Thanks a lot for your complete answer. However for the interval [a,b] we should break it into some 1/r interval and add them together. Am I right?
Also I have an intution. I think for the interval [a,b] (b-a=1/r) we can consider the number of packets as a Poisson prosess with rate lambda * s where lambda is the rate of file request. It is because of the fact that for interval [a,b] we have N_1 first packets that have poisson distribution(lambda). Also N_2 second packets with the same Poisson distribution(lambda) ... until N_S. Then since they have disjoint interval; they are independent Poison and we can add them together and finally get Poisson process with rate (lambda * s). For the interval [b,c] (c-b=1/r) it the same. However we can not calculate the distribution for [a,c] since [a,b] and [b,c] are not independent. Is there any way to calculate the distribution of [a,c] by using [a,b] and [b,c].
Also Is it possible to find the packet interarrival distribution. Thanks a lot.