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carfollowinga - Courtesy of Richard W Rothery Used with...

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CAR FOLLOWING MODELS BY RICHARD W. ROTHERY 6 6 Senior Lecturer, Civil Engineering Department, The University of Texas, ECJ Building 6.204, Austin, TX 78712 Courtesy of Richard W. Rothery. Used with permission.
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CHAPTER 4 - Frequently used Symbols = Numerical coefficients t = Collision time c a = Generalized sensitivity coefficient T = Reaction time a (t) = Instantaneous acceleration of a following U = Speed of a lead vehicle , m f vehicle at time t U f = Speed of a following vehicle a (t) = Instantaneous acceleration of a lead vehicle at time t = Numerical coefficient C = Single lane capacity (vehicle/hour) = Rescaled time (in units of response time, T ) = Short finite time period U f = Final vehicle speed U f = Free mean speed, speed of traffic near zero concentration U i = Initial vehicle speed U rel = Relative speed between a lead and following vehicle u (t) = Velocity profile of the lead vehicle of a F = Amplitude factor = Numerical coefficient k = Traffic stream concentration in vehicles per kilometer k j = Jam concentration k = Concentration at maximum flow platoon V = Speed V f = Final vehicle speed = Frequency of a monochromatic speed oscillation x ¨ f ( t ) = Instantaneous acceleration of a following m k f = Concentration where vehicle to vehicle interactions begin k = Normalized concentration vehicle at time t x ¨( t ) = Instantaneous speed of a lead vehicle at time t n L = Effective vehicle length x ¨ f ( t ) = Instantaneous speed of a following vehicle -1 L = Inverse Laplace transform at time t = Proportionality factor x ( t ) = Instantaneous speed of a lead vehicle at i = Sensitivity coefficient, i = 1,2,3,... time t ln(x) = Natural logarithm of x x f ( t ) = Instantaneous speed of a following vehicle q = Flow in vehicles per hour at time t q = Normalized flow x ( t ) = Instantaneous position of a lead vehicle at n <S> = Average spacing rear bumper to rear bumper S i = Initial vehicle spacing S f = Final vehicle spacing S = Vehicle spacing for stopped traffic time t x f ( t ) = Instantaneous position of the following vehicle at time t x i ( t ) = Instantaneous position of the i th vehicle at time t o S(t) = Inter-vehicle spacing z(t) = Position in a moving coordinate system S = Inter-vehicle spacing change T = Average response time < x > = Average of a variable x T = Propagation time for a disturbance o t = Time = Frequency factor
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4. C AR F OLLOWING M ODELS It has been estimated that mankind currently devotes over 10 million man-years each year to driving the automobile, which on demand provides a mobility unequaled by any other mode of transportation. And yet, even with the increased interest in traffic research, we understand relatively little of what is involved in the "driving task". Driving, apart from walking, talking, and eating, is the most widely executed skill in the world today and possibly the most challenging. Cumming (1963) categorized the various subtasks that are involved in the overall driving task and paralleled the driver's role as an information processor (see Chapter 3). This chapter focuses on one of these subtasks, the task of one vehicle following another on a single lane of roadway (car following).
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