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It can be seen from Fig. 5.1.5:

(1) The average speed will reduce with the increase of vehicle density and proportion of large vehicles.

(2) When vehicle density is less than 0.15,Xa,Xa1andXa2are almost the same under both control conditions.

(3) When vehicle density is greater than 0.15, Xa and Xa1will decrease with the increase of vehicle density and proportion of large vehicles, but that of the speed control decreases faster.

(4) When the traffic flow reaches non-free flow state, the two control conditions,Xa,

Xa1andXa2are almost the same under both control conditions. ? Effect of different control conditions on traffic flow

Fig.5.1.6

Fig. 5.1.6 Relationships among vehicle density, proportion of large vehicles and traffic flow under different

control conditions. (Figure a1 indicates passing lane control, figure a2 indicates speed control, and figure b indicates the traffic flow difference between the two conditions.

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It can be seen from Fig. 5.1.6：

(1) When vehicle density is lower than 0.15 and the proportion of large vehicles is from 0.4 to 1, the traffic flow of the two control conditions are basically the same.

(2) Except that, the traffic flow under passing lane control condition is slightly larger than that of speed control condition. 5.1.3 Conclusion

In this paper, we have established three-lane model of different control conditions, studied the overtaking ratio, speed and traffic flow under different control conditions, vehicle density and proportion of large vehicles.

By analyzing lots of data and graphics, we conclude a solution as follow:

Firstly, taking the vehicle density, proportion of large vehicles, the average speed and traffic flow into account, we found that when vehicle density is lower than 0.15, the average speed and traffic flow are almost the same under both control condition. We define the state of the freeway: light traffic.

In addition, with the increase of the vehicle density, when vehicle density is greater than 0.15, the traffic flow will decrease with the increase of the vehicle density and proportion of large vehicles, but the traffic flow and the average speed of the speed control rule decreases faster, so the rule of keep right except passing is more effective, the state of freeway was called: heavy traffic.

This is because, under speed control condition, when the high-speed lane reaches saturated state, the rest of the vehicles must be traveling on the low-speed lane, in this situation, the speed of the fleet will be determined by slow vehicles; while under passing lane control condition, high-speed vehicles can surpass low-speed vehicles by making use of passing lane. High-speed and low-speed vehicles will separate, and the high-speed vehicles will continue to maintain high-speed travel.

Finally, we take the safe factor into consideration. By lots of analysis, we found that the overtaking ratio under the keep right rule is much higher than that under the lane speed control rule, but when the proportion of large vehicles is greater than 0.5, the overtaking ratio decrease faster under the rule of keep right, so the rule of keep right is more suitable for the situation; when the proportion of large vehicles is about 0.5, the overtaking ratio will reach its peak value; the overtaking ratio under keep right control condition is higher than that of lane speed control rule relatively.

In general, the lane changing process is very complex. We combine the traffic flow, the safe factor, vehicle density with other influence factors, and draw a conclusion that the rule of keep right except to pass is more effective than that of speed control condition overall.

But, if we flexibly adjust freeway rule according to the massive influence factors, such as proportion of large vehicles，the weather condition, the size of the vehicle and so on, we can manage the freeway efficiently.

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5.2 The solving of second question

5.2.1 The building of the stochastic multi-lane traffic model

For the second question, in countries where driving automobiles on the left is the norm, it requires us to argue whether or not our solution can be carried over with a simple change of orientation, or would additional requirements be needed.

In this section, we build our model to design a stochastic traffic model for a multi-lane road. In the process of building, we present the multi-lane model as a union of communicating single-lane CCA [6] where the transfers of the vehicles from one lane to another are done by some transfer operators. This communication includes only the safety criteria where a vehicle desiring to change its lane asks to the target lane if it is possible to perform a safe (collision-free) lane-changing. Before we describe the multi-lane model, we first give a brief description of how this lane-changing process works.

