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Erstellt / Aktualisiert 20.06.2021 / 10.08.2022
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Capacity drop phenomena

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  • 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
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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)

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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
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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)
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Car-following model

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Used in microscopic traffic flow models

--> model the movements and interactions of individual vehicles

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Macroscopic traffic flow models

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Traffic flow control - Supply

  • Urban traffic lights
  • Ramp metering
  • Variable speed limits (VSL)
  • Variable message signs (VMS)
  • Route guidance
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Traffic flow control - Demand

  • Car pooling
  • Congestion pricing
  • Mode choice
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Network components


  • main road
  • freeway
  • link road
  • local street
  • etc...


  • Stop sign
  • Overpass
  • Ramp
  • Level crossing
  • Traffic light
  • stop sign
  • roundabout
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Levels of automation

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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
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Measurement methods


  • ...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

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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
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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
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Loop signatures

Vehicle classification:

Different types show distinct signature data

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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
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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.

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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)
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Calling and extension detectors

  • Detectors that
    • call for green (presence)
    • ask for green extension (queue)
  • Utilized in many cities with advanced management systems
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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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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.

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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.

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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:    \(CP_{\phi_i,\phi_j} = v_i \cdot v_j\)

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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.

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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).

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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.

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Macroscopic Fundamental Diagram (MFD)

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Aggregated relationship between network accumulation and total flow (production).

Useful tool for control.

  1. undersaturated: minimize delays!
  2. saturated: maximize capacity!
  3. oversaturated: queue management, gating!
  4. blocked: call the police or walk home!
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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

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Movements on an intersection do not receive a constant green indication. Capacity accounts for the hourly volume that can be accommodated on an intersection.

\(c=s \frac{g}{c} [\frac{vehicles}{hour}] \\s \ \text{ is the saturation flow in vehicles per hour.} \\g \ \text{is the green time in seconds} \\C \ \text{is the cycle length in seconds}\)

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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.

\(t_L = t_{sl} + t_{cl} \\ \\t_L \ \text{is the lost time for a movement during a cycle in seconds} \\t_{sl} \ \text{is the start-up lost time in seconds} \\t_{cl} \ \text{is the clearence lost time in seconds}\)