CN BY KUROSE AND ROSE

Question

 Statistical multiplexing  in which an example is provided with a 1Mbps link.Users are generating data at a rate of 100kbps when busy,but are busy generating data only with probability p=0.1.

a)Now consider packet switching and a user population of M users.Give a formula (in terms of p,M,N) for the probability that more than N users are sending data. ??

My solution is :

i think M users are send the data without any problem because it allows upto M users 

So send data with probability=p*M 

and remaining (N-M) users are send data with (1-p) probability.

=p*M+(N-M)*(1-p)

This is my approach ,please correct me if i did wrong.

Comments

It is asking for probability such that more than n users are able to send and m is the total no of users.(this is what i understood after reading the question).Ideally it looks like binomial distribution.I came up with probability= 1 - sum of using i = 0 to n (mCn (0.1)^i (0.9)^m-i).i.e Sum up all binomial probabilities from i =0 to n and subtract from 1.

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Here total no of users ready to send the data are 'N' in which M users can send without any problem.