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q1_cee3604_2009V2_solution - CEE 3604 Introduction to...

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CEE 3604: Introduction to Transportation Engineering Fall 2009 Exam 1 (1.25 hours) Instructor: Trani Problem 1 (25%) Using loop detectors in the pavement, a traffic engineer estimates that the jamming condition of a two-lane undivided highway occurs when vehicles are spaced 11 meters apart (i.e. distance between front bumpers of successive vehicles). The speed for maximum flow is estimated to be 35 km/hr. Using the same traffic sensors and doing some analysis of the traffic data, the engineer suspects Greenberg’s model applies to the traffic situation. a) Find the maximum flow per lane on this highway in a busy day of traffic. The Greenberg model is known to be: u = c ln k j k where: u is the space mean speed (km/hr), k j is the jam density (veh/la-km), k is the density of the flow (veh/la-km) and c is a model parameter (km/hr). From the data given: c is 35 km/hr k j = 1000 11 veh/la-km q max = ck j e = 35(90.91) e = 1,108 veh/hr per lane b) Calculate the travel time between two highway interchanges located 2.5 km away from each other one day when the highway loop detectors register an average spacing between vehicles of 31 meters. When the spacing between vehicles is 31 meter, k = 1000 31 = 32.26 veh/la-km u = c ln k j k = 35ln 90.91 32.26 = 36.26 km/hr To travel 2.5 km the travel time is 0.0689 hours or 4.13 minutes.
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