华电美赛一等奖论文.docx

For office use onlyT1_T2_T3_T4_Team Control Number30413Problem ChosenAFor office use onlyF1_F2_F3_F4_Improved Highway Traffic RulesSummaryWith the development of the economy, the accelerated pace of life, the increasing number of vehicles, and the increase of car speeds, traffic flow and traffic safety have become the most important factors which have influenced the development of highways. In order to evaluate the current traffic rules the first model was established based on driving on the right. The first model, from the physics perspective, simulates the overtaking process and relates it to the calculation of the maximum traffic flow. In this way, a function relationship is set up between the maximum traffic flow max, the space headway D0, speed v, acceleration a, time t, and traffic flow density k. After calculating our model based on the actual data and analyzing the parameter sensitivity, our model is with a relatively small error under both the heavy and light traffic, and max is more sensitive to time t. And, multiple linear regression is used to set up the second model which is a function relationship between the traffic degree of safety S and each variable as a result, the method of parameter estimation is produced.When applying the rule of driving on the left to our model, we actually received a slightly different result because of the physiological nature of humans. It shows that the current rules do not enhance the flow of traffic. The improved traffic rules have proposed combining the advantages of two current rules. For example, the choice of left or right is decided by the weather condition, the pavement condition, the traffic flow and so on; Or build a double-layer highway for different models.Then the cellular automata theory is used to set up the model three which is a practical rule for the overtaking. This model attaches the cellular automata theory to the lane changing rules of the highway, calculates and simulates the different conditions of traffic flow. Based on the different traffic rules and road conditions, the influence which comes from the different road-changing rules on the traffic flow and other parameters have been discussed. The result shows that this model does not only improve the road capacity, but also enhances the efficiency of utilizing road resources. This model also ensures traffic safety and reduces the rate of accidents.Finally, under the intelligence system control there are two schemes standing out. In the first scheme, the highway is completely controlled by the system without any element of artificiality. Controlled by this scheme, we would see a safer and more efficient system. However, if the intelligence system was to collapse completely it would cause the highway traffic flow to break down. In the second scheme every vehicle is a control system working by itself. Although there are some artificial factors, the stability of the system is higher. If schemes one and two were to be utilized cohesively, then the transportation efficiency of models one and three would be improved greatly and the traffic accident rate would also decrease.Improved Highway Traffic RulesTeam #30413February 10SummaryWith the development of the economy, the accelerated pace of life, the increasing number of vehicles, and the increase of car speeds, traffic flow and traffic safety have become the most important factors which have influenced the development of highways. In order to evaluate the current traffic rules the first model was established based on driving on the right. The first model, from the physics perspective, simulates the overtaking process and relates it to the calculation of the maximum traffic flow. In this way, a function relationship is set up between the maximum traffic flow max, the space headway D0, speed v, acceleration a, time t, and traffic flow density k. After calculating our model based on the actual data and analyzing the parameter sensitivity, our model is with a relatively small error under both the heavy and light traffic, and max is more sensitive to time t. And, multiple linear regression is used to set up the second model which is a function relationship between the traffic degree of safety S and each variable as a result, the method of parameter estimation is produced.When applying the rule of driving on the left to our model, we actually received a slightly different result because of the physiological nature of humans. It shows that the current rules do not enhance the flow of traffic. The improved traffic rules have proposed combining the advantages of two current rules. For example, the choice of left or right is decided by the weather condition, the pavement condition, the traffic flow and so on; Or build a double-layer highway for different models.Then the cellular automata theory is used to set up the model three which is a practical rule for the overtaking. This model attaches the cellular automata theory to the lane changing rules of the highway, calculates and simulates the different conditions of traffic flow. Based on the different traffic rules and road conditions, the influence which comes from the different road-changing rules on the traffic flow and other parameters have been discussed. The result shows that this model does not only improve the road capacity, but also enhances the efficiency of utilizing road resources. This model also ensures traffic safety and reduces the rate of accidents.Finally, under the intelligence system control there are two schemes