2014美赛a题 北师o奖.pdf

Team #30532 Page 1 of 29 For office use only T1 ________________ T2 ________________ T3 ________________ T4 ________________ Team Control Number 30532 Problem Chosen A For office use only F1 ________________ F2 ________________ F3 ________________ F4 ________________ 2014 Mathematical Contest in Modeling (MCM) Summary Sheet We build a simulation and statistical model to analyze the performance of Keep-Right-Except-To-Pass rule in light and heavy traffic. We extend the famous Cellular Automaton single-lane Traffic flow simulation model (NaSch model) to multi-lane model using our new lane-changing rules. The factor analyze method is employed by us to study the tradeoffs between traffic flow, safety, max velocity limits and other metrics. Besides the Keep-Right-Except-To-Pass rule mentioned in the problem, we also propose two other rules: Keep-Right-Or-Left rule and High-Velocity-Left -Low-Velocity-Right-Except-To-Pass rule. A deep compare between the three rules has be done. The result shows that when traffic density, the probability of lane-changing and the velocity limits are low, Keep-Right-Or-Left rule is able to promote traffic flow and safety. In general, Keep-Right-Or-Left rule performs the best, while High-Velocity-Left -Low-Velocity-Right-Except-To-Pass rule performs the worst. In countries where driving automobiles on the left is norm, our Keep-Right-Except-To-Pass model is also suitable with a simple change of orientation. Considering the other two models set no limit on the lane in which vehicles drive, the model can be applied without modification to those countries driving to the left. Last, if the whole traffic is controlled by an intelligent system, we will simulate the random behaviors of the model parameters to optimal parameters under ideal circumstances and also analyze the effects to the three rules. Under the control of an intelligent system, the safety of three rules is almost the same. And the rule of Keep-Right-Except-To-Pass promotes the traffic flow the least while the range of difference is the greatest and the other two rules promote the traffic flow to a similar degree that is greater than that promoted by the Keep-Right-Except-To-Pass rule. Team #30532 Page 2 of 29 Simulating and Scoring the Performance of Traffic Driving Rules Simulating and Scoring the Performance of Traffic Driving Rules SUMMARY . 3 1 INTRODUCTION therefore, it is a must to pin down measurable parametric factors related to tradeoffs between traffic flow and safety as well as the ways in which this rule performs under different Team #30532 Page 5 of 29 load conditions. Load and speed of vehicles will be held as independent variables while the parametric factors will function as dependent variables and the evaluating indicators of the performance of the rule. In addition, a reference model for comparison will be established and used for evaluating the Keep-Right-Except-To-Pass rule. In case this rule, compared with the reference group, is not capable of promoting traffic flow, a new driving rule will be drafted against the yardstick of previously-stipulated evaluating indicators to ensure a better performance. The analyzing procedure can be illustrated by the flowchart below: The performance of The Keep-Left-Except-To-Pass rule can be compared with that of the Keep-Right-Except-To-Pass rule once the rule is changed in analog simulation and the outputs of the two calculations are obtained. It is a limiting case if vehicle transportation on the same roadway was fully under the control of an intelligent system, which rules out the random cases ; thus the third question can be addressed by following the method in previous questions and compare distinct outputs for difference. 3 Assumptions  All vehicles involved are assumed to be to be under ideal condition and the road in the analysis in the analysis is also ideally flat. Besides, all vehicles drive The performance of rule Light traffic Heavy Traffic flow Safety Velocity Density Lane change Vehicle types Max speed limit Number of lanes Random brake probability … … Team #30532 Page 6 of 29 straightly forward all the time with no direction change, rollover or sway.  When under the circumstances of change lanes, the acceleration and deceleration processes of the vehicles will not be taken into consideration. If the lane-changing conditions are satisfied, the vehicles will directly shift to the adjacent lane. 4 Model Development 4.1 Multi-lane Traffic Model for Cellular Automaton 4.1.1 Single Lane Model We extend the famous Nagel-Schreckenberg(NaSch)[3] single lane model to multi-lane model to simulate the traffic flow by defining our traffic rules. For the convenience of the readers we would like to outline the single lane model. The system consists of a one dimensional grid of L sites with periodic boundary conditions. A s。