Lane-changing is performed only if a vehicle desires to change lane. The desire for lane-changing di(t)depends on the stress parameter si(t)resulting with a tendency of changing lane to the right if the stress is positive and to the left otherwise [7]. Note that we allow this parameter to assume values only in the interval [smin,smax]. The stress is an accumulative quantity, for this reason we define the accumulated stress as the sum of the previous stress and a quantity showing how much the vehicle is above or below its optimal velocity. For the update of the stress, we decrease or increase the accumulated stress according to some situations: it is decreased by a factor of 2 to avoid frequent lane-changing in the case there is a traffic jam and the queue is moving (sense of satisfaction as a result of seeing the traffic begins to flow); it is increased by a factor of (1??)to make the vehicle change the lane instead of braking if the front vehicle is close and tends to brake (??[0,1]represents the degree of this situation). In other cases the updated stress si(t?1)is assumed to be the accumulated stress, in Ref.8.

The update of the desire of lane-changing is carried out by means of a Bernoulli processB(2,p)[9]where the probabilities of lane-changing to the left and right are calculated by applying the functions PL(x)and PR(x), respectively, to the stress. Thus, if the stress is positive we applyB(2,PR(x)), otherwise we applyB(2,PL(x)). In the case the stress is negative; we also consider the jam situation while making the decision. More specifically, if a driver is in a jam situation, applying B(2,PL(x)) results with a tendency of moving to the left lane for this driver. However in reality, drivers tend to find an emptier lane in a jam situation. For this reason, we apply a Bernoulli process B(2,0.7) where the probability of moving to the left is

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0.7and to the right otherwise, if the vehicle is on a middle lane [10]. It is clear that in the case there exists no lane on the left (right), the driver can only move to the right (left) lane. We consider these different probabilities since the drivers desiring to go faster usually tend to move to the left lane more than the right lane. The other situations taken into account are: a sense of satisfaction after performing a lane-changing and reducing the ping-pong phenomenon which are both achieved by decreasing the stress a factor of 5. This reduction is decided according to some empirical observations in the simulations. The ping-pong effect occurs only in jam situations, since the vehicles try to find a relatively better lane [11]. Note that there is just a local knowledge while trying to change the lane, and the gain parametrized by the stress cannot be known for the whole target lane so the best strategy of finding a better lane is to try randomly. 5.2.2 Conclusion

On one hand, from the analysis of the model, in the case the stress is positive, we also consider the jam situation while making the decision. More specifically, if a driver is in a jam situation, applying B(2,PR(x)) results with a tendency of moving to the right lane for this driver. However in reality, drivers tend to find an emptier lane in a jam situation. For this reason, we apply a Bernoulli process B(2,0.7) where the probability of moving to the right is 0.7and to the left otherwise, and the conclusion is under the rule of keep left except to pass, So, the fundamental reason is the formation of the driving habit.

On the other hand, we take the ping-pong effect into account, It is a sense of satisfaction after performing a lane-changing and reducing the ping-pong phenomenon which are both achieved by decreasing the stress a factor of 5.

Note that there is just a local knowledge while trying to change the lane, and the gain parameterized by the stress cannot be known for the whole target lane. So from the ping- pong effect, the choice of the changing lane is random.

From what has been discussed above, the original changing lane choice is random, but under different freeway rule, the driver foster different driving habit during the long period, So in countries where driving automobiles on the left is the norm, our solution can be adopted completely.

5.3 Taking the an intelligent vehicle system into a account

For the third question, if vehicle transportation on the same roadway was fully under the control of an intelligent system, we make some improvements for the solution proposed by us to perfect the performance of the freeway by lots of analysis. 5.3.1 Introduction of the Intelligent Vehicle Highway Systems

The ever-increasing demand for mobility and transportation results in a growing traffic congestion problem. One of the promising approaches to reduce the frequency and impact of traffic jams is the optimal and efficient usage of the existing system. This approach will result in integrated traffic management and control systems that incorporate intelligence in both the