standing out. In the first scheme, the highway is completely controlled by the system without any element of artificiality. Controlled by this scheme, we would see a safer and more efficient system. However, if the intelligence system was to collapse completely it would cause the highway traffic flow to break down. In the second scheme every vehicle is a control system working by itself. Although there are some artificial factors, the stability of the system is higher. If schemes one and two were to be utilized cohesively, then the transportation efficiency of models one and three would be improved greatly and the traffic accident rate would also decrease.Key words: traffic flow model; multiple linear regression analysis; cellular automata model; intelligent system; traffic rulesTeam#30413 22 / 201. IntroductionNowadays traffic flow and traffic safety are two issues which staffs pay close attention to. For the current international research, there are some important algorithms for the study of traffic flow, for example: The Queuing Theory Algorithm, Car-following Theory and Hydrokinetics Simulation Theory. And on this basis some optimization models are put forward. For example, Junchen Jin1 proposed an improved Car-following Theory based on the ACC system; Mndez, A. R. and Velasco, R. M. put forward an improved macroscopic traffic flow model.2 Most of these methods assume that each lane is independent of each other, without analyzing the influence of overtaking process. For overtaking model, it is mainly used for the calculation of urban dual carriageway. For example, Runqi Wang3 put forward two-lane highway passing sight distance calculations; S. Jamison; M. McCartney proposed a vehicle overtaking model of traffic dynamics.4 However, the researches of overtaking at one-way lane highway are not many, and these researches cant be used to calculate the vehicle flow.Chinese and American cars both are left-hand and keep to the right. American highway general speed limit is 60-75mile/h (about 95 km/h -120 km/h), and each lane are all the same rules. However, in china, the speed limit varies on different lanes of even the same highway. For example, the left side speed limit is not less than 100 km/h and the right side is not less than 60 km/h, when the car drives on the two-lane highway; Or, the left side speed limit is not less than 100 km/h, the middle is not less than 90 km/h, and the right side is not less than 60 km/h, when the car drives on the three-lane highway. Compared with the American highway, Chinese highway is more straightly and the traffic flow is relatively small. Therefore, Chinese two-lane highway is selected to be discussed in this paper.We take advantage of the same variables in the traffic flow model and overtaking model to analyze and set up an improved model. In this way, the inadequacies in each model are improved .The maximum vehicle flow and safety factors are calculated, the performance under the light and heavy traffic has been taken into consideration, the correctness of the conclusions is tested and verified, and the sensitivity has been analyzed based on the improved model and the actual data. On this basis, we discussthe advantages and disadvantages ofdriving on the leftandright, and put forward an ideal traffic operation and management program. Lastly, the model has been analyzed and discussed under the intelligent control system.2. Model assumptions(1).Vehicles move along an infinitely long and unidirectional driveway；(2).Vehicles move in one direction in the unidirectional driveway；(3).The unidirectional driveway is completely closed, that is no vehicles entering or exiting the forks；(4).The performance and the size of the vehicles are consistent and the vehicles are not anchored； (5).Ignore the vehicle length, and regard the vehicle as a particle；(6).There is no accidents.3. Sign conventionD0the space headwaytraffic flow densityvehicle flowvfunimpeded velocityKjjamming densitySsafety factoraaccelerationv1the driving speed in carriagewayv2the driving speed in passing lanet1the time of changing to the left lane t2uniformly accelerated time in passing lanet3the time of changing to the right laneCnthe lane which the car N is ondnthe distance between the car N and the car aheaddn,otherthe distance between the car N and the car ahead in the adjacent lanedn,backthe distance between the car N and the car behind in the adjacent lanedsafethe safe lane changingdistance 4. Model 1（simulation of the overtaking process and the calculation of the maximum vehicle flow）The following discussion is based on vehicles driving on the right. In the traditional model of traffic flow, 5 the basic variables include the speed v, traffic flow density, flow q and time t. Vehicle conservation equation is established by the relationship between variables. This paper starts from this idea. Several typical variables are used in order to discuss and estimate the rule of driving on the right: acceleration a, time t, space headway D0, traffic flow density.The relationship between the maximum vehicle flow and all dependent variables are obtained by simulating overtaking process on the highway and discussing the functional relationship between the speed v and all independent variable.4.1The simulation of overtaking process Figure 1 shows overtaking on two-lane highway. It is considered that the size and the performance of cars is concordant, the weather is fine, the car can only overtake one, and the influence of import and export of forks have no need to be considered. And the overtaking vehicle is represented as C1, the overtaken vehicle is represented as C2, and the car from overtaking lane is represented as C3. In order to ensure the safety of overtaking, 5 factors should be taken into consideration:(1)In order to prevent the vehicle in front, which suddenly slow down or emergency brake, and vehicle behind from rear end collision, the space headway D0, which represents the distance between the overtaking vehicle C1 and the overtaken vehicle C2 before overtaking, should be considered.