Lecture 4 - Vehicle Mobility Modelling
27 Feb 2023
Mozhgan Pourmoradnasseri, Ph.D.
4. Economic analysis: evaluate the economic impacts of transportation.
5. Emergency response: plan for and respond to disasters or other emergency situations, by providing information on traffic flow patterns, evacuation routes.
Real World
Model World
Scenario & Metrics
Encode
Decode & Evaluate
Model specification
Source: Traffic Flow Modelling, Femke Kessels
Relation between spacing and speed?
A simple example is the observations by Greenshields of vehicles passing his camera in the 1930s.
Plotting the distance between the vehicles (spacing) and their change in position in consecutive photographs leads to a theory that spacing and speed are related. Subsequently, this leads to a model with a linear relationship between spacing and speed.
General pattern: start with a model which is simple, transparent, insightful... and also wrong. This simple model can then be improved in ways to make it more correct and useful.
A model is a set of mathematical equations that tries to describe (or replicate) a physical process (ex. evolution of traffic congestion over time and space).
…all models are approximations. Essentially, all models are wrong, but some are useful. However, the approximate nature of the model must always be borne in mind…
1. Trip generation: estimated number of trips made by each zone.
1. Trip generation: estimated number of trips made by each zone.
2. Trip distribution: trips are assigned to different destinations, such as homes, workplaces, or shopping centers.
3. Mode Choice: determining how people will travel to their destinations, such as by car, bus, or train.
1. Trip generation: estimated number of trips made by each zone.
2. Trip distribution: trips are assigned to different destinations, such as homes, workplaces, or shopping centers
3. Mode Choice: determining how people will travel to their destinations, such as by car, bus, or train.
4. Route Assignment: the trips are assigned to specific routes or transportation facilities, such as highways, transit lines, or bike paths.
Limited scope: Focuses primarily on passenger travel
Simplistic assumptions: Relies on assumptions about travel behavior and decision-making that may not accurately reflect real-world behavior.
Data availability: Requires a large amount of data to be effective, including data on population, employment, land use, and transportation infrastructure.
Lack of sensitivity: Not sensitive enough to capture small changes in travel behavior or transportation infrastructure.
Difficulty in modeling congestion: May not accurately predict the impacts of congestion on travel behavior or the transportation network.
What influenced your choice?
Every choice has some consequences; spent time, cost, discomfort, ...
\(U_i = a_i c +b_i t\)
Utility of choice for person \(i\)
weights of attributes
cost time
Mode | Cost | Time |
---|---|---|
Bus | 1 | 5 |
Car | 3 | 1 |
\(a_3=-1, b_3=-2\)
\(a_1=-3, b_1=-1\)
\(a_2=-1, b_2=-1\)
\(U_1^B=-8, U_1^C=-10\)
\(U_2^B=-6, U_2^C=-4\)
\(U_3^B=-11, U_3^C=-5\)
Plan
Plan
Plan
Plan
Plan
Plan
Plan
Plan
Plan
Plan
Plan: Sequence of activities, Activity timing, route choice, Mode choice
Agents are
1. Every agent has a set of day plans.
Each agent selects a plan from its memory.
2. Mobility plans are simulated.
3. Plan scores are computed after each mobsim run.
4. A certain share of the agents (often 10%) are allowed to replan.
5. The iterative process is repeated until the average population score stabilizes.
Smith, J., Blewitt, R. at al: Traffic Modelling
Guidelines. Transport for London (2010)
Agent-based models
Continuum models
Water: outflow equals inflow, up to a maximum.
Granular: at low inflows, outflow equals inflow. When the inflow is too high, particles ‘get stuck’ in bottleneck, and outflow is lower than with a medium inflow.
High Densities, Low Speeds and Vice Versa
The precise relationship between variables such as density, headway, speed, and flow, is an important subarea of traffic flow research.
A simple human behaviour: drivers tend to choose a speed that is as high as possible, while still safe. Therefore, traffic flow models commonly use a decreasing—or at least nonincreasing—relationship between density and speed.
Thus, maximum flow (density × speed) occurs at some intermediate density and speed values.
Given a road segment, space is discretized (\(dx\)). We have:
This is a mathematical abstraction inspired by fluid mechanics.
We assume in \(dx\) space we have homogeneous conditions for density and speed.
Greenshields fundamental diagram (1934)
Daganzo fundamental diagram (1994)
Linear in the density-velocity plane and thus parabolic in the density-flow.
Most widespread due to its simplicity. It is bi-linear (triangular) in the density-flow plane.
flow = density × speed
Gipps, P. G. (1981). A behavioural car-following model for computer simulation. Transportation Research Part B: Methodological, 15(2), 105-111.
Gipps, P. G. (1986). A model for the structure of lane-changing decisions. Transportation Research Part B: Methodological, 20(5), 403-414.
The earliest car-following models include a car-following rule based on the safe following distance by expressing the position of the leader as a function of the position of its follower.
Timid drivers would keep a longer distance when the leader decelerates into congestion, while aggressive drivers tend to keep shorter following distances.
We expect in a rational model:
Lane-change models consist of three steps: