I'm interested in generating random arrivals that should simulate the call arrivals of a call center. I chose to use a Poisson distribution, but the greatest problem comes with the fact that it's a discrete distribution.
So I thought that I could use it to generate an arrival rate in a time frame of 1 second; this way every second I re-compute the arrival rate, and spread every call in this frame of time.
But the problem is: to generate calls with a realistic rate, how should I "spread" the calls? I mean: if for example between a time frame of [4.0, 5.0], the generated arrival rate is 5, to just generate every calls every 0.2 seconds (arrivals: 4.0,4.2,4.4,4.6,4.8) is unrealistic.
A second problem comes with the fact that in reality the variance is much greater than the mean, but in a poisson process they're equal. A workaround could be to general arrival rates in a larger time frame, so that the variance increases, but this would make the process not homogeneous. Suggestions?