Traffic Modeling with MATLAB University Honors Program Tessa

Traffic Modeling with ® MATLAB University Honors Program Tessa Wiedmann, Colin Fralick, Jacob Fedders, Christopher Stone Objectives Solution Tolerance • Create a code that models how humans move through a hallway • Design a way to control traffic in the hall to reduce the frequency of traffic jams • Set a range of tolerances that can be applied depending on the circumstances • Created a method to restrict traffic flow entering hall once hall was filled past a specific proportion • When reached, the number of people entering is halved until a value below the proportion is measured • The Table below is from running 1000 trials to find how often the hall jams • The code was terminated if a jam was recorded • A jam corresponds to over 400 people in the hall Hallway filling up Operating normally Jammed Introduction • When classes are released across campus there is a build up of foot traffic • This code in MATLAB® is capable of modeling this process on a four way hallway • The rate people enter into the hall is modeled by a cosine curve • New ways to optimize traffic flow within the hallway were implemented MATLAB® Code Flowchart Dot destination key: North South West Figure 1: Visual display of hallway at various traffic conditions • Each dot has a pre-specified destination based on color • The title above the hall operationally defines the different points in the hall operation Figure 2 Create: The program begins by creating an empty hallway and enters the main loop East Figure 3 Loop Display: The hall and all of the people in it are shown on the plot Exit: People who have reached their destinations are removed from the hall 0. 11 0. 12 0. 13 0. 14 0. 15 0. 16 0. 17 0. 18 0. 19 0. 21 0. 22 Cutoff Ratio 0. 23 0. 24 0. 25 0. 26 0. 27 0. 28 0. 29 0. 31 0. 32 0. 33 0. 34 0. 35 Number of Trials where Jam Occurred (out of 1000) 56 52 124 240 385 628 830 944 990 997 1000 Conclusion • A rate cutoff proportion of 0. 18 had least amount of jams • The hall jams less than 10% of the time for any rate cutoff proportion below 0. 24 • The hall jams over 25% of the time if the rate cutoff proportion exceeds 0. 27 • Beyond a value of 0. 33 the hall always jams and other factors must be analyzed to solve the problem Generate: People are generated at a spawn rate that is controlled by a wave function and the hall density Move: The people in the hall move according to their current location, destination, and available space to move Cutoff Ratio Number of Trials where Jam Occurred (out of 1000) 23 22 23 19 18 13 11 14 9 12 12 15 23 • Graphs of total number of people in the hall as code progresses • Figure 2 shows hall without traffic regulation • Figure 3 demonstrates controlled traffic with a rate cut at a proportion equal to 0. 275 • Color coding represents the hallway fill conditions shown in Figure 1 References More Traffic Modeling Projects: • http: //math. mit. edu/projects/traffic/ More Traffic Modeling Software: • http: //www. caliper. com/transmodeler/ • http: //www. trafficware. com/products/planninganalysis-software/