A taxicab company has a small fleet of three taxis that operate from the company's station. The time it takes a taxi to take a customer to his or her destination and return to the station is exponentially distributed with a mean of 1/μ hours. Customers arrive according to a Poisson process with average rate of λ customers per hour. If a potential customer arrives at the station and finds that no taxi is available, he or she goes to another taxicab company. The taxis always return to the station after dropping off a customer without picking up any new customers on their way back.
a. Give the state-transition-rate diagram of the process.
b. What is the probability that an arriving customer sees exactly one taxi at the station?
c. What is the probability that an arriving customer goes to another taxicab company?