Simulating Poisson Waiting Times

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++;   开发者_Python百科  
        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.

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.

If you want to simulate earthquakes, or lightning or critters appearing on a screen, the usual method is to assume a Poisson Distribution with an average arrival rate λ.

The easier thing to do is to simulate inter-arrivals:

With a Poisson distribution, the arrivals get more likely as time passes. It corresponds to the cumulative distribution for that probability density function. The expected value of a Poisson-distributed random variable is equal to λ and so is its variance. The simplest way is to 'sample' the cumulative distribution which has an exponential form (e)^-λt which gives t = -ln(U)/λ. You choose a uniform random number U and plug in the formula to get the time that should pass before the next event. Unfortunately, because U usually belongs to [0,1[ that could cause issues with the log, so it's easier to avoid it by using t= -ln(1-U)/λ.

Sample code can be found at the link below.

https://stackoverflow.com/a/5615564/1650437