A taxi cab company has three taxis that operate from the airport. The time it takes for a taxi to take the customer to their destination is exponentially distributed with parameter u. Customers arrive according to a Poisson process with an average of rate 2. If a customer arrives when no taxi is available, they go to another taxi cab company. The taxis always return to their base station at the airport after dropping off a customer without picking up any new customers on their way back. a) Identify the states of the system, arrival and departure rates in each state, and draw the state transition diagram of the system.
b) Derive an expression of the probability that all the taxis are available.
c) What is the probability that an arriving customer goes to another taxi cab company?