Traffic Operations: Introduction to Traffic Modelling

Car following modelling

Interrupted traffic flow

Traffic variables over a specific point 𝑠0

Hydrodynamic modelling

Delays due to interactions between vehicles

Studying interactions between vehicles on a microscopic level

Direct and unbiased measurement of traffic density and vehicle trajectories

Complex vehicle tracking algorithms

FCD records the spatiotemporal location of all vehicles while trajectory data only collects data on a few probe vehicles

A transponder on the vehicle, a tag reader antenna, and a host computing system

At high flow levels, congestion is experienced causing a decrease in vehicle flow

Bluetooth signals of mobile phones

GPS receivers of probe vehicles

(ℎ𝑖 ) Spacing between two GPS points divided by the respective time instances

Position of gas/brake pedals, turning signals, angle of steering wheel

Load passing through a specific location during a period 𝑇

Spatial observation = Observer records traffic variables over a road segment at a specific time Observation in movement = Observer enters the traffic stream to record traffic variables Temporal observation = Observer standing in a specific point records traffic variables during a period of time Traffic flow theory = Modelling traffic as a stream and studying traffic variables aggregately

Hydrodynamic modelling = Traffic is modelled as a stream and variables are studied aggregately Car following modelling = Deals with interactions between vehicles on a microscopic level Uninterrupted traffic flow = Traffic flows in highway segments without compulsory stops, allowing for speed changes and full stops due to vehicle interactions Interrupted traffic flow = Deals with traffic interrupted by intersections, stations, bus stops, or parking facilities, focusing on delays, queues, and externalities like congestion and pollution

Bluetooth readers = Allows for precise identification of individual vehicles and their movements Floating car observation = Provides real-time data on vehicle movements and traffic conditions Automatic Vehicle Identification (AVI) = Enables electronic toll collection and efficient vehicle tracking Camera-based data collection = Offers detailed visual information about traffic patterns and behaviors

Floating car data (FCD) = Data collected from vehicles equipped with GPS or other tracking devices Extended Floating Car Data (xFCD) = Includes additional information such as vehicle speed, acceleration, and fuel consumption Trajectory data from cameras = Information derived from visual recordings of vehicle movements Headway = The time gap or distance between a vehicle and the one in front of it

Traffic flow (𝑞) = Measures the rate of flow of vehicles through a given point or section of roadway over time Speed-flow relationship = Describes the correlation between vehicle speed and traffic flow under continuous circulation Interrupted traffic = Deals with traffic interrupted by intersections, stations, bus stops, or parking facilities Car following modelling focus = Mainly concerned with interactions between vehicles on a microscopic level

Automatic Vehicle Identification (AVI) = Enables precise identification of vehicles for electronic toll collection purposes Electronic Toll Collection (ETC) = Facilitates automatic payment of tolls without requiring vehicles to stop at toll booths Bluetooth readers = Allow for seamless identification of individual vehicles and their movements Camera-based data collection methods = Provide detailed visual information about traffic patterns and behaviors

Camera-based data collection = Direct and unbiased measurement of traffic density Floating Car Data (FCD) = Collects data on a few probe vehicles Automatic Vehicle Identification (AVI) based on an electronic toll collection (ETC) system = Consists of a transponder on the vehicle Bluetooth Readers = Recognize passing traffic using Bluetooth signals of mobile phones

Trajectory data from cameras = Extracts vehicle trajectories 𝑥𝑎 (𝑡) Floating Car Data (FCD) = Derived from GPS receivers of probe vehicles and processed with map-matching algorithms Automatic Vehicle Identification (AVI) based on an electronic toll collection (ETC) system = Based on an electronic toll collection system Bluetooth Readers = Recognize passing traffic using Bluetooth signals of mobile phones

Flow (𝑞) = The number of physical units 𝑛 that pass through a specific location during a period 𝑇 Headway (ℎ𝑖 ) = The time interval between two consecutive vehicles passing a point Instantaneous speed 𝑣(𝑡) = The derivative of the trajectory at a point 𝑡0 Extended floating car data (xFCD) = Includes additional information such as gas/brake pedals, turning signals, angle of steering wheel

Car following modeling = Deals with interactions between vehicles on a microscopic level Continuous traffic flow modeling = Models oriented towards delays, queues, and externalities such as congestion and pollution Interrupted traffic flow modeling = Deals with traffic interruptions such as traffic signals and stop signs Aggregate traffic flow modeling = Models traffic as a stream and studies traffic variables aggregately

Covers small road section = A few hundred meters at most Expensive = Requires mounting camera(s) on top of tall building, airplane or drone Complex vehicle tracking algorithms = Required for camera-based methods Errorprone = Associated with complex vehicle tracking algorithms

Gas/brake pedals, turning signals, angle of steering wheel = Additional information included in xFCD GPS points divided by time instances = Used to derive speed of a probe vehicle Position of GPS receivers of probe vehicles processed with map-matching algorithms = Method used to collect FCD Direct and unbiased measurement of traffic density, vehicle trajectories, and lane changes = Main advantage of camera-based methods

Transponder on the vehicle = (1) Part of AVI system Tag reader antenna at each toll lane = (2) Part of AVI system Host computing system = (3) Part of AVI system Mobile phones = (Primarily) recognized by Bluetooth readers

Speed 𝑣(𝑡) = Instantaneous speed derived from the trajectory at a point 𝑡0 Flow (𝑞) = Number of physical units passing through a specific location during a period 𝑇 Headway (ℎ𝑖 ) = The time interval between two consecutive vehicles passing a point Congestion state = Experienced when flow decreases at a certain level

Continuous circulation theory = Depicts relationship between speed and flow under continuous circulation Congestion theory = Describes how congestion leads to decreased vehicle flow Car interaction theory = Deals with interactions between vehicles on a microscopic level Aggregate flow theory = Models oriented towards delays, queues, and externalities such as congestion and pollution

Collects data on a few probe vehicles = Difference from trajectory data derived from cameras Does not record which lane a vehicle is using = Difference from trajectory data derived from cameras Derived from GPS receivers of probe vehicles and processed with map-matching algorithms = Method used to collect FCD Records spatiotemporal location of all vehicles within a given road segment and time interval = Difference from FCD