Road Transport Systems

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

• 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!

Queue spillback:

• Wasting of green time
• Increased delays (all movements)
• Blocked exits
• Accelerated queue increase
• Serious infrastructure degradation
• ....
  ....
• Gridlock: Infrastructure breaks down

Macroscopic Fundamental Diagram (MFD)

• Heterogeneity
  • Partitioning into smaller regions
  • Variance of measurements
  • Compact regions
     
• MFD hysterisis
  • Clockwise
  • Counter clockwise

• 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!

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 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)

• traffic lights
• physical barriers (toll plaza)
• variable speed limits
• emerging vehicle-to-infrastructure technologies
• some lanes may be free
• control algorithm:
  • a) exit flow regulation
  • b) distribution per (controlled) lane
  • c) translation of control decisions
• ramp metering (motorway on-ramps)

Variable Speed Limits

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)

Autonomous Vehicle

Autonomous Vehicle (AV)

• less congestion
• shorter travelling time
• less pollution
• less energy consumption
• less accidents
• more parking space
• higher mobility (elderly, kids, etc.)

Adaptive Cruise Control

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.