In an article published in the European Journal of Operational Research, the vehicle-dispatching decisions of an airport based taxi service were investigated. In modeling the system, the authors assumed travel times of successive taxi trips to and from the terminal to be independent exponential random variables. Assume β = 20 minutes.

a. What is the mean trip time for the taxi service?

b. What is the probability that a particular trip will take more than 30 minutes?

c. Two taxis have just been dispatched. What is the probability that both will be gone for more than 30 minutes? That at least one of the taxis will return within 30 minutes?