Poisson processes prescription, please?

[Fusion_power]

Does anyone have a good link that explains Poisson processes, in particular compound Poisson processes? I've looked up a few on the web but so far have not found the info I need. I am working with a complex telephone office traffic model to represent traffic flow across two fabrics, one the standard TDM fabric and the second an IP fabric in a mixed model. I'm writing a program to simulate call traffic on same fabric and cross fabric.

I've visited wikipedia and mathworld already.

Thanks,

Fusion

[R.D. Silverman]

Originally Posted by Fusion_power

Does anyone have a good link that explains Poisson processes, in particular compound Poisson processes? I've looked up a few on the web but so far have not found the info I need. I am working with a complex telephone office traffic model to represent traffic flow across two fabrics, one the standard TDM fabric and the second an IP fabric in a mixed model. I'm writing a program to simulate call traffic on same fabric and cross fabric.

I've visited wikipedia and mathworld already.

Thanks,

Fusion

My old dissertation advisor, Linus Schrage, wrote an excellent book
Bratley, Fox, Schrage, A Guide to Simulation
that covers time-varying Poisson processes. It is an excellent book.

[ewmayer]

Here's an amazon.com link to the book Bob mentions:

http://www.amazon.com/Guide-Simulati.../dp/0387964673

It's expensive, but it looks like there is no shortage of used copies to be had at reasonable prices. Save the planet ... recycle.

[wblipp]

Originally Posted by Fusion_power

Does anyone have a good link that explains Poisson processes, in particular compound Poisson processes? I've looked up a few on the web but so far have not found the info I need. I am working with a complex telephone office traffic model to represent traffic flow across two fabrics, one the standard TDM fabric and the second an IP fabric in a mixed model. I'm writing a program to simulate call traffic on same fabric and cross fabric.

I've worked as a teletraffic engineer for 35 years, originally at Bell Labs.

Are you talking about the situation where the Poisson process depends on a state that is itself a Markov Process - ala Meier-Hellstern and Lucatoni and Neuts? Or perhaps a batch arrival model? Are you having trouble simulating this, or fitting the parameters? And are you sure simulation is the way to go - Neut's Matrix-Geometric methods makes many of these problems tractable analytically, whereas reliable simulation estimates of rare events is a tricky thing.

William

[Fusion_power]

Wblipp, You are in the ballpark. The problem is that someone wrote an app to simulate traffic flow in an office and I can not accept the mechanism it uses. It is a Poisson algorithm that simulates traffic flow in a multifabric environment. The current algorithm does not allow the granularity that I need to manipulate this office. My job is to balance the traffic across both fabrics and without overloading any of the peripherals handling the traffic. I have to model the traffic by fabric and also by peripheral. I want to write an equivalent algorithm that will simulate traffic by peripheral instead of by fabric. The two are equivalent at the office level, but "the devil is in the details" as they say.

I've made a bit of progress today. Within a week I should have this resolved.

Bob, Thank you for the info on the book. I am going to order a copy. It looks like something I can actually use!

Fusion

[wblipp]

Does "balance the traffic" mean that you are more interested in average flow values than in 10^-11 blocking or overflow probabilities? Simulation could be an effective method of studying the average flow.

It sounds like you already know that Poisson is an optimistic assumption for everything except first offered voice traffic. Peaked traffic models are preferred for overflow voice traffic, and fractal models seem to fit data traffic best.

Good luck with the project.

William