Question: Passengers arrive at a bus stop according to a Poisson process with rate lambda . Buses depart from the stop according to a renewal

Passengers arrive at a bus stop according to a Poisson process with rate \lambda . Buses depart from the stop according to a renewal process with interdeparture time A.
Using a renewal-reward process, prove that the long-run average waiting time per passenger equals E[A^2]/2E[A]
Specify the regenerative process you need to prove this result.
Can you give a heuristic explanation of why the answer for the average waiting time is the same as the average residual life in a renewal process?

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