Suppose that taxis arrive at a passenger pickup location according to a Poisson process with rate and passengers arrive according to an independent Poisson process with rate . Passengers who find that there are no taxis at the pickup location join a line for taxis. Similarly, taxis which find no passengers waiting at the pickup location lineup to wait for passengers. Suppose that initially there are no passengers and no taxis at the pickup location.

What is the probability that the first passenger to arrive does not wait for a taxi?

What is the probability that the second passenger does not wait for a taxi?

What is the expected time until the first passenger leaves with a taxi?