I am trying to solve the following problem.
A pedestrian needs at least 8 seconds to cross a dual-lane carriage-way. Suppose the flow on the carriage-way is non-homogeneous such that the combined near-side and far-side flows have rate $\lambda(t) = 10t$ where t is the time in minutes after 0800. What is the probability that the pedestrian will not need to wait before crossing the road?
To be honest I am rather clueless how to approach this problem as I am not sure how to apply the definition of Non-homogeneous Poisson process here.
Any help would be much appreciated.
Pedestrian can only cross if no cars arrive so, One strategy which comes to mind would be to evaluate $P(N(0800 + 8/3600) = 0)$ would that be correct ? It kind of feels wrong as i am only interested in evaluating the probability of no cars arriving between 0800 and 0800 + 8/3600. Not sure how to use the definition to evaluate this though.