Cars arrive at a state inspection center at a mean rate of 15 per hour. Assume that the arrival rate is Poisson-distributed. The inspection center has three parallel lines, and the mean service time in each line is 10 minutes. Assume service times are exponentially distributed. If cars form single line while waiting and cars enter any one of the three service cells when one becomes available on a first-come, first served basis. The system is assumed to be in steady state.

a. What is the probability that there are no cars in line or being inspected?
b. What is the expected time a car will spend at the inspection station?
c. Someone suggested that if the three service lines were distributed, as individual lines about the city, each serving one-third of the cars, the time car would spend at an inspection station would be less. Do you agree and why?