I’m doing some research on computer networking and trying to use a model for simulating burst of sending data packets. After searching around for a while it seems that the most common one for this purpose is to use Poisson distribution. But I’m having a hard time wrapping my head around it.
If I understand the distribution correctly it should be possible to use Poisson distribution to generate X number of bursts, when to execute each burst in a given time period Z, where each burst contains a random number of data packets.
Am I correct in this assumption? If yes, then how would such an algorithm look?
Generally just poisson is not enough, since that describes the number of bursts but not the timing. So you may use Poisson to determine how many bursts in some interval $[0,T]$ but not the timing of the bursts. Even if you assume regular transmission times, $kT,k\geq 1,$ you still need to decide exactly at which of those times there is a transmission.
If you have a stationary setup, you can generate an i.i.d. sequence $X_i$ with each $X_i$ exponentially distributed with some mean.
This gives you burst times, $$T_1=X_1,T_2=X_1+X_2,\ldots.$$
Then you could use the poisson distribution to determine the number of packets in each burst.