Customers arrive at a bus stop according to a Poisson process of rate . Independently, buses arrive according to a renewal process with the inter-renewal interval distribution FX(x). At the epoch of a...

Customers arrive at a bus stop according to a Poisson process of rate . Independently, buses arrive according to a renewal process with the inter-renewal interval distribution FX(x). At the epoch of a bus arrival, all waiting passengers enter the bus and the bus leaves immediately. Let R(t) be the number of customers waiting at time t.

a) Draw a sketch of a sample function of R(t).

d) Use part c) to find the time-average expected wait per customer.

e) Find the fraction of time that there are no customers at the bus stop.