# Estimate arrival time of a ship given the average of the ships in a day in a Poisson Distribution

I'm working in a simulation of a Port where ships come to specific stations of the port. I already know that the average amount of ships is given by a Poisson distribution and the service time (On each station of the port) is given by a normal distribution.

Is there any way to estimate the time between each ship that comes to the station? given that the average amount of ships in a day (24 hours) is given by the Poisson distribution. So far I think is hard to estimate, but I'm not sure.

• Does the Poisson parameter represent the average at a particular station or the whole port?
– user17794
Commented Jun 25, 2014 at 22:09
• Yes, it does represent it. Commented Jun 25, 2014 at 22:15

Yes, this is described by exponential distribution http://en.wikipedia.org/wiki/Exponential_distribution. Briefly, if $\lambda$ the mean of your Poisson distribution, namely the averaged number of ships per day, then $1/\lambda$ is the averaged time ( in day units) between ships.. Very natural.