soo-hyeong Lee shlee at mmlab.snu.ac.kr
Tue Apr 3 23:05:55 PDT 2001

Thank you very much for kind reply. However,

> According to Crovella and Lipsky's chapter in 'Self-similar Network
> Traffic and Performance Evaluation' edited by Park and Willinger, if
> you're measuring average throughput and using heavy-tailed file sizes 
> with a small alpha, say 1.2, you'll need to simulate 10^12 samples to 
> get 2-digit accuracy. 

Crovella and Lipsky's paper is about getting average by taking independent samples from a heavy-tailed random variable, and doesn't mention anything about relation between throughput and file size. It doesn't take into consideration the long-range dependence either.

The situation of my interest is more related with long-range dependence among traffic loads of different time instance or high variability of time span of ON,OFF period.
The type of workload I want to simulate with is a kind of ON-OFF source whose OFF period follows Pareto distribution and ON period is devoted to transfer a file whose size is Pareto-distributed. This is a simplified version of what is proposed in Barford's paper(Barford, Paul; Crovella, Mark. Generating Representative Web Workloads for Network and Server Performance Evaluation, In Proceedings of ACM SIGMETRICS '98.).

I hope that there may be some research, because this type of traffic trace is what is dominating the real network.

> For metrics like 90% quantile of the throughput

Do you mean 90-percentile value in the random variable named 'average throughput measured in small interval', below which most(90%) of the small-interval-average-throughput lie?

> 1. plot the 90% quantile of the file sizes for different numbers of
>    samples (using MATLAB or Splus, see the attached ps for example)

I am afraid that you seem to switch arbitrarily between throughput and file size.
Could you explain why 90-percentile of the file size is related with 90-percentile of throughput?

> 2. identify where the value converges
> 3. simulate at minimum that amount of samples

On what ground are you thinking that 90-percentile converges much faster that average?

> This might not be sufficient theoretically but necessary intuitively.
> And I hope this helps.
> -Polly
> On Tue, 3 Apr 2001, Soo-hyeong Lee wrote:
> > 
> > Hello,
> > 
> > Could you please tell me how long should I run a simulation to obtain a sufficiently confident result when using a self-similar traffic trace?
> > I want to show the performance of a scheme in the 'general' case which consists of mixture of busy period and silent period.
> > However, a self-similar traffic trace can have very long busy period and very long silent period with unnegligible probability. Then any fixed simulation time can be entirely filled with either busy period or silent period with unnegligible probability.
> > Is there any recommendation on simulation time (or how many independent simulations should be run) to yield something like 90% confidence interval.
> > 
> > Thanks and regards.
> > 
> > Soo-hyeong
> > 
> > 
> > 

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