I am currently doing some bus stop designs. I have not done statistics for a while but remember once doing poisson distributions at Uni.

The problem I have, I think, requires a specific arrangement of the poisson formula for cumulative distribution.

If I have x number of buses arrive per hour and they each stay on average y seconds how many bus stops would I require so that the number of buses at the stops exceeds the number of stops z%?

e.g. buses per hour = 30

buses wait time = 60 seconds

poisson random distribution for arrival times

probability of exceeding number of bus spaces = 5%

bus spaces = ?

I would appreciate any guidance to solving this problem. I have researched formulas but can't seem to find one that allows me to perform this calculation.

Many Thanks!