Road Transport Systems
ETHZ / D-BAUG / Spring Semester 2021
ETHZ / D-BAUG / Spring Semester 2021
Wardrop principle
Journey times in all routes actually used are equal and less than those that would be experienced by a single vehicle on any unused route.
user equilibrium (UE)
AV
Autonomous Vehicle
Anticipated effects from AVs
Autonomous Vehicle (AV)
- less congestion
- shorter travelling time
- less pollution
- less energy consumption
- less accidents
- more parking space
- higher mobility (elderly, kids, etc.)
ACC
Adaptive Cruise Control
Fundamental Diagram to Space-Time Diagram
MOBIL (Model)
Minimizing Overall Breaking deceleration Induced by Lane Changes
General lane-changing model for car-following models (simulations)
Characteristics:
- safety criterion (prevents collisions from lane-changes)
- incentive criterion
Parameters:
- safe deceleration
- "politeness" factor
- changing threshhold
Safety criterion
Part of the MOBIL-model
Prevents critical lane changes and collisions.
How it works:
- If the following car is slower
- it's safe to lane change
- it's safe to lane change
- if the following car is faster
- it's not safe to lane change
Discrete Time Simulations (DTS)
- Models evaluated and state updated only at predefined time intervals - Δt
- Update every Δt even if there is no change on inputs or states
- Need to execute at finest time granularity (time resolution)
- State changes only happen at the closest interval
- Master clock required for the overall simulation time
- Computational time lost were nothing happens - every simulation step is executed whether states change or not
Convenient for systems that can be described by PDEs (time discretization of the continuous functions)
Discrete Event Simulation (DES)
- Instantaneous events responsible for the changes in the system state
- In between events, no change to the system is assumed to occur
- Also requires master clock
- All events are ordered (even if they happen at the exact same time)
- It is normally very efficient since it allows to jump in time from one relevant event to the next one
Usually used for systems that are complex and difficult to be described by PDEs.
Basic concepts:
- System: a collection fo entities that interact together over time, e.g. vehicles and traffic lights
- System state: a collection of variables that contain all the information necessary to describe the system at any time (redundancy)
- Model: an abstract representation of the system
- Events: instances that trigger the change (update) of system state, e.g. arrival, departure, change of signal phase
- No notion of Δt: time difference between two consecutive events may vary a lot
Microscopic traffic flow models
car following + lane changing
Public Transport Priority
The goal of public transport priority is to increase the attractiveness of PT by increasing its speed and reliabilty.
This can be achieved by implementing following measures:
- Dedicated right-of-way
- Roadway improvements and regulations
- Traffic signal prioritization
- Operational improvements
- Complimentary measures (e.g. traffic calming)
Green Waves in Zürich
Network-wide approach of public transport prioritization.
- IT and PT form two independent networks:
- Optimize capacity for IT
- Minimize travel time for PT
- Synchronization is achieved when:
- PT stops at predefined places (e.g. bus stops) without interaction with IT
- PT can be decoupled from IT when on seperate lanes
- Arterial roads
- Arterials have IT Green Waves. The PT follows
- Besides the IT Green Wave main direction,
there is a PT Green Wave in the opposite direction
- Downtown areas
- There are no IT Green Waves
- PT decides the behavior
Gravity Model
In traffic modelling the Gravity Model is a popular method for trip distribution.
The gravity model assumes that the trips produced at an origin and attracted to a destination are directly proportional to the total trip productions at the origin and the total attractions at the destination.
Analogy to Newton's Law of Gravity:
- Greater mass / More attractions --> higher force between them
- Longer distance between two bodies / nodes --> lesser force
Logit Model
Simple model used for mode choice and route choice.
