# Solved – Modeling a Poisson process with 10000 events per minute

modelingpoisson distributionrubysimulation

I am trying to model a system that generates events modeled by a Poisson process.

I am using the following ruby code:

INTERVAL = 0.005
LAMBDA = 167.0
events = Hash.new(0)

def f(x, lambda)
1 - Math.exp(-lambda * x)
end

random_gen = Random.new
start = Time.now.to_f

while Time.now.to_i - start < 60
if random_gen.rand < f(INTERVAL, LAMBDA)
bucket = (Time.now.to_f - start).round.to_i
events[bucket] += 1
end

sleep(INTERVAL)
end

I am trying to generate about 10000 events per minute, or 167 events/second, so I am using $\lambda = 167$.

I am using function f as $1 – e^{(-\lambda x)}$ where $x$ is the interval I am sleeping, I am using this function so that the inter-arrival time of events follows an exponential distribution.

However, I am not getting the expected results, this code generates about 7194 events per minute, with a mean of about 117 events per second. I would expect this code to generate 10000 events per minute with an mean of about 167 events per second.

What am I doing wrong?

How are you getting more than $20$ events per second if you are sleeping for $1/20$ of a second between checks? In case you are actually using intervals of length $0.005$ then you could see up to $200$ events, but you are throwing out each event after the first in each interval. This would lead to an average of $200(1-\exp(-167/200)) = 113.225$ per second, with a binomial distribution instead of a Poisson distribution. You might see slightly fewer if you are actually sampling less often than once every $0.005$ seconds. You should at least test how often your loop is run.