How do I generate discrete random events with a Poisson distribution?

Question

I\'m aware of Knuth\'s algorithm for generating random Poisson distributed numbers (below in Java) but how do I translate that into calling a method, generateEvent()

Answer 1

If you are looking to simulate the inter-event arrival time, you want the exponential distribution.

Take a look at Pseudorandom Number Generator - Exponential Distribution

Your code would then look like this:

// Note L == 1 / lambda
public double poissonRandomInterarrivalDelay(double L) {
    return (Math.log(1.0-Math.random())/-L;
}

...

while (true){
    // Note -- lambda is 5 seconds, convert to milleseconds
    long interval= (long)poissonRandomInterarrivalDelay(5.0*1000.0);
    try {
        Thread.sleep(interval);
        fireEvent();
}

Answer 2

The Poisson random numbers you are generating, as Scott mentioned, represent the frequency of your events. Once you have the frequency, you can fit their occurrences over the interval using a second distribution, say Uniform.

Suppose the number of events generated for an interval of N is k. Then you simply need to generate (k+1) random numbers that sum to N.

|<----------------------- N ------------------------->|
--r_0--(event)---r_1-..-(event_k)--r_(k+1)--

To do so, simply generate (k+1) random numbers and divide them by their sum, divided by N. The first k of these numbers become the timestamps of your events.