\(P_m = \frac{e^{U_{ijm}}}{\sum_{m} e^{U_{ijm}} } \\P_m: \text{Probability of taking mode m} \\U_m: \text{Utility of mode m for an individual} \\U_m = f(travel \ time, \ cost, \ etc.) \\\text{With Condition:} \\\sum_m P_m = 1\)
User equilibrium vs. System optimum
User equilibrium (UE): Find a feasible assignment in which all used paths have equal and minimal travel times.
- This principle follows directy from the assumptions that:
- drivers choose minimum time paths
- drivers are well-informed about network conditions
- most widely used trip assignment method for auto trips
- UE does not minimize congestion
- Total system travel time may not be the minimum
System optimum (SO): Find a feasible assignment which minimizes the total system travel time.
- SO is not a natural process --> measures have to be taken to reach SO
Dynamic Traffic Assignment (DTA)
DTA must involve the following concepts:
- A model for how congestion (travel times) varies over time
- A concept of equilibrium route choice
- Equilibration based on experienced travel times, not instantaneous travel times
Compared to Static Traffic Assignment (STA) DTA-Simulations are more realistic.
Problems:
- Limited link capacity (high computing cost)
- multicommodity flow (e.g. trucks, toll roads)
- elastic demand
- multi-mode supply
Calibration of microscopic models
Three step strategy:
- Capacity calibration
- Route choice calibration
- System performance calibration
Calibration Process:
- Select parameters to calibrate
- Global
- Link specific
- Collect field data
- Set calibration goals
- Search for optimal parameter values
Microsimulation - Operational outputs
Operational outputs specifications
- link level demand
- speed
- density
- throughput
- delay
- post processing data
- queues
- travel time
- 2D, 3D visualization
ALINEA
ALINEA is a local feedback ramp-metering strategy.
Behavioral differences - AVs vs. human drivers
- Human drivers anticipate disturbances downstream
--> inability of traffic anticipation can lead to platoon instability - AVs drive with lower speed variations at stable following conditions
- Reaction times of humans are larger than of controllers (yet comparable)
- Controllers drive based on time headway strategies but humans don't
Such behavioral differences directly impact traffic congestion, energy consumption, driving behaviors and possibly other dimensions.
Capacity drop phenomena
- Many studies have revealed that there is a stochastic nature of bottleneck capacities.
- Banks (1991) first suggested that discharge flow at bottlenecks diminishes once queues start forming upstream of the location
What is a model?
A set of mathematical equations (or rules) that tries to describe (i.e. replicate) a physical process (e.g. evolution of traffic congestion over time and space)
Why do we need models?
- Process analysis and understanding
- Planning (forecasting)
- introduction of a new mode (multimode)
- modification/extension of infrastructure - Operations (control)
- Design of model-based control strategies
- Estimation/prediction models
- Testing the control performance - Traffic simulation
Classification of traffic models
- Microscopic (mainly for simulation):
car following + lane changing
- Mesoscopic
vehicle platoons with similar characteristics
- Macroscopic
macroscopic traffic variables (in analogy to fluid mechanics --> LWR-Theoy)
- Network (or region) level (MFD)
macroscopic fundamental diagram (regional accumulations, flows)
Car-following model
Used in microscopic traffic flow models
--> model the movements and interactions of individual vehicles
Macroscopic traffic flow models
Traffic flow control - Supply
- Urban traffic lights
- Ramp metering
- Variable speed limits (VSL)
- Variable message signs (VMS)
- Route guidance
Traffic flow control - Demand
- Car pooling
- Congestion pricing
- Mode choice
Network components
Links:
- main road
- freeway
- link road
- local street
- etc...
Nodes:
- Stop sign
- Overpass
- Ramp
- Level crossing
- Traffic light
- stop sign
- roundabout
Levels of automation
Definition of telematics
- Telematics
- IT: Information Technologies
- Communications
- Hardware/Software - Long distance transmission of data and computerized information
- Sensor, road network instrumentation, wireless communications
- Algorithms for traffic estimation, prediction and traffic management
Measurement methods
measurements...
