Question

Suppose you’re designing a bridge for vehicle traffic over the Cache la Poudre River. Cars are expected to arrive at the central toll plaza at a rate of 70 per hour. You will have four toll booths, which can each process cars at a rate of 30 cars per hour. Assume cars arrive into the toll plaza according to a Poisson distribution and wait in queue until the next available toll booth opens up. Assume car processing times are exponentially distributed.

(a) What is the probability that there are no cars in the toll plaza?

(b) What is the average length of the waiting line?

(c) What is the average time spent by a car in the toll plaza?

Answer 1