# Realistic single-lane traffic flow

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## WHAT IS IT?

This models the flow of traffic on a single-carriageway. It is different from other models in that the "car following" rules are simple, realistic and could mirror actual driving practices. Acceleration/deceleration is smooth and within comfortably achievable bounds for the average car. Each car adjusts its `headway-secs`

(i.e. the number of seconds it is behind the `car-ahead`

when passing a fixed point) towards its desired `tailgate-secs`

(i.e. the target `headway-secs`

that that an individual driver prefers). A realistically achievable hard braking is applied whenever there is a chance of shunting the `car-ahead`

.

The road is effectively a continuous loop, as the world wraps. The model demonstrates how wave-like traffic congestion forms, even without any accidents or road works.

## HOW TO USE IT

Set `traffic-density`

to the desired %occupancy of the total road space.

Click `setup`

to create randomly distributed stationary cars with heterogoneous `tailgate-secs`

(between 1 and 2 seconds, in line with the general actual driving practices in European countries, despite the recommended "two second rule").

Click `go-forever`

to drive the cars.

Experiment with `safe-headway`

(the minimum seconds it is safe to follow at) and `brake-factor`

(the factor by which the normal deceleration limit is multiplied by in order to brake hard when avoiding the chance of shunting the car ahead) to see how the "Red Car speed" plot varies, and what are the threshold values for avoiding shunts (which raise an error mssage and stop the run). The default values of these parameters are the minimum ones that have been experimentally found to avoid shunting in all circumstances.

The car following rules have been kept simple enough to be intuitively approximate-able by humans. Cars accelerate/decelerate by a factor based on `headway-secs - tailgate-secs`

. Thus a car accelerates when `headway-secs > tailgate-secs`

and decelerates when `headway-secs < tailgate-secs`

. This factor is bounded by the range -1 to +1 and multiplied by `max-accel`

to give the acceleration at each tick, where `max-accel`

is a realistic limit for normal acceleration and deceleration. The factor is reset to - `brake-factor`

when there is a possibility that the car `could-shunt`

the `car-ahead`

. This causes the car to brake hard to avoid the possible shunt. The `could-shunt`

test is basically a simple comparison of `distance-to-car-ahead`

verses `closing-speed * safe-headway`

, something which a human driver could feasibly approximate in his head.

Optimum speed limits for the fastest constant flow of traffic at each `traffic-density`

, can be determined as follows:

Click `optimise-speed-limit`

to incrementally reduce the `speed-limit`

from its current value until all cars can consistently reach this `speed-limit`

after an initial settling down period. Thereafter all cars continue to travel at this constant speed and optimum throughput is achieved for the current density (the values of which are logged to the `output`

area).

Click `optimise-speed-limits`

to run `optimise-speed-limit`

as the `traffic-density`

is incrementally increased from its current value. So, as this proceeds the `traffic-density`

increases and the `speed-limit`

decreases. It terminates when the `minimum-speed-limit`

is reached.

## THINGS TO NOTICE

Cars that are clustered together move slowly, causing cars behind them to slow down also. As this effect ripples back a traffic jam forms. Even though all of the cars are moving forward, the traffic jams often move backwards. This behavior is common in wave phenomena: the behavior of the group is often very different from the behavior of the individuals that make up the group. An example random car is painted red and highlighted for easy watching. Its speed plot eventually settles down either to periodic oscillations, or to the speed limit.

## EXTENDING THE MODEL

Try other realistic car following rules in follow-car.

## RELATED MODELS

This is an improvement of "Traffic Basic" which is patch-based, only looks one-patch ahead and decelerates impossibly jerkily in just one step to slower than the car-ahead. In contrast this model looks as far ahead as the next car and accelerates / decelerates smoothly and realistically.

