Two questions about using Poisson process

[yagmai]

Dear experts here,
I am facing some problem in the following qns. I need some guidance on this qns.

In a CSMA based random access system, Poisson process is considered to be a good model for aggregated traffic for a large number of similar users. In such a system, the probability of n terminals communicating at the same time is given by

p =( (1.5G)^n * e^(-1.5G) ) / (n-1)!

where G is the traffic load in the system.

i) For what value of n is the above system optimum and determine the optimum value of p.

ii) How many terminals transmit under this condition and will there be any collision?

 

[shashankthebest]

Re: Poisson Process

You could solve this problem by minimizing the function p for n. Differentiate it once and identify the critical points. Next differentiate it again and identify at which points you get a minima. This you need to do for different values of G, and if you plot all the solutions, you will get a range describing the best values of G and n and their probabilities.

Cheers!

 

[harsha_jois]

Poisson Process

HI Yagmay.
Your problem can as well be solved using z- transforms. They give the range of values the independent variables can possibly assume to keep the system stable. So the best way would be to get all the zeroes and poles of the system. Hope this helps. tara...