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Robust Synchronization of Actuated Signals on Arterials. Project #2008-003: Simulation-Based Robust Optimization for Actuated Signal Timing and Setting. Lihui Zhang Yafeng Yin. Outline. Background Introduction Bandwidth Maximization Robust Coordination Model Numerical Example

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Robust Synchronization of Actuated Signals on Arterials

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Robust synchronization of actuated signals on arterials

Robust Synchronization of Actuated Signals on Arterials

Project #2008-003:

Simulation-Based Robust Optimization for Actuated Signal

Timing and Setting

Lihui Zhang

Yafeng Yin


Outline

Outline

  • Background Introduction

    Bandwidth Maximization

  • Robust Coordination Model

  • Numerical Example

  • Concluding Remarks


Background coordination

Background -- Coordination

  • Synchronize traffic signals to provide smooth progression for major traffic movements along arterials

  • Offset + Cycle length


Background

Background

  • Actuated signals

  • Current practice performing coordination

  • Uncertainty of start and end of the green

  • Semi-Actuated signal coordination


Background1

Background

  • Two approaches:

    by maximizing green bandwidth

    (MAXBAND and PASSER-II )

    by minimizing total delay

    (TRANSY-7F )


Coordination

Coordination

Distance

Bandwidth

Offset

Cycle length

Signal i

Trajectory

Signal h

Speed

Time

Red Interval


Little s bandwidth maximization

Little’s Bandwidth Maximization

Offset Cycle lengthRed interval

s.t.


Bandwidth maximization

Bandwidth Maximization

Geometry of the Green Bands


Background early return to green

Background --Early Return to Green


Synchronization of actuated system

Synchronization of Actuated System

  • Stochastic optimization to generate robust synchronization plan

  • Scenario based

    Scenario set K={k: Rk=(r1k, r2k……rnk)}

    Represent traffic uncertainty

    Loss function

  • Deal with 10% worst case scenarios


Model formulation

Model Formulation


Numerical example

Numerical Example

  • Network (Corsim: ActCtrl Example)

  • Plan Generation

  • Plan Evaluation

    Macro-simulation

    Micro-simulation

    Modeling System: GAMS Solver: CPLEX


Numerical example plan generation

Numerical Example --Plan Generation

Robust Plan

  • 250 scenarios

  • Red times of the sync phases:

    independently normally distributed with

    specific mean and same variance.

  • Scenarios have equal probability to occur

  • Confidence level 0.90

    Nominal Plan

  • Red times: use fixed mean red times


Numerical example plan evaluation

Numerical Example --Plan Evaluation

Macro-Simulation

  • 2000 samples generated from independent normal distributions

  • 2000 samples generated from uniform distributions

  • Under Robust Plan and Nominal Plan

  • Performance measure:

  • Mean bandwidth

  • Worst case bandwidth

  • 90% CVaR

  • 90th percentile minimum

    bandwidth


Monte carlo simulation normal distribution

Monte Carlo Simulation--Normal Distribution


Monte carlo simulation uniform distribution

Monte Carlo Simulation --Uniform Distribution


Micro simulation and hypothesis test

Micro-Simulation and Hypothesis Test


Conclusions remarks

Conclusions & Remarks

  • Robust synchronization model: MILP

  • Perform better against high-consequence

    scenarios

  • Can be applied to design coordination plans as

    well as fine-tune plans

    Current research

  • Formulate and solve a deterministic integrated model for signal optimization, simultaneously optimizing cycle length, green splits, offsets, phase sequences

  • Formulate and solve a robust counterpart of the deterministic model considering day-to-day demand variations


Robust synchronization of actuated signals on arterials

Thank you ! Question?


Numerical example plan generation1

Numerical Example --Plan Generation

Computational time and plan difference


Robust synchronization cvar

Robust synchronization--CVaR


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