probability

Problem #5 (20 points) - What Kind of Queue Is This? A road checkpoint has two police agents who: (a) check the license tag for a stolen vehicle, (b) checks the driver for alcohol abuse and (c) searches the vehicle for drugs, guns, etc. The time to check the license tag is exponential with a mean of 3 minutes. The time to check the checks the driver for alcohol abuse is also exponential with a mean of 6 minutes, and the time to search the vehicle for drugs, guns, etc., is exponential with a mean of 9 minutes. In addition, all of these times are independent from one another. Assume that the cars arrive at a rate of 1 car every 15 minutes in accordance to a Poisson Process and every car goes through all three steps before it is allowed to pass. a.) (10 points) Compute the long-term average number of cars that will be waiting in line, and the long-term average time a car will be waiting in line. b.) (10 points) Compute the long-term average delay (in minutes) a car will have, as a result of the checkpoint