Intelligent controlled transportation system美赛数学建模文章-交通建模方面.doc

Team 25963 SummaryWith the rapidly developing of traffic, freeway gradually becomes the mainstream way of short-distance travel. In order to make the means of transportation become more perfect, we need to improve in as many aspects as possible. To measure the performance of a freeway, we must consider the following two factors: traffic flow and safety. These are the main aspects that we must take into consideration to weigh whether a freeway is good or bad. In order to better simulate the actual situation, we established a simulation model .We adopted the core ideas of the Cellular Automata Model, on whose basis, we established a new model suitable to the simulation of the performance on freeway. The key point of our model is regarding time and space to be discrete which is actually continuous. Every vehicle must be in certain discrete position. In this problem, we divide the road into many same-size rectangular grids, the vehicle must move in a fixed place. he number of grids stands for the distance, the number of the grids that a vehicle move per unit time stands for its speed. According to different rules, different small models are respectively established to study which rule is better. In a word the model we designed has combined the advantages of the Cellular Automata Model and the most important aspects of the actual situation on the highway. To study the performance more accurately, We have studied under the following three conditions: 1. under very light traffic load;2. under a medium traffic load (normal traffic conditions)(main part);3. under a very heavy traffic load.In each case, we have analyzed the performance on freeway and discussed the traffic flow both in theory and by simulation. We have also calculated how the drivers on freeway guarantee their safety quantitatively. After that, we examined tradeoffs between traffic flow and safety, and analyzed the how each case limit the speed and overtaking ratio. Through analysis, we have got relatively reasonable conclusions.Differently, in case1, we gave an actual example to test our model. In case 2, we respectively analyzed the following and passing phenomenon in detail.Safety on freeway is so important that we have studied how much the traffic flow and speed influence it, we have calculated the two safety correlation coefficients of the traffic flow and speed and conclude that speed influence safety most.We have made comprehensive evaluation of “ the rule that requires drivers to drive in the right-most lane unless they are passing another vehicle, in which case they move one lane to the left, pass, and return to their former travel lane” , and designed a new rule that“ two lane used equally” to promote greater traffic flow while guaranteeing safe. The new rule has been tested by simulation.In countries where driving vehicles on the left is the norm, we have analyzed their performance on freeway, we found that my solution cannot be carried over with a simple change of orientation, additional requirements that the position of cab be changed should be needed. If vehicle transportation on the same roadway was fully under the control of an intelligent system, the most obvious change is the change of overtaking ratio (becomes almost 100%), this change will decrease traffic flow in our earlier analysis.ContentsAssumption and its Rationality 51. Model 51.1 Basic model 51.2 Feasibility and rationality of the model 61.3 How we set the parameters in the model 61.4 Simulation of different situation that we use in the article61.4.1 Rules of the single-lane Cellular Automata model 61.4.2 The lane changing model 71.4.2.1 The lane changing rules 71.4.2.2 Explanations of the lane changing rules 71.4.3 Lane Changing Model verification 82. Different traffic density 82.1 Under very light traffic load 92.1.1 Traffic flow calculation and simulation 92.1.2 Safety guarantee102.1.3 Speed limit 112.1.4 Overtaking ratio limit 112.1.5 An actual example 112.2 Medium traffic load (Normal traffic conditions) 122.2.1 Three factors influencing on traffic flow and simulation 122.2.2 Safety guarantee 162.2.2.1 Following phenomenon 162.2.2.2 Overtaking phenomenon 172.2.3Speed limit 182.2.4 Overtaking ratio limit 182.3 Very heavy traffic load182.3.1 Safety factors analysis 182.3.2Influence on traffic flow and simulation 192.3.3Speed limit(very low speed) 192.3.4 Overtaking ratio limit 192.4. Safety correlation coefficient 193. A better rule 203.1 Description 203.2 Simulation 214. For countries driving on the left 215. Intelligent controlled transportation system 22Futher analysis of our model 22Conclusion 23Reference 24Assumption and its RationalityAll the length is dispersive. Our model describes the movement of each individual vehicle according to