AUT University School of Engineering, Computer and Mathematical Sciences MATH803: Mathematical Modelling and Simulation Assignment 2 Queuing Theory and Traffic Congestion Problem The purpose of this assignment is to assess your analytical and computing skills on the queuing theory with application on traffic congestion problem using SAS. Total Possible Marks: 60 marks, which contribute 30% towards your final grade in this paper. Deadline: 5pm, Friday, May 21, 2021 Submission: Submission must be made through Blackboard. Data: Data must be collected from New Zealand Transport Agency (NZTA) website. Instructions are provided below. SAS: All computing tasks must be done using SAS. Report: Incorporate your SAS code and output graphs in your report. Page Limit: Maximum number of pages is 12 including pictures, graphs and SAS code. Plagiarism: If this is the case for your project, your case will be referred to an appropriate university’s office. Questions\Tasks: 1. Data Collection (15 marks) Choose one of the following two road ramps through the links: -SH1 Esmonde Road http://www.journeys.nzta.govt.nz/traffic/cameras/40 -SH1 Greenlane Interchange http://www.journeys.nzta.govt.nz/traffic/cameras/80 The websites above provide snapshots of the road ramps with the ran- dom update time. During the peak hours, e.g., 7:30-8:30am where the 1 ramp lights are operating, take the snapshot pictures for 5 minutes (you can simply copy the image), see example below: Then, for each snapshot picture, count the number of cars waiting at the ramp lights. Obtain all necessary data to calculate parameters for a queuing model. (a) Describe this traffic problem in terms of queuing theory, e.g., how to apply the queuing theory to model this type of data, and dis- cuss the data collection from the chosen ramp. (10 marks) (b) Verify your data collection by showing some snapshot pictures and explain how to calculate all necessary parameters. Note that the time stamp at each snapshot needs to be clearly seen and in the assignment period (otherwise, your assignment won’t be marked). (5 marks) 2. Queuing System (20 marks) (a) Discuss the queuing process in this problem. (5 marks) (b) Explain the queue configuration. (5 marks) 2 (c) Explain the queuing model including all parameters. (10 marks) 3. Results and Implications (25 marks) (a) Report and discuss the results. (10 marks) (b) Suggest a solution to the problem. (10 marks) (c) Use a simulation to demonstrate your suggested solution in (b). (5 marks) 3




















































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