(2)The normal driving distance D2 of the overtaken vehicle C2 during the overtaking process should be considered.(3)The space headway D0, which represents the distance between the overtaking vehicle C1 and the overtaken vehicle C2 after overtaking, should be considered.(4)The safety distance between the overtaking vehicle C1 and C3 after overtaking should be considered, that is the space headway D0 between the overtaking vehicle C1 and C3 after back to the original driveway should be considered.(5)The normal driving distance D3 of the overtaken vehicle C3 during the overtaking process should be considered, that is no interference on C3 while overtaking. Fig. 1：Schematic diagram of overtakingAfter analysis, it can be divided into three stages when C1 is overtaking:1)C1C1: changing to the left lane at the speed of uniform acceleration (trajectory is approximately a straight line) process, setting the time as t1 and the distance as L1;2)C1C1: in the overtaking lane uniform acceleration phase, setting the time as t2, and the distance as L2;3)C1C1: changing to the right lane at the speed of uniform acceleration (trajectory is approximately a straight line), setting the time as t3 and the distance as L3.The speed of carriageway is set asv1, and the speed of overtaking lane is set asv2. Because cars would accelerate when overtaking, v2v1. Withthe normal running of the vehicle,twolane vehicledistances is L . According to the knowledge of the physics, it can be gotten:L1=v1t1+12at12 (1) L2=(v1+at1)t2+12at22 (2)L3=v1+a(t1+t2)t3 (3)L12-L2+D0-v2t=D0 (4)L12-L2+L2+L32-L2-v1(t1+t2+t3)=2D0 (5)Due to LL1，LL2,L can be ignored. The relationship between v1, v2, and other variables can be solved, that is:v1or v2=f(a,D0,t1,t2,t3)On the simultaneous of (1) to (5), it can be seen that:v1=2D0-12at12+t22-a(t1t2+t1t3+t2t3)t1 (6)v2=2D0-12at12-a(t1t2+t1t3+t2t3)t1 (7)Among them:vminv1vmaxvminv2vmaxUse (6) and (7) to calculate the speed. If the calculation results v1 or v2 is more than superior limit or less than the lower limit, the results should be modified to be the threshold value.While we research on vehicles along the highway and factors which are associated with the vehicle flow in highway, a model of traffic flow in highway can be established. Then the vehicle flow is estimated according to the speed of traffic flow v and the traffic flow density .According to the definition of each variable, it can be known that:=K1v1+K2v2 (8)In practice, it can often be seen that: the pilot was forced to reduce the speed, when road vehicles increased or traffic flow density increased. It indicates that there is a relationship between the speed and density, and speed decreases with the increase of traffic density. It can be assumed that the speed reduces linearly with the increasing of traffic density.That is:dv dK=-c0 （9）Among them: c00, c0R, v=v1,v2.The decrease rate of speed v increases with the increase of the actual traffic density. So, the above model can be corrected to be:dv dK=-c0K （10）It is easy to be known that this model is a quadratic objective function model.When the traffic density=0, the speed v can get the theoretical maximum, which is the unimpeded velocity vf. Thus it can be derived that:v0=v|K=0=vf （11）When the traffic densityruns up to the jamming density, the road is blocked and the speed is 0. That is:vKj=v|K=Kj=0 （12）According to (9), (10), (11), it can be known that:v=vf1-K Kj2, 0KKj (13) Therefore:=K1vf11-K1Kj12+K2vf21-K2Kj22 (14) This is the model that we derive. This model explains the relationship between the vehicle flow, speed and the traffic flow density. Then the maximum traffic flow that the highway can bear will be discussed according to the conclusion above.In order to find out the jamming density, the average vehicle length is expressed as l, and the minimum average space headway is expressed as D0. When the average vehicle distance d is less than the minimum average space headwayD0, dD0 , the road will be blocked, conversely the road is smooth. Thus, it can be seen that:Kj1=Kj2=Kj=103l+D0 （15）Among them: =5m.Then establish the Lagrangian Function: 6Lvf1,vf1,=K1vf11-K1Kj12+K2vf21-K2Kj22+v1-vf1+v2-vf2,Among them, is the Lagrange Multiplier.Solving equations:Lvf1=K11-K1Kj12- =0; Lvf2=K21-K2Kj22- =0; L=v1-vf1+v2-vf2=0Make:K11-K1Kj12=K21-K2Kj22= When:K1=K2 (16)The vehicle flow reaches the maximum value max.On the simultaneous of (6), (7), (8), (14), (15) to (16), we can know that:max=4D0-at12-12at22-2a(t1t2+t1t3+t2t3)t1K11-K1Kj12 （17）It is the functional relationship between the maximum vehicle flow max and each independent variable. The formula (17) shows that there is a positive correlation between K1, D0 and max and a negative correlation between a, t1, t2 , t3 and max. This is consistent with the actual situation. Meanwhile max is greatly influenced by a, t1, t2, t3. Then formula (17) will be verified by the actual data in highway, at the same time parameter sensitivity analysis will be conducted.actual dataactual data4.2 Verify result