the study for their interaction by taking vehicles as dispersive particles. Cellular Automata model divides a section of road into many cells of 2 meters in length.The time interval is one second. As length is dispersive, the time is dispersive. We make the minimum time interval is one second. One second is short enough to describe the motion of the car.The length of the car is the same. In some freeway the big truck is prohibited. The number of small cars dominates. We just study the situation that small car driving on the freeway. The length of the car is 4 meters or so. We take it as a average 2 cell length.The number of the cars on a selected section of the road is a constant. We only study a section of the road. We designed it as a closed loop which means one car gets out and one car enters. So the number of the cars on a selected section of the road is a constant. In this way, the density of the cars on the road is a constant.We ignore the factor of weather and season. Different weather may lead to different traffic. The situation is complex that we have to ignore these factors.The steering wheel is on the right side of the car. It is a common that n countries where driving vehicles on the left is the norm the steering wheel is on the right side of the car. It is also a fact in US and China.Passing is not allowed to single road. At the same time a cell can be occupied by only one car. So the car cannot pass another car in front on the same road.Analysis of the problem1. Model1.1 Basic model The key point of our model is regarding time and space as discrete which is actually continuous. Every vehicle must be in certain discrete position. In this problem, we divide the road into many of the same size rectangular grids, the vehicle must move in a fixed place. The number of grids stands for the distance, the number of the grids that a vehicle move per unit time stands for its speed.1.2 Feasibility and rationality of the modelWhen we analyze the problem, the distance we consider is long enough, and time is also long enough, dividing time and space into many small parts will not influence the results of analysis and simulation so much. On the contrary, the way we make time and space discrete will simplify the analysis and calculation process to a great extent, it can also make simulation much more easy. 1.3 How we set the parameters in the modelConsidering the various aspects of factors, the Basic parameter definiteness is as follows: In this model, the length of each cell is 2 meters, per 2 successive cells contain one vehicle and these 2 successive cells are in the same state at moment t, i.e. thespeed of vehicle contained. Maximum speed of vehicle is 120km/h（33m/s）. Minimum speed of vehicle is 80km/h（22m/s）.Thus in this model, maximum speed (vm) is 16 cell length/second, minimum speed(vmin) is 11 cell length/second. Speed value range is vminvm and renewal time interval is 1 second. 1.4 Simulation of different situation that we use in the article1.4.1 Rules of the single-lane Cellular Automata model Variable symbols used in this Model are defined as follows.xn(t):the position of the vehicle at moment t; vn(t):the speed of the vehicle at moment t; an(t):the acceleration of the vehicle at moment tt+1; gn(t):the number of free sites ahead of the vehicle, i.e. gn(t)xn-1(t)xn(t)2.The states of all vehicles on road conduct synchronous renewal according to the following rules.Acceleration Rule: if vn(t) gn(t), the vehicle will accelerate.If gn(t) - vn(t) < 2, then an(t) = gn(t) - vn(t).If gn(t) - vn(t) 2, then an(t) = 2.If vn(t) = vm, then an(t) = 0.Deceleration Rule: If vn(t) > gn(t), the vehicle will decelerate.If gn(t) - vn(t) > -2, then an(t) = gn(t) - vn(t).If gn(t) - vn(t) -2, then an(t) = -2.Correction Rule: If the acceleration of the vehicle is an(t) at moment t, on the assumption that the forward vehicle is decelerated at maximum deceleration, then at moment t+1.If vn(t+1) gn(t+1), then the acceleration of the vehicle is an(t).If vn(t+1) > gn(t+1), then the acceleration of the vehicle is an(t)-1, and recalculate the vn(t+1) and gn(t+1), until vn(t+1) gn(t+1). Thus, the actual acceleration of the vehicle is a corrected value. 