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chapter5_notes_ - Chapter 5 Fundamentals of Traffic Flow...

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Chapter 5 Fundamentals of Traffic Flow and Queuing Theory 5.1 INTRODUCTION Highways seek high mobility (speed) while considering safety. Understanding traffic flow and queuing is the key to evaluating highway performance (mobility provided) 5.2 TRAFFIC STREAM PARAMETERS Consider uninterupted flow: No stop signs No traffic signals 5.2.1 Traffic Flow, Speed, and Density Traffic flow: q = n t (5.1) Where: q = traffic flow in vehicles per unit time, n = number of vehicles passing some designated roadway point during time t , t = duration of time interval. In addition to the total number of vehicles passing a point in some time interval, consider the time between the passing of successive vehicles Headway - time between the passage of the front bumpers of successive vehicles, at some designated highway point Time headways are related to t , as defined in Eq. 5.1, by t = h i i = n 1 (5.2) Where: t = duration of time interval, h i = time headway of the i th vehicle (the time that has transpired between the arrival of vehicle i and i -1), n = number of measured vehicle time headways at some designated roadway point. Substituting Eq. 5.2 into Eq. 5.1 gives n i = i h n q = 1 (5.3) or
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h q = 1 (5.4) Where: h is the average time headway, ( n h i / ), in unit time per vehicle. Average traffic speed is defined in two ways. 1. Time-mean speed, n u u n i = i t 1 = (5.5) Where: t u = time-mean speed in unit distance per unit time, u i = spot speed (the speed of the vehicle at the designated point on the highway, as might be obtained using a radar gun) of the i th vehicle, and n = number of measured vehicle spot speeds. 2. Space-mean speed, example: You own two cars, they are both driven an equal distance and one gets 20 mpg, the other 50mpg Is the average mpg 35 (50+20)/2? No. ...say they are each driven 100 miles. The 50mpg car consumes 2 gallons the 20mpg car, 5 gallons. This gives 7 gallons for 200 miles or 28.75mpg (not 35 mpg) Must use the Harmonic mean: () = = n i i s t l n u 1 1 1 1 (5.9) For the mpg problem: mpg 57 . 28 20 1 50 1 2 1 1 mpg average = + = Next, traffic density is defined as k = n l (5.10) Where: k = traffic density in vehicles per unit distance, n = number of vehicles occupying some length of roadway at some specified time, and
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= length of roadway. The simple identity provides the basic relationship among traffic flow, speed (space- mean speed), and density is, q = uk (5.14) Where: q = flow, typically in units of vehicles per hour (veh/h), u = speed (space mean speed), typically in units of mi/h (km/h), and k = density, typically in units of veh/mi (veh/km).
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chapter5_notes_ - Chapter 5 Fundamentals of Traffic Flow...

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