Assignment 2: Report and Marking Scheme

Report

For your report, you are to produce a single pdf, with 2.5cm margins, two columns, and 10pt font (Times New Roman). Aim for half a page of content. Max one page. This should include your and your partners' names and student numbers. Add the pdf, named report2.pdf, into your "a2" repository, and commit the file. Be sure to cite any sources you use.

I recommend LaTeX for producing your documents; you may, however, use Word or OpenOffice and convert the file to pdf. A single bonus mark will be given to students who use LaTeX to produce their reports. If you do so, hand in the .tex file along with the .pdf file to demonstrate to the marker that you used LaTeX. I have provided a LaTeX template for you to use (output).

There are three sections to your report; please indicate them clearly.

  1. Section 1: Our simulation typically adds a new train at Kipling every five minutes. A train typically proceeds at 1 km/min, and in our simulation, Kennedy is 82 km away from Kipling.
    1. How many minutes would you expect it to take train 0 to get to Kennedy?
    2. Set SIM_TIME in the simulation to 82 minutes. What do you see happening on the track? What station is train 0 at? Why?
    3. Run the simulation with SIM_TIME = 60*2, 60*4, 60*16, 60*24. What is going on at each of these times? How long does it take train 745 to go from Kipling to Kennedy?
  2. Section 2: Set SIM_TIME to 60*100, and run the simulation. For this section we will examine the output of data.csv -- load it into your favourite scientific plotting software (Matlab, R, Octave, etc).
    1. Plot the average distance between trains as a function of time. What do you observe? How long does the system take to reach a steady state? When it does, what is the equilibrium (average distance).
    2. Plot the number of trains as a function of time. What do you observe? How long does the system take to reach a steady state? When it does, what is the equilibrium (number of trains)?
    3. Plot the average distance between trains as a function of time. What do you observe? How long does the system take to reach a steady state? When it does, what is the equilibrium?
  3. Section 3: Elizabeth is watching the Spadina streetcar stop at Adelaide as she has a coffee break. As she sits there for a couple hours, she only sees six people show up. (It's not a peak time.) The people show up individually at t = 34, 37, 64, 71, 81, 93 min, where t = 0 is when Elizabeth begins her observation.
    1. Let's say a streetcar came every 20 minutes -- t = 20, 40, 60, 80 etc. What is the average waiting time of the six passengers?
    2. Let's say that instead, streetcars came at random intervals: at t = 14, 21, 26, 42, 54, and 101. What's the average waiting time of the six passengers?
    3. In reality, however, as Elizabeth observes the streetcar, it comes at t = 24, 25, 62, 63, 80, and 117. Assuming the streetcars left Spadina station at regular 20-minute intervals, why do they arrive to Adelaide in pairs? What is the average waiting time of the six passengers?

As an aside: Transportation simulation is an important part of civil planning, and far more sophisticated simulations are out there. If you'd like to learn more about simulating Toronto's transit, check out the ILUTE Model produced by the Transportation Engineering group at U of T!

Marking Scheme