1.4.2 The lane changing model Lane changing is the emphasis and difficulty of multi-lane road traffic flow simulation. A lane change decision process is assumed to have the following three steps: production of lane changing desire, feasibility analysis on lane changing activity and implementation of lane changing activity (Zou,2002).Based on the single-lane NS model, K. Nagel has put forward the multi-lane traffic simulation model, in which, the vehicles moving in each lane shall conform to the NS rule and satisfy the Lane-changing rules (Nagel,1998/ Wagner,1997) when changing lanes. This article put forward a kind of lane-changing model that is suitable for vehicle movement in order on the urban roads under the unobstructed condition, which is shown to match the real vehicle activities well through computer.Simulation.1.4.2.1 The lane changing rulesVariable symbols used in this model are defined as follows. gn(t) = xn-1(t) - xn(t) - 2 (1)Here: gn(t)-the number of free sites ahead of the vehicle on the present lane at moment tgl(t)-the number of free sites between the vehicle and the forward vehicle on target lane at moment tgb(t)-the number of free sites between the vehicle and the backward vehicle on target lane at moment t vl(t) -the speed of the forward vehicle on target lane at moment t vb(t)-the speed of the backward vehicle on target lane at moment t sb(t) -the emergency braking distance of the backward vehicle on target lane at moment tThe lane changing model is as follows:(1) if gn(t) < vm, then the vehicle will produce lane changing desire(2) if gl(t) gn(t) and vl (t) > vn-1 (t) and sb(t) sb(t), then the vehicle will change lane at vn(t) at probability p change Here, sb(t) = vb + max(vb - 2,0) + max(vb - 4,0) . (2)1.4.2.2 Explanations of the lane changing rules In this model, gn(t)<vm means due to the reason that the speed of forward vehicle is slower, that this vehicle will produce the desire of changing lane in order to reach faster speed and obtaining more free driving space.After producing the desire of changing lane, a vehicle will determine the feasibility of changing to adjacent lane according to observation. In general, a vehicle may chan- ge its lane only when the spaces between it and forward vehicle and it and backward vehicle are large enough. On condition of meeting gl(t)gn(t) and vl(t) > vn-1 (t), a vehicle can ensure that it will not collide with forward vehicle on target lane after changing its lane. On condition of meeting sb(t)sb(t), a vehicle will not collide with backward vehicle on target lane because the emergency braking distance of backward vehicle on target lane is less than the space between them. Only when meeting these conditions, a vehicle will implement lane changing activity at a certain probability.1.4.3 Lane Changing Model verificationWe select 500-meter sections of two innermost lanes on the 4th Ring Road in Beijing as observation objectives to survey the lane changing condition at different time and under different flow in the condition of free flow. Observation period is 2 hours. Diamond shape points in Figure 1 are the survey number of lane changing under different volume. By linear regression fit, we can find that the relationship between number of lane changing and volume is linear.In accordance with the aforesaid lane-changing Cellular Automata model, we make a computer simulation for the lane-changing condition under the condition of free flow. During the simulation, we set up 500 cells, among which, 250 cells on the preparatory section (500m) and the other 250 cells on simulation section (500m), and the simulation time is 3900 seconds. The simulation within 0300 seconds is the stage to clear up the bad effect, after a movement of 300 seconds, the road is full of vehicles. The simulation begins from the 301st second and simulation data is recorded after the first 250 cells, the flow diagram of lane-changing Cellular Automata model simulation is as follows.Simulations were conducted according to the above-mentioned process under different flows (i.e. 2500veh/h, 2600veh/h, 2700veh/h, 2800veh/h, 2900veh/h, 3000 veh/h), each flow is simulated for five times to acquire the average values, and thus, the lane-changing times under different flows are obtained. Comparing those simulated results (while pb=0.5 and pc=0.8)with the observed values, they are matching with each other by a large while pb and pc value are correctly selected so as to verify the validity of this Lane Changing Model.2. Different traffic densityTheres different performance under different traffic load so we must analyze in three parts:2.1 Under very light traffic loadWhen in light traffic, a vehicle is almost not constrained by other vehicles (free running). Drivers will run at a speed as much as possible to get the more benefits of driving such as shortening the travel time. It may raise traffic flow in some degree, however, this psychological state will cause certain threat to the safety. So the traffic flow and safety assessment in light traffic is necessary. 2.1.1 Traffic flow calculation and simulationThough under low traffic load vehicles can run at a very high speed, the very low vehicle density plays a negative role. Whats worse, the low vehicle density influence more on traffic flow in this case. In other words, the traffic flow will be very low.We assume that any vehicle can pass each other freely. The average interval of the vehicles i