Follow up on this question Average bus waiting time
I am interested in the case where we assume that the busses are initialized uniformly and we arrive at a uniform random time. How much time do we have to wait if the bus arrival times are themselves also uniform?
The existing answers all investigate when we assume that the arrival times are discrete time intervals but the initialization is uniformly distributed. This is not the same as this question because
P(W>t) = Probability that we wait at least t minutes $!= \prod (1-t/m_k)$
I think that in this scenario we have to condition on when we saw the last bus, and evaluate from there. Does anyone have any insight into this question?
