Assessment 3 Brief

School of Civil and Environmental Engineering Term 2, 2023 CVEN9415: Transport Systems Part II Assessment 3: Data Analysis and Simulation Techniques (Individual Assessment) PART A: Data Analysis (20 Points) Inputs required (refer to Data Description Document on Moodle) • Intersection diagram files • Traffic counts CSV file to be opened with SQLite browser. PLEASE name the SQL Table as countsdata in SQLite Browser. NOT doing so will attract penalty Solve the questions given below for the following TCS IDs: 686 Questions Points 1 Provide the intersection diagram, Google Satellite image of the site 2 2 Discuss the intersection layout based on the following: 3 A Determine the postcode where this intersection is located 1 B Detector IDs per approach 2 3 Student specific: Give the total hourly traffic counts on each incoming approach on all Wednesdays and Sundays for the month and time allocated to you (in Q3 excel sheet), answer the following: 7 A Write an SQL query to extract the total, average, maximum and minimum traffic count information separately for Wednesdays and Sundays for the given inputs 3 B Tabulate and compare the statistics obtained in step (A) 3 C Comment on the observation made in the tables 1 4 Student specific: Give the total daily hourly traffic counts on each incoming approach for the first 7 days of the month and 2 time periods allocated to you (in Q4 excel sheet), answer the following: 8 A Write an SQL query to extract the total, average, maximum and minimum traffic count information separately each time period for the given inputs 3 B Tabulate and compare the statistics obtained in step (A) 4 C Comment on the observation made in the tables 1 Total 20 # Students MUST refer to the spreadsheet “ Student Allocation.xlsx” and its association sheets on Moodle to get the time period(s) assigned to them. NOT complying with the made allocations will result in ZERO Points.

PART B: Simulation Techniques Use Excel wherever necessary and provide screenshots of results. You can also upload the spreadsheet showing the calculations (Optional). Questions 1. Develop a Linear Congruential Generator (LCG) using the properties given by Hull and Dobell (1962). Consider m=500 in the LCG. Steps Point A Show calculations to generate the first 3 random numbers from this LCG. 1 B Determine the period of this LCG by generating more random numbers (use excel if necessary). Is it consistent with the property proposed by Hull and Dobell? 1 C Plot the first 100 random numbers (R i ) from step (b) on a number line. Comment on the plot KS 1 Point Plot 1 Point 2 2. Halton sequence: i. Generate a random number using the equation: X i = (171*X 0 + 83) mod 373 where the seed value (X 0 ) is the last 2 digits of your ZID . ii. Pick the 1 st 2-digit prime number that appears in the resulting X i sequence. Use this prime number to generate a Halton sequence comprising 200 random numbers. Steps Point A Provide pseudo-code for generating Halton sequence. Discuss each step of the pseudo-code 2 B Provide screenshots of the command used to generate the remaining Halton sequence 1 C Plot the first 100 random numbers (R i ) on a number line. Comment on the plot and compare it with the one presented in Question 1 (c) 2 3. A wheel of fortune is divided into ten equal sectors numbered from 1 to 10. Devise a Monte Carlo simulation of this roulette and produce the result of five spins for which each outcome is given by the following three events: A: x < 3 B: 3 ≤ x ≤ 7 C: x > 7 Generate random number using the LCG: X i = (172*X 0 + 17876) mod 30307 where the seed value (X 0 ) is the first 4 digits of your ZID . Show necessary calculations. Comment on the obtained result and how it can be improved ( 3 Points) 4. A random variable Y follows Gumbel distribution, the CDF of which is: 𝑃(𝑌 ≤ 𝑦) = 𝑒 −𝑒 −𝑦 . Simulate 10 random numbers from this distribution using the LCG: X i = (171*X 0 + 24316) mod 30269 where the seed value (X 0 ) is the first 4 digits of your ZID . Show necessary calculations. ( 3 Points) 5. Passengers arrive at an airport check-in counter at an average rate of 54 passengers/hr. The operator at the counter has a variable service time (following a distribution B) with an average of 1.5 minutes per passenger. Use the following LCG to simulate random numbers: LCG: Xi = (170*X 0 + 22834) mod 30323 where the seed value (X 0 ) is the first 4 digits of your ZID . a. Are analytical methods of queueing applicable to the available information? Give reasons (1 Point)