2.15. Customers arrive at a shuttle stop according to a Poisson process with rate 3 per hour. Shuttles arrive at the stop according to a Poisson process with rate 1.5 per hour. Suppose that each shuttle can hold at most 2 customers. Suppose that at most 4 people wait for the shuttle (subsequently arriving customers are turned away). (a) Model this process as a continuous- time Markov chain. Give the rate transition matrix Q. (b) Give the probability transition matrix P of the embedded discrete-time Markov chain. (c) Solve for the stationary probabilities pi (of the CTMC) and 17: (of the embedded DTMC). (d) What is the average number of customers who enter a shuttle