Road Transport Systems

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

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
     
• if the following car is faster
  • it's not safe to lane change

• 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)

• 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

car following + lane changing

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)

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

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

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 (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

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

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

Operational outputs specifications

• link level demand
• speed
• density
• throughput
• delay
• post processing data
• queues
• travel time
• 2D, 3D visualization

ALINEA is a local feedback ramp-metering strategy.

• 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.

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)

• 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

• 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)

Used in microscopic traffic flow models

--> model the movements and interactions of individual vehicles

• Urban traffic lights
• Ramp metering
• Variable speed limits (VSL)
• Variable message signs (VMS)
• Route guidance

• Car pooling
• Congestion pricing
• Mode choice

Links:

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

Nodes:

• Stop sign
• Overpass
• Ramp
• Level crossing
• Traffic light
• stop sign
• roundabout

• 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

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

• 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/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

Vehicle classification:

Different types show distinct signature data