Simulating Poisson Waiting Times

Question

I need to simulate Poisson wait times. I've found many examples of simulating the number of arrivals, but I need to simulate the wait time for one arrival, given an average wait time.

I keep finding code like this:

public int getPoisson(double lambda) 
{   
    double L = Math.exp(-lambda);   
    double p = 1.0;   
    int k = 0;   

    do 
    {    
        k++;     
        p *= rand.nextDouble(); 
        p *= Math.random(); 
    } while (p > L);   

    return k - 1; 
} 

but that is for number of arrivals, not arrival times.

Efficieny is preferred to accuracy, more because of power consumption than time. The language I am working in is Java, and it would be best if the algorithm only used methods available in the Random class, but this is not required.

Answer 1

Time between arrivals is an exponential distribution, and you can generate a random variable X~exp(lambda) with the formula:

-ln(U)/lambda` (where U~Uniform[0,1]). 

More info on generating exponential variable.

Note that time between arrival also matches time until first arrival, because exponential distribution is memoryless.