difference between poisson and exponential distributions in the context of client server systems?

Question

I am studying client's request arrival patterns on web and application servers. About web server's request arrival pattern I read that "The request arrival rate on web server follows Poisson distribution". And about application server I read the sentence "The request arrival rate on application server follows exponential distribution. Now kindly explain " is there any difference between Poisson and exponential distribution in the context of client's request arrival pattern on server". Is there any difference between poisson and exponential distributions?

Answer 1

The Poisson models the number of arrivals in a certain fixed time. It is a discrete distribution, taking on values $0,1,2,\dots$. The exponential models the waiting time between consecutive arrivals. It is a continuous distribution. There is a connection, since they are used in modelling two different features of the same phenomenon. But they are quite different distributions.

The connection is that if the waiting times between any two consecutive arrivals are independent exponentially distributed with parameter $\lambda$, then the number of events in unit time has Poisson distribution with parameter $\lambda$.