# 2014 MCM

Topics: Road, Lane, Time Pages: 29 (9468 words) Published: May 27, 2014
Team Control Number

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31285
Problem Chosen

A

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2014 Mathematical Contest in Modeling (MCM) Summary Sheet

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 a simple change of orientation, the models that we build can be carried to the situations with vehicles driven on the left. If more conditions, like the effect of dominant hands, are taken into consideration, some additional requirements are needed.

We design several algorithms to serve as the intelligent system to control the vehicle transportation. Simulate Anneal Arithmetic Method can improve the traffic flow during the beginning time slots and has high traffic flow in long run. But this algorithm takes too much time to compute and the IPEA is not satisfying. An greedy algorithm, which has an acceptable IPEA, can promote the traffic flow nearly as high as the Simulate Anneal Arithmetic Method. In our opinion, this greedy algorithm is a suitable choice for the intelligent system to perform global control on vehicle transportation.

Team # 31285

Page 2 of 29

Contents
1

Introduction ....................................................................... 3

2

Previous work .................................................................... 4 2.1 Single-lane Model .............................................................

4

2.2 Multi-lane Model ..............................................................

4

3

Restatement and Analysis of the Problem.......................... 5

4

The Basic Assumption........................................................ 6

5

Model ................................................................................. 8 5.1 NaSch Model....................................................................

8

5.2 Improved Model I .............................................................

8

5.3 Improved Model II ............................................................ 10

6

Model Simulation and Analysis ......................................... 11 6.1 Model II .......................................................................... 11 6.2 Comparison between Effects of Different rules...

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.