2014 MCM
Team Control Number
For office use only
T1 ________________
T2 ________________
T3 ________________
T4 ________________
31285
Problem Chosen
A
For office use only
F1 ________________
F2 ________________
F3 ________________
F4 ________________
2014 Mathematical Contest in Modeling (MCM) Summary Sheet
(Attach a copy of this page to your solution paper.)
Type a summary of your results on this page. Do not include the name of your school, advisor, or team members on this page.
Simulation-based Evaluation and Intelligent
Improvement of Passing Lane Control
In this paper, we introduce NaSch model which is based on Cellular Automata as well as build Model I and
Model II at the base of the single-lane model to simulate the road status.
By simulating these two models and analyzing the performance of the given rule in light and heavy traffic respectively, we draw the following two conclusions: fewer lanes are used fully in light traffic than in heavy traffic; too many lanes are not necessary instead four are enough. We also assess the tradeoffs between traffic flows and safety and assert that the traffic flow is low when the speed limitation is over-low, but over-high speed limitation do not means a higher traffic flow. Short safe distance does make sense for improving the traffic flow as the speed level becomes very high. Meanwhile, it also means low safety level, which is dangerous in reality.
We compare our multi-lane models following Keep-Right-Except-To-Pass Rule (short for KRETP) with models following common lane-changing rules. We find KRETP Rule not so effective in promoting better traffic flow in long run but it does work when there are not so many vehicles. An index called Individual 's Passing
Efficiency Average (short for IPEA) is defined with which we can measure the utilization ratio of the highest speed of vehicles. Models with KRETP Rule have the highest IPEA which means it works pretty well in this aspect. With
For office use only
T1 ________________
T2 ________________
T3 ________________
T4 ________________
31285
Problem Chosen
A
For office use only
F1 ________________
F2 ________________
F3 ________________
F4 ________________
2014 Mathematical Contest in Modeling (MCM) Summary Sheet
(Attach a copy of this page to your solution paper.)
Type a summary of your results on this page. Do not include the name of your school, advisor, or team members on this page.
Simulation-based Evaluation and Intelligent
Improvement of Passing Lane Control
In this paper, we introduce NaSch model which is based on Cellular Automata as well as build Model I and
Model II at the base of the single-lane model to simulate the road status.
By simulating these two models and analyzing the performance of the given rule in light and heavy traffic respectively, we draw the following two conclusions: fewer lanes are used fully in light traffic than in heavy traffic; too many lanes are not necessary instead four are enough. We also assess the tradeoffs between traffic flows and safety and assert that the traffic flow is low when the speed limitation is over-low, but over-high speed limitation do not means a higher traffic flow. Short safe distance does make sense for improving the traffic flow as the speed level becomes very high. Meanwhile, it also means low safety level, which is dangerous in reality.
We compare our multi-lane models following Keep-Right-Except-To-Pass Rule (short for KRETP) with models following common lane-changing rules. We find KRETP Rule not so effective in promoting better traffic flow in long run but it does work when there are not so many vehicles. An index called Individual 's Passing
Efficiency Average (short for IPEA) is defined with which we can measure the utilization ratio of the highest speed of vehicles. Models with KRETP Rule have the highest IPEA which means it works pretty well in this aspect. With
References: [1] Nagel K, Schreckenberg M. A cellular automaton model for freeway traffic[J]. Journal de Physique I, 1992, 2(12): 2221-2229. [3] Mathematical Models[M]. HIGHER EDUCATION PRESS, 1993. Matter and Complex Systems, 1998, 5(3): 793-800. [8] Wolfram S. Theory and applications of cellular automata[J]. 1986. [11] Nagel K, Wolf D E, Wagner P, et al. Two-lane traffic rules for cellular automata: A systematic approach[J]. Physical Review E, 1998, 58(2): 1425. [14] Bertsimas D, Tsitsiklis J. Simulated annealing[J]. Statistical Science, 1993: 10-15.