Phy234_FinalProject.nb

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Cell[TextData[StyleBox["Physics 234  \nFinal Project",
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Cell[TextData[StyleBox["Eric Shao, Ziyang Gao\n5/2018",
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Cell["Section 0: Progress report", "Section",
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Cell["\<\
  A clear statement of your project: Please see section 1 below.
  Results from a search for appropriate applets: Please see section 4 below.
  What you hope to accomplish, including a time schedule. \
We\[CloseCurlyQuote]ve finished coding speed changes for each car in the left \
lane (remaining lane) of a traffic simulation. In the next stage we plan to \
animate the actual process of road diet after the appearance of 1 signal (by \
next Tuesday), and hopefully extend to multiple switching of lanes, for \
example, when 4 lanes dieting to 2 (by next Thursday).
  Problems and concerns: Please see sections below.
  If you' re a pair, indicate how you are breaking up responsibilities: We \
pair programmed the  following(with a switch of coding/navigating \
responsibility every half an hour), with the navigating one also in charge of \
writing up sections 1-3.\
\>", "Text",
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Cell["Section 1 : What is the problem about", "Section",
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Cell[TextData[StyleBox["\tA road diet, also called a lane reduction or road \
rechannelization, is a technique in transportation planning whereby the \
number of travel lanes and/or effective width of the road is reduced in order \
to achieve systemic improvements. The situation of a road diet is one of the \
major causes of traffic jam and without proper road management and signal \
design, drivers will have to spend an unexpectedly long time trying to get \
through a short distance near the dieting place.\n\tOur main concern is about \
where to put the sign(s) to have maximum efficiency for avoiding congestion. \
We chose this topic because road diet is one of the main reason for traffic \
jam, which is a major problem for citizen in big cities.",
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Cell["Section 2 : Parameters of concern in our model", "Section",
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Cell[TextData[{
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road diet.\n\nThe explanatory variables:\n1. The position and the number of \
signs;\n2. Number of cars in total of consideration;\n3. Number of lanes \
before the diet;\n4. Number of lanes after the diet;\n\nThe constants of the \
model: \n1. Car length(s) and its distribution; ",
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\n3. The percentage (30%) of drivers who will change lane if a more preferred \
lane is next to his current one",
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Cell["Section 3 : Model logistics:", "Section",
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Cell[TextData[StyleBox["\tIn this section we will explain on a high level \
that how our model is built and the steps we will follow to derive a \
satisfiable conclusion. Here it\[CloseCurlyQuote]ll be helpful to state some \
underlying assumptions first: \n\t1. Any car will not be willing to share one \
lane with another car when a second lane is available. \n\t2. When there is \
no empty lanes, any car will choose the lane with the fastest speed as his \
top choice, the lane of second fastest speed as his second choice and etc. \
There is a constant portion (30%) of drivers who will change lane if a more \
preferred lane is next to his current one. \n\t3. For simplicity, we assume \
that one insertion will affect the whole lane\[CloseCurlyQuote]s traffic \
speed by a certain percent (3%).\n\t4. When a road diet happen, a car will \
allow insertion of other cars upon request (by light/sound signals). \n\tThe \
user will need to insert the values for explanatory variables: position of \
signs([L_1], [L_2]....[L_n]), number of signs [Sn], number of cars in total \
of consideration [Cn],  number of lanes before diet [k0] and number of lanes \
allowed after diet [k1]. \n\tWe will set the initial state of the model as \
having same amount of cars on all Sn of lanes and all the cars moving at a \
constant speed. Whenever the cars passing a road diet sign, randomly choose \
50% of cars on the edge lane to insert into its neighbor lane. After all \
insertions are done, recalculate the speed of the lane and rearrange the car \
distribution for all Sn lanes, according to assumption 2. We will repeat the \
above process whenever the edge lane encounters an assigned diet signal. In \
the end, the model returns the time elapse from beginning of the process till \
the road diet is complete.",
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Cell["Section 4: Code Development", "Section",
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We will first develop a model concerns two lines emerge to one.\
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Cell["Set Up", "Subsection",
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For the line that will not be closed, there will be a list represent the cars \
on it with each element store the position and velocity of the car. For the \
other line that will be closed, there will be two list of cars, one list \
represent the cars that want to emerge, the other represent the cars that \
will not.\
\>", "Text",
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To begin the simulation, we will generate a random number of 1 and 0 for each \
time interval. If it is 1, a car will appear on Lane1. If it is 0, a car will \
appear on Lane2 with no intention to emerge. These car will have position 0 \
and a velocity around the 3m/s range of the speed limit.\
\>", "Text",
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In the model, without the loss of generality, we will assume the line that be \
closed will always be the left lane (lane1). 
For the driver, there will be two kinds of decision to make. First, speed up, \
slow down or stay the same. A driver will speed up if it is less than speed \
limit +3 and there are plenty of space ahead, slow down if there is a car too \
close ahead or there is a car want to emerge. (For the latter one, it only \
apply to Lane1 for a random probability). Second, emerge or not. For the \
driver on lane2, each time they pass through a sign, a percentage of the \
drive will move from \[OpenCurlyDoubleQuote]not want merge\
\[CloseCurlyDoubleQuote] to \[OpenCurlyDoubleQuote]want to merge\
\[CloseCurlyDoubleQuote]. For the driver want to emerge, they will speed down \
linearly and try to emerge to lane1. As soon as they find there is a gap \
besides them larger than the safe distance, they will emerge. Also for the \
driver on lane2 that \[OpenCurlyDoubleQuote]not want to merge\
\[CloseCurlyDoubleQuote], they will merge if there is a gap on lane 1 with \
twice the safe distance.\
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