Consider an airport where taxis and customers arrive (exponential interarrival times) with respec-tive rates of 1 and 2 per minute. No matter how many other taxis are present, a taxi will wait. Ifan arriving customer does not find a taxi, the customer immediately leaves the airport by takingshuttles.

1. Model this system as a birth-and-death process (hint: determine what the state of thesystem is at any given time). In particular, draw the transition rate diagram of this CTMC.
2. In the long run, what is the average time a taxi spends at the airport before it carries acustomer and leaves?