- ...at a (cross-sectional) point
- ...along a short distance
- ...along a length
- ...along an arterial or small area (by e.g. moving observer method)
other real-time large-scale monitoring methods
Data fusion
- the process of combining data from multiple, heterogeneous data sources such as cross-sectional data, floating-car data, police reports, etc.
- each of these categories of data describes different aspects of the traffic situation and might even contradict each other
- the goal of data fusion is to maximize the utility of the available information
Autonomous vehicles - Challenges
- Autonomous/connected vehicles and planning models
- Implications to traffic flow and operations
- Simulation: traffic, wireless communications
- Trajectory processor for particle-based simulators
- Lane changing in connected environment: game theory
Loop signatures
Vehicle classification:
Different types show distinct signature data
Traffic stream - definition
Basic independent control unit.
- At least
- 1 Detecting element
- 1 Display element
- Possible traffic streams
- Automobile traffic
- Bus transit
- Light rail transit
- Pedestrians
- Bicyclists
- Emergency vehicles
Floating car data
Driving a vehicle in the traffic stream, trying to maintain an "average" position in the traffic stream, i.e:
passing only as many vehicles as pass you.
Inductive loop detectors
- The most widely used sensors (for TM)
- magnetic field
- easy to install, inexpensive
- Measurements:
- time occupancy (%)
- flow (number of vehicles)
- speed (for double loops)
Calling and extension detectors
- Detectors that
- call for green (presence)
- ask for green extension (queue)
- Utilized in many cities with advanced management systems
Traffic Lights
Traffic lights exist to control the flow of traffic and are expected to bring benefits:
- Increased safety
- Minimize accident frequency and severity
- If properly timed, a traffic signal increases the traffic handling capacity of an intersection
- Manage traffic and travel times
- Provide directions to drivers
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Lernkarten
Floating car data
Driving a vehicle in the traffic stream, trying to maintain an "average" position in the traffic stream, i.e:
passing only as many vehicles as pass you.
Inductive loop detectors
- The most widely used sensors (for TM)
- magnetic field
- easy to install, inexpensive
- Measurements:
- time occupancy (%)
- flow (number of vehicles)
- speed (for double loops)
Calling and extension detectors
- Detectors that
- call for green (presence)
- ask for green extension (queue)
- Utilized in many cities with advanced management systems
Traffic Lights
Traffic lights exist to control the flow of traffic and are expected to bring benefits:
- Increased safety
- Minimize accident frequency and severity
- If properly timed, a traffic signal increases the traffic handling capacity of an intersection
- Manage traffic and travel times
- Provide directions to drivers
Phase, Stage, Cycle
Phase: The sum of the displayed green, yellow and red times for a movement or combination of movements that receive the right of way simultaneously during the cycle.
Stage: A group of phases that receive the right of way simultaneously during the cycle for an intersection.
Cycle: The sum of the phase lengths is the cycle length.
Protected/Permitted movement
Protected movement: A movement that has the right of way and does not need to yield to conflicting movements, such as opposing vehicle traffic. Through movements, which are always protected are given a green indication.
Permitted movement: A movement that must yield to opposing traffic flow. This movement is made during gaps.
Can be determined by using the cross-product.
Cross product rule
Cross product rule helps us identify if a movement should be protected or permitted. The cross-product is a simple approach that is only dependent on the peak-hour traffic flows \(\nu\).
Generally, we take the peak-hour traffic flow value of the traffic movement we want to check on protected movement and the opposing traffic movements. The determined values are checked against thresholds.
- Cross product exceeds 50'000 vehicles during peak-hour for one opposing lane
- Cross product exceeds 90'000 vehicles during peak-hour for two opposing lanes
- Cross product exceeds 110'000 vehicles during peak-hour for three or more opposing lanes
Cross Product: \(CP_{\phi_i,\phi_j} = v_i \cdot v_j\)
Traffic Signal - Stage
A stage is a group of phases (i.e. movements) that don't create conflicts and are compatible, i.e. they can operate together.