## COPYRIGHT AND LICENSE

by Ian J Heath is licensed under a Creative Commons Attribution 4.0 International License
http://creativecommons.org/licenses/by/4.0/

## Comments and Questions

globals [ticks-per-sec patches-per-tick-per-kph patches-per-km world-width-km number-of-cars min-speed-limit min-distance red-car max-accel speed-limit-ok-count] breed [cars car] cars-own [speed tailgate-secs] to setup clear-all set ticks-per-sec 30 set min-speed-limit 30 set min-distance .001 set max-accel .001 * 3600 / ticks-per-sec ;; accel per tick ~ 1m per sec per sec let patch-length 5 ;; just big enough for a 5m car set patches-per-km 1000 / patch-length set world-width-km world-width * patch-length / 1000 let km-per-tick-per-kph 1 / 3600 / ticks-per-sec set patches-per-tick-per-kph km-per-tick-per-kph * 1000 / patch-length ask patches with [abs pycor < 2] [ set pcolor white ] ;; setup-road setup-cars end to setup-cars clear-turtles clear-all-plots set-default-shape cars "car" set number-of-cars round (world-width * traffic-density / 100) foreach sort n-of number-of-cars patches with [pycor = 0] [ ?1 -> ask ?1 [sprout-cars 1 [ set color blue set heading 90 set speed 0 set tailgate-secs 1 + random-float 1 ;; 1-2 secs behind the car ahead ]] ] set red-car one-of cars ask red-car [ set color red ] watch red-car reset-ticks end to go foreach n-values number-of-cars [ ?1 -> number-of-cars - 1 - ?1 ] [ ?1 -> ask car ?1 [follow-car ] ] ;; Reduce chance of shunting by always moving the car ahead first (for all except the last car) tick end to follow-car ;; car following: adjust speed by targeting own tailgate-secs let car-ahead car ((who + 1) mod number-of-cars) let distance-to-car-ahead ((([xcor] of car-ahead - xcor) mod world-width) - 1) / patches-per-km ;; bumper-to-bumper distance in km if speed > 0 and distance-to-car-ahead < 0 [error word " Shunt !!! distance-to-car-ahead = " distance-to-car-ahead] ;; in case safe-headway and brake-factor have not been set to avoid shunts let headway-secs max (list 0 (distance-to-car-ahead - min-distance)) / (speed + .000000001) * 3600 ;; Secs to travel headway (- min-distance) at the current speed (+ .000000001 to avoid ZeroDivide) let accel-factor max list -1 min list 1 (headway-secs - tailgate-secs) ;; +ve if headway-secs > tailgate-secs, else -ve (capped at -1 to +1 to avoid excessive acceleration) ;; reset accel-factor for hard braking, if closer than safe-headway let closing-speed speed - [speed] of car-ahead let could-shunt (distance-to-car-ahead - min-distance) < (safe-headway / 3600 * closing-speed) if could-shunt [set accel-factor 0 - brake-factor] ;; hard brake if could-shunt set speed max list 0 min list speed-limit (speed + accel-factor * max-accel ) ;; observe the speeed-limit, and no reversing fd speed * patches-per-tick-per-kph end to optimise-speed-limits setup set traffic-density traffic-density - 1 ;; compensate for incrementing before the first optimise-speed-limit while [speed-limit >= min-speed-limit] [ set traffic-density traffic-density + 1 ;; repeat for traffic-density = 2,3,... optimise-speed-limit ] end to optimise-speed-limit set speed-limit-ok-count 0 while [speed-limit-ok-count < 300] [ if speed-limit < min-speed-limit [ output-print word "Finished optimising speed limits down to min-speed-limit of " min-speed-limit stop ] decrement-speed-limit ] let cars-per-hr number-of-cars * speed-limit / world-width-km output-print (word "For traffic-density " substring (word traffic-density " ") 0 2 " speed-limit = " substring (word speed-limit " ") 0 3 " cars-per-hr = " cars-per-hr) end to decrement-speed-limit setup-cars let ticks-per-traverse-at-speed-limit 3600 * ticks-per-sec * world-width-km / speed-limit repeat 3 * ticks-per-traverse-at-speed-limit [ go if all? cars [speed = speed-limit] [ set speed-limit-ok-count speed-limit-ok-count + 1 stop ] ] set speed-limit speed-limit - 1 end

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a a

## question (Question)

please,can i get any reference or paper about this model to understand the problem

## Posted about 7 years ago

Ian Heath

## In answer to a a

This is original work and there are no other papers or references beyond the references made in the "Info" of this model. I would be interested if you have any comments on this model though once you have played (sorry, experimented) with it.

## Posted about 7 years ago