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Showing posts from July, 2009

Why model Packet Arrivals as a Poisson Process?

In queuing theory-based analysis, we always assume arrivals to be according to a Poisson process. "Why we do so, why not it's uniform or some other distribution?" This was a question raised by my supervisor & a colleague while I was preparing for my Qualifying Exam. As I was not able to answer well, my supervisor gave some hints. I was worried that the same question may come up during the exam so searched for an answer on web. Unfortunately, no specific answer was found. So I'm trying to lay down an answer by adding bits & pieces from here & there & my supervisor's answer.

It can be answered by looking at the properties of a Poisson Process. Recall that Poisson Processes are used to model statistically rare events.

A counting process {Nt, t ≥ 0} is a Poisson process if:
N0 = 0Nt has stationary independent increments Nt1 - Ns1 is independent from Nt2 - Ns2MemorylessInter arrival times are independently & identically distributed set of exponential…

Failed - But not forever...

We fail in many endeavors...
But never quit trying...
You may succeed either in the same or different area...
Even if you succeed in a different area, it because of the previous failure....
Here are some well-known failures that could inspire you...