Chapter 345: 3 models

Chapter 345
"The impact of the scheme of turning the steering wheel on the right of a motor vehicle on the safety"
"Mechanics Analysis of my country's High Speed ​​Cars Moving Right on the Road"
"Analysis of Two-lane Highway Capacity Based on Overtaking Behavior"
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"Research on Expressway Vehicle Equivalent Conversion Coefficient Based on Simulation Analysis"
After searching for more than a dozen papers related to modeling topics on the Internet, Cheng Nuo basically browsed through ten lines at a glance.
After half an hour, Cheng Nuo closed the web page of the last paper, closed his eyes, and frowned slightly.
This question may seem simple at first, but after careful consideration, uh...it's really not too difficult!
But if you want to be unique among the thousands of mathematical models submitted, so that the judges want to award you an O award as soon as they see it. This is not so simple.
In fact, when browsing the paper just now, Cheng Nuo had no less than ten modeling schemes in his mind, but he was not satisfied.
Because there are no bright spots and no new ideas.
Cheng Nuo was thinking.
He was thinking about a modeling solution that would allow his team to securely win the O award.
Time passed slowly.
Cheng Nuo supported his chin with one hand, and his thoughts kept colliding fiercely.
The next teammate in charge of programming raised his wrist and looked at the time: 9:15.
The game time has been one hour and fifteen minutes.
He glanced at the other teams in the engine room.
Most of the teams have already selected the topic and started to work in full swing.
On their side, Cheng Nuo, the main force, had been sitting there for almost half an hour without moving a word.
He couldn't help but became anxious, "Cheng Nuo, don't you have any ideas yet?"
Didn’t Cheng Nuo be cheating? But judging from today's performance, it is indeed somewhat unsatisfactory!
In modeling alone, they are almost an hour behind the other teams.
Cheng Nuo's brows tightened again, "Give me time for another song."
"Tightly turn that hug into eternity?" The man subconsciously continued.
I rub!
That's not right, how come you have fallen into Cheng Nuo's rhythm.
Okay, let's give you time for a song to see if you are "enchanting" as in the rumors.
Four minutes later, Cheng Nuo's slightly squinted eyes opened.
In my eyes, there seems to be a string of data flowing.
Well, the "road" he wanted has been found.
He picked up the black carbon pen on the desktop, sorted out his ideas, and started the preliminary modeling work on the draft paper.
After constant deduction in his mind, he decided to build a model based on the metacellular automata and the Monte Carlo method to discuss the influence of the "keep to the right" rule.
First of all, it is necessary to break the movement process of the car and establish the corresponding inflow model of the sub-model ar-. For vehicles traveling at a constant speed, it is necessary to establish a following model and an overtaking model.
To put it simply, it is necessary to construct three models in different situations to reflect the overtaking mathematical model required in the question.
The inflow model can simulate the vehicles arriving at the intersection of the expressway. For each lane, the first six cells are set as vehile-regions in the cellular automaton.
We assume that the arrival of each vehicle obeys a binomial probability distribution, let ts denote the sampling time interval and N denote the total number of vehicles in ts time, and then N can approximately obey the Poisson probability distribution. Let Pt(N) denote the possibility of N, then:
Pt(N)=λ^N/N!e^(-λ), N＞0
Following the model, in each cycle, according to the speed and position of each vehicle, calculate the gap, and then determine the driving behavior, if the gap G is safe enough...
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Cheng Nuo's thoughts are very clear because he "deduced" it in his mind a long time ago.
The flow model, the following model, the overtaking model, and the three models, Cheng Nuo spent less than two hours in total to complete the modeling by formula.
The next step is to design rules to simulate the vehicle's motion model.
Cheng Nuo designed two sets of regular CA models.
One set is the right-hand driving rule, and the other is the unrestricted driving rule.
At the same time, a road hazard index evaluation formula is designed.
Risk factor per unit time:
d=0, Gs-Gr﹤0
d=Gs-Gr, Gs-Gr≥0
At this point, Cheng Nuo's main modeling work has been completed.
Looking at the time, it is only 12 o'clock noon now.
And as early as the moment Cheng Nuo constructed the inflow model, he sent the data to the teammate of the Academy of Accounting and asked him to start programming.
In terms of progress, at this point in time, he completed less than one-third of the work when he last participated in the national competition.
But that time he was doing the work of three people alone, so the progress was naturally slow.
Without time to eat lunch, Cheng Nuo worked hard to design the distribution of acceleration and deceleration probability and the mechanism to avoid collisions.
Finally, sort out all the formulas and theories and send a copy to two teammates.
The teammate of the Academy of Accounting who was typing the code at the computer saw the QQ icon flashed on the computer. He opened it subconsciously and saw the file sent by Cheng Nuo.
File name: Modeling formula for question A (full version)
He turned his head to look at Cheng Nuo in surprise, his tone not quite sure, "Have you done it all?"
Cheng Nuo unscrewed a bottle of mineral water, shrugged with a smile, "Well, it's easy."
"This..." For a while, teammates shouldn't say what is good.
Cheng Nuo got up from his seat and smiled, "I'm going to the cafeteria, do you want to bring lunch?"
"Barbecue bibimbap."
"Brown chicken." The two replied subconsciously.
Cheng Nuo nodded, "OK."
Looking at Cheng Nuo's fading back, the two looked at each other and murmured softly, "The name of the evildoer. It's really worth it!"
…………
After lunch, Cheng Nuo, who had finished his work, was bored. While yawning, he watched them typing codes and writing papers.
After watching it for a while, Cheng Nuo thought to himself.
Judging by the speed of the two, if you want to finish it, at least tomorrow morning. But he said that he would end the game in one day, and then work with Professor Fang to sort out the BSD guess paper.
It seems that I must do something!
Cheng Nuo moved his chair ~EbookFREE.me~ to come to the teammate of the Academy of Planning, glanced at the screen, and said, "Where is the progress?"
"The inflow model is almost ready to be programmed."
"Well, I will follow the model and the overtaking model. You should hurry up and design the two sets of sports models." Cheng Nuo said, with a relaxed and casual tone.
"Well, what?!" The teammates of the Academy of Accounting wondered if they had misheard.
Isn't programming your own task? How come Cheng Nuo came to intervene.
Moreover, the work of programming the two models was also taken over at once.
Having spent more than five hours programming "flow into the model", he naturally knows how complicated these three models are.
He glanced at Cheng Nuo up and down, "Are you sure?"
Cheng Nuo smiled, showing a row of neat white teeth, "Of course!"
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