10 Consider an airport where taxis and customers arrive

(exponential interarrival times) with respective rates of 1 and 2 per minute. No matter how many other taxis are present, a taxi will wait. If an arriving customer does not find a taxi, the customer immediately leaves.

a Model this system as a birth–death process (Hint:

Determine what the state of the system is at any given time and draw a rate diagram.)

b Find the average number of taxis that are waiting for a customer.

c Suppose all customers who use a taxi pay a $2 fare.

During a typical hour, how much revenue will the taxis receive?