MATH803 Mathematical Modelling and Simulation

AUT University
School of Engineering, Computer and Mathematical Sciences
MATH803: Mathematical Modelling and Simulation
Assignment 1
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, March 27, 2020
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. Also
include the DCT/SECMS assignment cover page, otherwise your
assignment WILL NOT be marked.
Page Limit: Maximum number of pages is 5 excluding 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.
QuestionsnTasks:
1. Data Collection (20 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
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The websites above provide snapshots of the road ramps with the random update time. During the peak hours, e.g., 7:30-8:30am where the
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 discuss 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. (10 marks)
2. Queuing System (20 marks)
(a) Discuss the queuing process in this problem. (5 marks)
(b) Explain the queue configuration. (5 marks)
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(c) Explain the queuing model including all parameters. (10 marks)
3. Results and Implications (20 marks)
(a) Report and discuss the results. (10 marks)
(b) Suggest a solution to the problem. (10 marks)
(c) (Bonus) Use a simulation to demonstrate your suggested solution
in (b). (10 marks)
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