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Engineering
Civil Engineering
Vehicles begin to arrive at an amusement park entrance at 8:00 A.M. at a rate of 1000veh/h. Some of these vehicles have electronic identifiers that allow them to enter the park immediately, beginning at 8:00 A.M., without stopping (they are billed remotely). All vehicles without such identifiers stop at a single processing booth, but they wait in line until it opens at 8:10 A.M. Once open, the operator processes vehicles at μ(t) = 8 + 0.5t [where μ(t) is in vehicles per minute and t is in minutes after 8:10 A.M.]. An observer notes that at 8:25 there are exactly 20 vehicles in the queue. What percent of arriving vehicles have electronic identifiers and what is the total delay (from the 8:00 A.M. until the queue clears) for those vehicles without the electronic identifiers (assume D/D/1 queuing)?

Vehicles begin to arrive at an amusement park entrance at 8:00 A.M. at a rate of 1000veh/h. Some of these vehicles have electronic identifiers that allow them to enter the park immediately, beginning at 8:00 A.M., without stopping (they are billed remotely). All vehicles without such identifiers stop at a single processing booth, but they wait in line until it opens at 8:10 A.M. Once open, the operator processes vehicles at μ(t) = 8 + 0.5t [where μ(t) is in vehicles per minute and t is in minutes after 8:10 A.M.]. An observer notes that at 8:25 there are exactly 20 vehicles in the queue. What percent of arriving vehicles have electronic identifiers and what is the total delay (from the 8:00 A.M. until the queue clears) for those vehicles without the electronic identifiers (assume D/D/1 queuing)?

Traffic and Highway Engineering
Traffic and Highway Engineering
5th Edition
ISBN:9781305156241
Author:Garber, Nicholas J.
Publisher:Garber, Nicholas J.
Chapter8: Intersection Control
Section: Chapter Questions
Problem 26P
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Vehicles begin to arrive at an amusement park entrance at 8:00 A.M. at a rate of 1000veh/h. Some of these vehicles have electronic identifiers that allow them to enter the park immediately, beginning at 8:00 A.M., without stopping (they are billed remotely). All vehicles without such identifiers stop at a single processing booth, but they wait in line until it opens at 8:10 A.M. Once open, the operator processes vehicles at μ(t) = 8 + 0.5t [where μ(t) is in vehicles per minute and t is in minutes after 8:10 A.M.]. An observer notes that at 8:25 there are exactly 20 vehicles in the queue. What percent of arriving vehicles have electronic identifiers and what is the total delay (from the 8:00 A.M. until the queue clears) for those vehicles without the electronic identifiers (assume D/D/1 queuing)?
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