Saturation
Undersaturated conditions: all the vehicles that are queued during the red phase are served by the green.
Saturated conditions: vehicles spend in the intersection more than one cycle (cycle failure).
Signal control - Modes
Pre-timed: A signal whose timing (cycle length, green, red etc.) is fixed over specified time periods. This is not affected by traffic flow at an intersection.
Semi-actuated: A signal whose timing is affected when vehicles are detected (by video, loop-detectors or other sensors), on some, but not all approaches. This approach is met on major/minor roads (with difference on flows). The major gets green until some vehicles appear in the minor.
Fully-actuated: A signal whose timing is completely inflluenced by traffic flow. This approach is met on major/major roads where substantial variations exist in the approaching traffic volumes.
Macroscopic Fundamental Diagram (MFD)
Aggregated relationship between network accumulation and total flow (production).
Useful tool for control.
- undersaturated: minimize delays!
- saturated: maximize capacity!
- oversaturated: queue management, gating!
- blocked: call the police or walk home!
Saturation flow
The saturation flow is the hourly maximum volume that can pass through an intersection, from a given lane (or group of lanes), if that lane was allocated constant green over the course of an hour.
\(s= \frac{3600}{h} [\frac{vehicles}{h}]\)
s is the saturation flow in vehicles per hour
h is the saturation headway in seconds per vehicle
3600 is the number of seconds per hour
Capacity
Movements on an intersection do not receive a constant green indication. Capacity accounts for the hourly volume that can be accommodated on an intersection.
\(c=s \frac{g}{c} [\frac{vehicles}{hour}] \\s \ \text{ is the saturation flow in vehicles per hour.} \\g \ \text{is the green time in seconds} \\C \ \text{is the cycle length in seconds}\)
Lost time
Due to the traffic signal's function of continuously alternating the right-of-way between conflicting movements, traffic streams are continuously started and stopped. Every time this happens, a portion of the cycle length is not completely utilized, which translates to lost time.
\(t_L = t_{sl} + t_{cl} \\ \\t_L \ \text{is the lost time for a movement during a cycle in seconds} \\t_{sl} \ \text{is the start-up lost time in seconds} \\t_{cl} \ \text{is the clearence lost time in seconds}\)
Start-up lost time
Occur because when a signal indication turns from red to green, drivers in the queue do not instantly start moving at the saturation flow rate. The stopping of a movement also results in lost time. The yellow-red transition or all-red times are not fully utilized as well. This refers as clearance lost time.
All-Red
The amount of time within a cycle in which all approaches have red indication. This time is referred to as clearance intervall.
Scales of traffic modelling
Macro-level
Meso-level
Micro-level
Traffic Analysis Zones
TAZ divide the study area into smaller regions assumed to be homogeneous demographically and economically.
Zone selection criteria:
- Homogeneous socioeconomic characteristics
- Minimize the number of intra zonal trips
- Recognize physical, political and historical boundaries
Network representation elements
Zone Centroid: Special node whose number identifies a zone, located by (x, y) coordinates.
Node (Vertices): Intersection of links, located by (x, y) coordinates.
Links (Arcs): Indexed by from and to nodes (including centroid connectors), attributes include lanes, capacity per lane, allowable modes.
Turns: Indexed by at, from and to nodes.
Routes (paths): Indexed by a series of nodes from origin to destination (e.g. a public bus line)
Modes: Car, bus, HOV, truck, bike, walk etc.
Travel data sources
Surveys (traditional method)
ICT and Big-data movement (cities are data-factories!)
Internet (FB, Twitter, Foursquare, Instagram, etc.)
Cellular phones (Bluetooth)
https://opentransportdata.swiss/
Four Step Model
- Trip generation: What are the total number of trips people make to and from each zone?
- Trip distribution: What are the specific origins and destinations for this total number of trips?
