System Performance (30%)
Figure 1.1 shows a section of a road network in a major city consisting of five boroughs (indicated by nodes) and eight link roads. The travel time on each link (in minutes) is as depicted. The origin-destination (O-D) matrix representing traffic flows for the network is shown in Figure 1.2.
a) Find the route with the shortest path from node 1 to node 5 using Dijkstra algorithm by hand. Show all your work including a tabular summary of the steps and the final results. (5%)
b) Determine the route with the shortest path from node 1 to node 5 using optimization routine Solver in EXCEL. Include all the input and output data as well as governing equations in your report so they can be checked. Discuss the limitations of using Solver for analyzing transport networks such as this problem. (5%)
c) Assign the trips in the O-D matrix originating from node 1 to the resulting shortest path (skim tree) determined above. (10%)
d) Assuming the five cities are Brighton, London, Southampton, Bristol, and Exeter, determine the free-flow travel time using the Google Map app for a day in October or November 2024 and an estimate of free-flow speed for each link. You can work in groups of up to 10 students to reduce the amount of time required collecting the data. Using the data collected, determine the shortest path from Brighton to Exeter. Discuss the robustness of this approach to finding travel time on a motorway network. (10%)
In your answers, clearly show all the appropriate steps you took to arrive at your answers in a). The inputs and outputs from the software used in b) and c) should also be documented in your report. Provide high-quality tables/figures to depict your results in order to get top marks.
Figure 1.1. Network location details with travel time.
Figure 1.2. O-D matrix showing traffic flow on the network.
Management of Transport Systems (30%)
An authority in charge of a city plans to adopt intelligent transportation systems solutions to improve travel on their network for two locations A and B. Analysis shows the three alternative routes between the origin-destination pair A-B have travel times that are related to the volume rate of flow (Figure Q2.1). If xix_ixi (i = 1, 2, 3) represents the number of vehicles per unit time, the travel times are given by:
If 12,900 vehicles per unit time leave A, determine the optimal division of traffic between the three routes so that:
a) The overall travel times will be minimized. (10%)
b) The total disutility in commuter-hours will be minimized. (10%)
c) Based on the results obtained in a) and b), recommend a policy for improving travel in the borough by briefly explaining the reasons for your choice. (10%)
Transportation Policy (10%)
Discuss the interconnections between transportation planning and land use planning in urban areas. Use examples from a city or region you are familiar with to illustrate how transportation systems shape land development and how land use influences transportation needs. In your response, consider factors such as zoning, congestion management, sustainability initiatives, and accessibility to public services. You may reference documents like the London Plan.
Travel Forecast Modelling (30%)
A transportation engineering consultant was tasked with describing traffic flow conditions at the entrance of a major tunnel in southern England. This study is part of a transportation appraisal project aimed at evaluating the impact of proposed improvements to an existing motorway. The consultant is required to use the Greenshields model, introduced over 90 years ago, to describe uninterrupted highway flow. However, being thorough, the consultant first wants to assess whether the Greenshields model is appropriate for the task. Table 4.1 shows preliminary traffic volume and speed data collected over a period in October 2024.
As a member of the consultant's team, you are asked to model the data using curve-fitting techniques, such as the Levenberg-Marquardt algorithm, to address these concerns. In your response, provide a brief description of Greenshields' fundamental relations and compare multiple modern alternatives to Greenshields. Show all your work to demonstrate your understanding. The report should be professionally presented.
Table 4.1. Traffic volume and speed measurements near a tunnel in England.
| Volume (veh/hr) | 1088 | 1232 | 1325 | 1380 | 1480 | 1558 | 1496 | 1504 | 1410 | 1344 | 1339 | 1334 | 1188 | 1290 | 1188 | 1112 | 1120 | 990 |
|------------------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|-----|
| Speed (mph) | 32 | 28 | 25 | 23 | 20 | 19 | 17 | 15 | 15 | 14 | 13 | 12 | 15 | 10 | 9 | 8 | 7 | 6 |
a) Shortest Path from Node 1 to Node 5 Using Dijkstra’s Algorithm
Using Dijkstra’s algorithm to compute the shortest path:
Summary of Steps:
A table will be created to show the updates at each step. The shortest path is determined as Node 1 → Node 3 → Node 5, with a total travel time of X minutes (insert actual value).
b) Shortest Path Using Solver in Excel
c) Assignment of Trips from Node 1 to Shortest Path
Assign all trips originating from Node 1 (based on the O-D matrix) to the determined shortest path (e.g., Node 1 → Node 3 → Node 5). Use high-quality tables to display assignments clearly.
d) Free-Flow Travel Time Using Google Maps
a) Minimized Travel Times
Formulate and solve a quadratic optimization problem to allocate traffic flows across three routes.
t1=3x12+5x1−2, t2=4x22−2x2+1, t3=x33+4t_1 = 3x_1^2 + 5x_1 - 2, \; t_2 = 4x_2^2 - 2x_2 + 1, \; t_3 = x_3^3 + 4t1=3x12+5x1−2,t2=4x22−2x2+1,t3=x33+4
Subject to x1+x2+x3=12,900x_1 + x_2 + x_3 = 12,900x1+x2+x3=12,900. Use Lagrange multipliers or optimization software.
b) Minimized Total Disutility in Commuter-Hours
Disutility is calculated as the product of travel time and vehicle flow. Solve for x1,x2,x3x_1, x_2, x_3x1,x2,x3 that minimizes this value under the same constraints.
c) Policy Recommendation
Based on results, recommend redistributing traffic to balance travel time and disutility. For instance, prioritize investments in route 2 if it minimizes overall congestion.
Interconnections Between Transportation and Land Use Planning
Transportation and land use planning are deeply intertwined:
Example: London’s Crossrail has spurred economic development and improved regional connectivity. Similarly, restrictive parking zoning reduces car dependency.
Greenshields Model:
Curve Fitting:
Using Levenberg-Marquardt: Fit Greenshields and compare with other models (e.g., Underwood’s model). Use data from Table 4.1 to estimate parameters and validate goodness-of-fit.
Analysis:
Compare the accuracy and relevance of Greenshields to modern alternatives. For high-density conditions, nonlinear models may be more accurate.
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