Car following

# Car following - Traffic Flow Theory: Microscopic Car...

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1 Traffic Flow Theory: Microscopic Car following Models Hong K LO Civil Engineering HKUST

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2 Microscopic Density Characteristics • Concerns with the longitudinal space occupied by individual vehicles in the traffic stream • Relates to safety, capacity, and level of service • Car following models developed primarily in the 50’s and 60’s in Japan, and GM Research Lab. Recently, there is a renewed interest in car following models •No ta t ions and de f in i t
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5 Distance Headway characteristics Distance headway is defined as the distance from a selected point on the lead vehicle to the same point on the following vehicle. dt Lgt nn n ++ = + 11 af n + 1 : distance headway of vehicle n+1 at time t Lt n : physical length of vehicle n gt n + 1 : gap length between vehicle n and n+1 at t Time headway: dtht x n = & d n + 1 : distance headway of vehicle n+1 h n + 1 : time headway of vehicle n+1 at point p & x n + 1 : speed of vehicle n during the time period

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6 Traffic density is the macroscopic density characteristic and is defined as the number of vehicles occupying a length of roadway usually in a single lane over a length of 1 mile. k d = 5280 k: density in vehicles per mile per lane; 5280: the number of feet per mile; d : average distance headway (feet per vehicle) d d N n n N = = 1 d n : individual distance headway (feet per vehicle) N: number of observed distance headways
7 Pipes’ Theory • “A good rule for following another vehicle at a safe distance is to allow yourself at least the length of a car between your vehicle and the vehicle ahead for every ten miles per hour of speed at which you are traveling.” dx t x t L xt L MIN n n MIN n n n =− = L N M O Q P + + + a f a f a f a fa f 1 1 147 10 & . 1.47 is the conversion factor from m/h to ft/sec. Assuming an average vehicle length of 20 ft, t MIN n = + + 136 20 1 . & af and the time headway: h MIN n =+ + 20 1 . & a f

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9 Frobes’ Theory Considers that the reaction time needed for the following vehicle to perceive the need to decelerate and apply the brakes. That is, the time gap between the rear of the lead vehicles and the front of the following vehicle should always be equal to or greater than the reaction time. ht L xt MIN n n =+ Δ & a f

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10 Frobes conducted many field studies of minimum time gaps and found considerable variations between drivers and sites. Min time gaps varied from 1 to 2 to 3 seconds. Assuming a reaction time of 1.5 seconds and a vehicle length of 20 ft, h xt MIN n =+ 150 20 . & a f and hx t MIN n = + 20 . & af
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12 General Motor’s Theories • It bridges between the microscopic and macroscopic theories of traffic flow • Response = function (sensitivity, stimuli) • Response: acceleration and deceleration of the following vehicle; stimuli: the relative speed of the lead and following vehicle
13 The first model: && & & xt t x txt nn n ++ + = 11 Δ a f a f a f α The stimuli term could be positive, negative, or zero, which could cause the response to be an acceleration, deceleration, or constant speed: & & x t x t t n a f a f a f >⇒ + > 0 Δ & & x t x t t n af a f <⇒ + < 0 Δ & & x t x t t n a f a f a f =⇒ + = 0 Δ

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## This note was uploaded on 12/24/2011 for the course CIVL 563 taught by Professor Hklo during the Fall '10 term at HKUST.

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Car following - Traffic Flow Theory: Microscopic Car...

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