Question
Problem 10. (11 Points) Cars traveling from Canada to the United States through the Thousand Islands Border Crossing must stop for US Customs and Immigration. During the stop, each passenger in the car will present a passport for inspection by a US Customs Officer, answer questions, and declare certain valuables that may be in the car. On passports and release a car for entry into the United States Since the Thousand Islands Border Crossing is not heavily traveled at night, US Customs and lration nly keeps one lane open at the checkpoint plaza and one officer on duty to process arriving cars Between midnight and average, it takes a Customs Officer about four minutes to inspect hor 6:00 AM? a car arrives at the Border Crossing plaza athan average rate of nine an hour a) Assuming this scenario meets the assumptions of the M/M/1 model, how busy is this Customs Officer during that time period? utilizatlon_? pen hor M 605 Citieentper hour 4 atio b) What is the average wait to speak to that officer? he:E9154)] c) What is the probability that someone will be able to speak to the officer immediately upon arrival? 2 0 d) On average, how many cars are present at the Thousand Islands Border Crossing plaza during that time period? LS Version A
Explanation / Answer
Kendall's notation M/M/1 Comment Arrival rate A 9 per hour Service rate S 15 60/4 U Utilization ratio U=A/S 0.60000