Statement of a problem № m1364


Upon arrival at the Sunkist Gate at Naval Base Ventura County in Port Hueneme, California, there are two security guards, each assigned to one of the two vehicular lanes that lead up to the gate, to check the identification (i. e., the military Common Access Cards) of people in the vehicles going on to the base. In the morning, when the gate is the busiest, cars arrive every 12 seconds and randomly get into one of the two clearly marked “ No-Lane-Change” lanes. Once a car is at the beginning of their particular line, it takes the guard about 20 seconds, on the average, to check the IDs of everyone in every car. Usually that means just one person. However, some people carpool and there may be as many as six or seven in any particular vehicle. Given that the vehicular arrivals follow a Poisson distribution and the time to check IDs follows a negative exponential distribution, determine the average number of cars and the average waiting time in each of the queues.

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