Tasks regarding CSMA and 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?

 

[m_pourfathi]

Re: CSMA

for your first question, use lagrange coefficients to evaluate the optimum value of p within 0 and 1. for more info search google.com

Added after 3 minutes:

for your second question, there sure will be collision in practice, there are 2 techniques in csma, one is collision detection which is used on ethernet cables and the other one is collision avoidance which is used on wireless systems like ieee 802.11.
the number of terminals on this network depends on the capacity of the network. the more terminals in network, the more collision you will have.