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Pf3 The overtaking ratio of large vehicles over small vehicles Pf4 The overtaking ratio of large vehicles over large vehicles Xa The average speed of all the vehicles

Xa1 The average speed of all the small vehicle Xa2 The average speed of all the buses and trucks di(t) The desire for lane-changing

si(t) The stress parameter si(t?1) The accumulated stress

PR(x) The probability functions of lane-changing to the right lane PL(x) The probability functions of lane-changing to the left lane

Jperf(k) The corresponding performance function Tctrl The controller time step

N(0) The number of vehicles

K The number of time steps

qdem The constant demand used for the simulation

qout The outflow measured at the 20th segment

5. Models

By analyzing the problem, we decided to propose a solution with building a cellular automaton model.

5.1 Building of the Cellular automaton model

Thanks to its simple rules and convenience for computer simulation, cellular automaton model has been widely used in the study of traffic flow in recent years.

We study the three lanes in one direction of a two- way six-lane highway in this paper. Considering the road as three one-dimensional discrete grid point chains in parallel, we define

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the length of each chain is L, and each grid point will be occupied or empty at each moment. The first lane is the far left one, the second lane is the middle one, and the third lane is the far right one. Vehicles traveling on the highway are concluded as small vehicles (including cars, mini-buses, etc.), trucks and buses in this paper. And the three types of vehicles are randomly distributed in three lanes according to certain density and mixing ratio. Each small vehicle accounts for 1cell space, and each truck accounts for 3 cell space. The speed of small vehicles is 0–120km/h on highway, corresponding to 0–6cell space/s of the model and that of trucks and buses on highway is 0–100km/h, corresponding to 0–5 cell spaces.

Let xi(t)be the position of vehicle iat time t, vi(t) be the speed of vehicle iat time t,

pbe the random slowing down probability, and R be the proportion of trucks and buses, the

distance between vehicle i and the front vehicle at time tis:

gapi?xi?1(t)?xi(t)?1, if the front vehicle is a small vehicle. gapi?xi?1(t)?xi(t)?3, if the front vehicle is a truck or bus. 5.1.1 Verify the effectiveness of the keep right except to pass rule

In addition, according to the keep right except to pass rule, we define a new rule called: Control rules based on lane speed. The concrete explanation of the new rule as follow: There is no special passing lane under this rule. The speed of the first lane (the far left lane) is 120–100km/h (including 100 km/h)；the speed of the second lane (the middle lane) is 100–80km8/h (including80km/h)；the speed of the third lane (the far right lane) is below 80km/ h. The speeds of lanes decrease from left to right. ? Lane changing rules based lane speed control

If vehicle on the high-speed lane meets v?vcontrol, gapif(t)?min(vi(t)?1,vmax),

gapib(t)?gapsafe, the vehicle will turn into the adjacent right lane, and the speed of the vehicle after lane changing remains unchanged, where vcontrol is the minimum speed of the corresponding lane.

If vehicle on the low-speed lane meets v?vcontrol,gap(t)?min(vi(t)?1,vmax) and

bgapif(t)?gap(t) and gapi(t)?gapsafe, the vehicle will turn into the adjacent left lane with

probability pd, and the speed of the vehicle after lane changing will remain unchanged. ? The application of the Nasch model evolution

Rickert et al. examine d a two-lane cellular automaton based on the NaSch model [1].Nagel

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et al. summarized different approaches to lane changing and classi?ed the multitude of possible lane-changing rules for freeway traf?c [2]. They used a cellular automaton model for two-lane traf?c to generate the density inversion, and found in many European countries, the densities somewhat below the maximum ?ow density. Let al. proposed a symmetric two-lane cellular automata model to investigate the aggressive lane-changing behavior of fast vehicle and the effect of different lane-changing probability [3]. (1) Accelerating: vi(t?1/3)?min(vi(t)?1,vmax) ; (2) Decelerating: vi(t?2/3)?min(vi(t?1/3),gapi); (3) Randomly slowing down with probability: m (4) Location renewal: x(t?1)?x(t)?1.

Let Pd be the lane changing probability (taking into account the actual situation that some drivers like driving in a certain lane, and will not take the initiative to change lanes), gapif(t) indicates the distance between the vehicle and the nearest front vehicle, gapib(t) indicates the distance between the vehicle and the nearest following vehicle. In this article, we assume that the minimum safe distance gap safe of lane changing equals to the maximum speed of the following vehicle in the adjacent lanes.

? Lane changing rules based on keeping right except to pass

In general, traffic flow going through a passing zone (Fig. 5.1.1) involves three processes: the diverging process (one traffic flow diverging into two flows), interacting process (interacting between the two flows), and merging process (the two flows merging into one) [4].

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Fig.5.1.1 Control plan of overtaking process

(1) If vehicle on the first lane (passing lane) meets gapif(t)?min(vi(t)?1,vmax) and

gapib(t)?gapsafe, the vehicle will turn into the second lane, the speed of the vehicle after lane changing remains unchanged.

(2) If vehicle on the second lane meetsgap(t)?min(vi(t)?1,vmax), gapif(t)?gap(t)

bandgapi(t)?gapsafe, the vehicle will turn into the first lane with probabilitypd. If vehicle on

the second lane meetv?4(smaller than 80 km/h),

gapib(t)?gapsafeandgapif(t)?min(vi(t)?1,vmax), the vehicle will turn into the third lane, and the speed of the vehicle after lane changing will remain unchanged.

b(3) If vehicle on the third lane meetsv?4(larger than 80 km/h) gapi(t)?gapsafe and

gapif(t)?min(vi(t)?1,vmax) , the vehicle will turn into the second lane, and the speed of the vehicle after lane changing will remain unchanged.