- Mode choice: How many people will choose to drive, walk, cycle, use transit, etc.?
- Route choice: What are the specific routes that people will use for their trips?
OD matrix
Origin-Destination Matrix or Trip Table
Mode choice
For modelling Mode choice some consistent theory of decision-making is needed:
--> Microeconomic concept of utility maximization is most widely accepted
Basic assumption:
- Traveler will select the combination of the mode that gives the most utility economically
- this is modelled with a so called utility function
The utility function for Mode choice can include:
- location (proximity to bus stop)
- convenience
- cost
- travel time
- parking
- health
- environment
- privacy (i like to travel alone)
- ...
Logit model
Route choice
- Route choice is a classic equilibrium problem
- Route choices are primarily a function of route travel time that is determined by traffic flow
Wardrop's principle is often used.
Dynamic Traffic Assignment (DTA)
LWR-Theory
Lighthill-Whitham-Richards (LWR) models represent the behavior of traffic streams and is used for macroscopic traffic models.
Consists of:
- continuity equation (borrowed from fluid mechanics)
- fundamental equation of traffic flow (q=vk)
- equilibrium speed-density relationship
Microscopic traffic models
car following + lane changing
Driving sub-tasks in car-following
Perception: observation of the leading car motion in relation to the driver's car (vehicle speed, acceleration, inter-vehicle spacing, relative speed, etc.) and interpretation of the situation
Decision making: selection of a proper reaction (acceleration vs. deceleration, magnitude of reaction)
Reaction: change in speed
Behavioral (micro) parameters
Parameters for the car-following model
- minimum headway (time or space)
- speed acceptance
- minimum stopping distance
- acceleration, deceleration
- define mean and std. deviation (i.e. distributions)
- Most important: reaction time
Lane changing
Types of lane changing
Mandatory: a vehicle must exit its current lane
Discretionary: a vehicle attempts to change lanes if moving below its desired speed and adjacent lane(s) move faster
Anticipatory: a vehicle in a lane which may be involved in merging downstream attempts to change upstream in anticipation of congestion in the merge area
Cooperation: vehicle(s) in target lane adjust their speeds to accomodate the lane changing vehicle
Essential steps for microsimulation
- Network editing (topology, geometry, GIS data)
- Infrastructure (sensors, bus stops, road types)
- Demand data (traffic states, OD matrices)
- Rout choice (DTA, user equilibrium)
- Traffic management (control strategies, actuators, telematics, public transport schedules)
- Dynamic scenarios (e.g. incidents)
- Metrics and evaluation (statistical analysis of scenarios)
--> Calibration!
Fundamental Diagram
Saturation impact
Queue spillback:
- Wasting of green time
- Increased delays (all movements)
- Blocked exits
- Accelerated queue increase
- Serious infrastructure degradation
- ....
.... - Gridlock: Infrastructure breaks down
Main challenges of MFD
Macroscopic Fundamental Diagram (MFD)
- Heterogeneity
- Partitioning into smaller regions
- Variance of measurements
- Compact regions
- MFD hysterisis
- Clockwise
- Counter clockwise
Other control approaches
- Congestion pricing (London, Stockhol, Singapore)
- Protected zones (regulations, tolls)
- Gating
- Perimeter control
- Parking control
- Incentivize mode shift (e.g. public transport, car sharing)
--> in europe during peak hours the average number of passengers per car is 1.2!
Real-time control loop
Ramp metering
Ramp metering is the controlling of frequency with which vehicles enter the flow of traffic on the freeway.
Further effects:
- incident response
- increased traffic safety: less congestion, safer merging
Merging traffic control
Merging examples:
- merging of two highways
- motorway on-ramps
- toll plazas
- motorway work zones
If the arriving flow on M lanes > capacity on \(\mu \) lanes --> congestion --> capacity drop
The goal of merging traffic control is to restore the capacity flow (avoid capacity drop)
