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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.

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

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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.

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  • $\begingroup$ Does this answer account for the normal distribution of the service times? $\endgroup$
    – user17794
    Jun 25, 2014 at 22:08
  • $\begingroup$ Is quite correct to use that averaged time (1/λ) and compute Poisson with that average to estimate a random arrival time?, or its better to assign the average time to each ship? $\endgroup$ Jun 25, 2014 at 22:18
  • $\begingroup$ You were asking "the time between each ship that comes to the station". Service time is not related to this . If you mean something different - explain clearer. My answer is to your question. I don't understand why somebody considers this answer incorrect. $\endgroup$ Jun 26, 2014 at 1:13
  • $\begingroup$ @TimDuff How would the time to service ships in the station affect the rate of arrival of ships to the station? That would be an issue of queuing; a different question. $\endgroup$ Jun 26, 2014 at 1:33
  • $\begingroup$ I just put the time service with the intent of put the problem in context. $\endgroup$ Jun 26, 2014 at 2:08

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