SYDE 536: Modelling Transportation Systems
Estimated study time: 9 minutes
Table of contents
Sources and References
- Ortúzar and Willumsen, Modelling Transport (Wiley)
- Sheffi, Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods (Prentice Hall)
- Mannering, Washburn, Principles of Highway Engineering and Traffic Analysis (Wiley)
- Greene, Econometric Analysis (Pearson)
- TRB, Highway Capacity Manual
Chapter 1: The Four-Step Framework
1.1 Overview
Transportation modelling at regional scale has historically proceeded in four steps: trip generation, trip distribution, mode choice, and traffic assignment. Each step takes outputs of the previous one and applies a theoretically grounded or empirically calibrated transformation. Modern practice augments this sequence with activity-based, agent-based, and dynamic-traffic-assignment alternatives, but the four-step lens remains essential vocabulary.
1.2 Transportation as a System
Transportation systems couple land use, population, economics, infrastructure, and behaviour. Travel demand derives from activity patterns: commuting, shopping, schooling, socialising, freight. Supply-side characteristics — network topology, vehicle capacity, service quality — interact with demand through congestion and mode choice. Feedback between demand and supply, short-term and long-term, complicates analysis.
Chapter 2: Bayesian Modelling of Collision Rates
2.1 Collision Data
Collision data are counts by location, time, vehicle type, and severity — typically sparse at individual sites, heavy-tailed, and subject to reporting biases. Classical frequentist analyses treat observed rates as estimates of true risks, but small samples at specific locations give unreliable estimates.
2.2 Bayesian Framework
Bayesian methods combine a prior distribution with observed data via Bayes’ theorem:
\[ p(\theta | y) = \frac{p(y|\theta)\,p(\theta)}{p(y)}. \]For collision counts, a Poisson likelihood with a gamma prior for the rate yields a gamma posterior — the classical empirical Bayes approach. Hierarchical models pool information across sites while allowing site-specific deviation, shrinking unreliable individual estimates toward a group mean in proportion to their sample size.
2.3 Application
Bayesian collision models inform identification of hazardous sites, before-after evaluation of countermeasures, and allocation of safety funds. They also quantify uncertainty in ways decision-makers can use: credible intervals, posterior probability that rate exceeds a threshold, and probability that a site is among the top-k hazards.
Chapter 3: Discrete Choice of Travel Mode
3.1 Random Utility
Discrete choice models assume a traveller selects the alternative (car, bus, bike, walk, train) with maximum utility. Utility is random from the analyst’s perspective:
\[ U_{in} = V_{in} + \varepsilon_{in}, \]with systematic \( V_{in} \) capturing observed attributes and random \( \varepsilon_{in} \) unobserved heterogeneity.
3.2 Multinomial Logit
The most common specification assumes \( \varepsilon \) i.i.d. extreme-value, giving the multinomial logit (MNL) probability
\[ P_{in} = \frac{\exp(\mu V_{in})}{\sum_{j} \exp(\mu V_{jn})}, \]with scale \( \mu \). Attributes — travel time, cost, comfort, wait, transfers — enter \( V \) linearly with estimated coefficients, from which elasticities and values of time derive.
3.3 Beyond MNL
The MNL independence-from-irrelevant-alternatives assumption fails for correlated alternatives (blue bus / red bus paradox). Nested logit, cross-nested logit, mixed logit, and probit models relax this, at the cost of more complex estimation. Latent-class models segment travellers with distinct preference parameters. Willingness-to-pay for time savings, environmental quality, or reliability emerges from model coefficients.
Chapter 4: Emissions from Operating-Mode Time Series
4.1 Vehicle Emissions Mechanisms
Vehicle tailpipe emissions depend on engine load, speed, acceleration, temperature, and mileage. Key pollutants include CO2, NOx, particulate matter, hydrocarbons, and CO. Engine management, catalytic converters, and particulate filters reduce emissions per mile, but stop-and-go driving and cold starts raise per-mile rates substantially.
4.2 Operating Mode Framework
The EPA MOVES model and similar tools classify instantaneous driving into operating modes defined by speed and vehicle-specific power (VSP). Each mode has an emission rate; aggregate emissions
\[ E = \sum_k t_k \cdot e_k \]sum the product of time-in-mode \( t_k \) and rate \( e_k \) across modes. Time-series speed profiles from GPS-equipped vehicles or traffic simulations provide the mode distributions.
4.3 Applications
This approach captures how congestion, signal coordination, gradient, and driving behaviour alter emissions beyond what average speed models show. Signal optimisation, eco-routing, and speed management policies can be evaluated by simulating their effect on operating-mode distributions.
Chapter 5: Traffic Simulation
5.1 Macroscopic Models
Macroscopic traffic flow treats vehicles as a fluid with density \( k \), flow \( q \), and speed \( v \). Continuity gives
\[ \frac{\partial k}{\partial t} + \frac{\partial q}{\partial x} = 0, \]and fundamental diagrams link \( q, k, v \). Shockwave analysis follows congestion onset and dissipation.
5.2 Microscopic Models
Microscopic models simulate individual vehicles with car-following rules (Gipps, intelligent driver model) and lane-changing logic. Stochastic models capture driver heterogeneity. Calibration against real trajectories is essential and non-trivial.
5.3 Mesoscopic and Dynamic Assignment
Mesoscopic models balance detail with scale — aggregating individual vehicles into packets on links. Dynamic traffic assignment combines network-scale routing with time-varying conditions to model how traveller choices evolve during congestion onset and response to information.
Chapter 6: Modelling Transportation for Sustainable Communities
6.1 Global Models
At global and community scales, frameworks such as the ASIF identity (Activity × Structure × Intensity × Fuel) decompose emissions into travel demand, mode shares, energy intensity, and carbon intensity. Scenario analyses test how policies — electrification, densification, transit investment, mode shift — alter each term.
6.2 Traffic Operations and Congestion
Operational simulations evaluate traffic signal timing, ramp metering, transit signal priority, and incident management. Queue-based analytical models and microscopic simulations complement one another; the Highway Capacity Manual provides standard procedures for level-of-service estimation.
Congestion pricing, high-occupancy vehicle lanes, and active traffic management are modelled to predict effects on mode choice, route choice, and emissions. The efficiency gains from pricing often exceed those from capacity expansion; political feasibility, equity, and complementary transit investments determine adoption.
6.3 Multi-Modal and Connected-Autonomous Futures
Growing integration of walking, cycling, transit, shared mobility, and private vehicles demands multi-modal models that capture transfers, first-last-mile, and complementary uses. Connected and autonomous vehicles (CAV) introduce new behaviours — platooning, cooperative intersections, empty repositioning — with uncertain effects on congestion, safety, and mode choice. Scenario modelling explores plausible CAV futures.
6.4 Equity and Access
Transportation modelling increasingly measures access — to jobs, education, healthcare, food — by population group. Accessibility metrics include cumulative opportunities reachable within a time budget and gravity-based potentials. Environmental justice analyses trace how pollution, displacement, and investment fall across communities. Modelling without equity framing risks perpetuating historical inequities.
The course builds fluency across this modelling portfolio, preparing students to support the decisions that will shape 21st-century mobility — as planners, consultants, researchers, or policymakers.
