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An Optimal Control Model for Traffic Corridor Management. Ta-Yin Hu Tung-Yu Wu Department of Transportation and Communication Management Science, National Cheng Kung University, Taiwan, R.O.C. 2010.10.27. OUTLINE. Introduction Literature Review Methodology

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An optimal control model for traffic corridor management

An Optimal Control Model for Traffic Corridor Management

Ta-Yin Hu Tung-Yu Wu

Department of Transportation and Communication Management Science, National Cheng Kung University, Taiwan, R.O.C.

2010.10.27


Outline
OUTLINE

  • Introduction

  • Literature Review

  • Methodology

    • Research Framework

    • Model Formulation

    • Optimization Process

  • Numerical Experiments

    • A test network

    • A real city network

  • Concluding Comments

17th ITS WORLD CONGRESS


An optimal control model for traffic corridor management

  • Introduction

  • Literature Review

  • Methodology

  • Numerical Experiment

  • Concluding Remarks

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Background
Background

  • Basically, a traffic corridor includes three major parts:

    • Mainline Freeway segments

    • On-ramps and off-ramps

    • One or more parallel surface streets

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Motivation
Motivation

  • Traffic jams occur in many traffic corridors because of increasing number of vehicles and insufficient traffic infrastructure.

  • Under ITS, the intelligent corridor management can utilize route guidance, ramp control and signal control, to improve the efficiency and enhance the service quality of corridors.

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An optimal control model for traffic corridor management

  • Papageorgiou (1995) developed a linear optimal control model to optimize the traffic corridor, and the model takes freeways, on-ramps and parallel arterial streets into consideration.

  • The concept of the model is based on the store-and-forward model (Gazis and Potts, 1963)

  • The advantage of the store-and-forward model is that a single performance index is used to evaluate the system.

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An optimal control model for traffic corridor management

  • Objectives

    • to develop a linear mathematical model for the ICM based on the store-and-forward model

    • to explicitly consider route guidance strategies

    • to optimize related decision variables

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An optimal control model for traffic corridor management

  • Introduction

  • Literature Review

  • Methodology

  • Numerical Experiment

  • Concluding Remarks

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An optimal control model for traffic corridor management

  • Moreno-Banos et al. (1993) proposed an integrated control strategy addressing both route guidance and ramp metering.

  • Diakaki et al. (1997) described a feedback approach with consideration of the overall network.

  • Mehta (2001) integrated DynaMIT with the Traffic Management Center and MITSIMLab especially toward Boston’s Central Artery Network.

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An optimal control model for traffic corridor management

  • Kotsialos et al. (2002) proposed a generic formulation for designing integrated traffic control strategies for traffic corridor.

  • Kotsialo and Papageorgiou (2004) provided an extensive review for the methods used for the design of freeway network control strategies.

  • Papamichail et al. (2008) presented a non-linear model-predictive hierarchical control approach for coordinated ramp metering of freeway networks.

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An optimal control model for traffic corridor management

  • Introduction

  • Literature Review

  • Methodology

  • Numerical Experiment

  • Concluding Remarks

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Research framework
Research Framework

Collect the information, such as flow data

Establish the mathematical model for the traffic corridor including urban streets, ramp, and freeway.

Route Guidance Strategies

Solved the Problem by CPLEX

Results analysis for different traffic situations.

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Model formulation
Model Formulation

  • Assumptions:

    1. Discrete time interval, time-dependent problem

    2. The operation of traffic corridor is under the same management level; therefore, data and information can be exchanged

    3. For signalized intersection:

    • The cycle time is fixed.

    • Based on a fixed number of phases.

    • The total lost time of intersection is given.

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An optimal control model for traffic corridor management

  • Notations:

    • xij(k) is the queue length of movement from i to j at time interval k.

    • qi(k) is the inflow of section i at time interval k.

    • ui(k) is the outflow of section i at time interval k.

    • ri(k) is the metering rate of section i at time interval k.

    • τ is the time interval.

  • Objective Function:

    • Minimize the total queue length.

    • Min JD = τ × ΣΣ xij(k)

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An optimal control model for traffic corridor management

  • Mainstream of Freeway

    • Flow conservation

      qH2(k) = uH1(k) + uR1(k)

      qH3(k) = uH2(k) - qR2(k)

    • Queue length

      xHi(k+1) = xHi(k) + τ[qHi(k) - uHi(k)]

      xmax,Hi = βHi(ρmax,Hi – ρcr,Hi)

      0 ≦ xHi(k) ≦ xmax,Hi

qi(k):inflow

ui(k):outflow

qi(k):inflow

ui(k):outflow

xi(k):queue length

βHi :length of section

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An optimal control model for traffic corridor management

  • On-ramp Control

    • ALINEA

      ri(k+1) = ri(k) + H[oi* - oout,i(k)]

      oout,i(k) = (βv+ βd) × ρcr,Hj(k) / 1000

      ρcr,Hj(k) = qHj(k) / (βHj × nHj)

    • Outflow - on-ramp & off-ramp

      uRi(k) ≦ α × ri(k)

      uRj(k) ≦ usat,Rj

    • Queue length

      xRi(k+1) = xRi(k) + τ[qRi(k) - uRi(k)]

      0 ≦ xRi(k) ≦ xmax,Ri

qi(k):inflow

ri(k):metering rate

βHi :length of section

βv :length of vehicle

βd :length of detector

ni:number of lanes

ui(k):outflow

ri(k):metering rate

qi(k):inflow

ui(k):outflow

xi(k):queue length

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An optimal control model for traffic corridor management

  • Urban Streets

    • Cycle, Green time, Lost time

      Σ gγ,μ = c – Lγ

    • Exit flow of a section.

      sUi(k) = tij × qUi(k)

    • Queue length

      xUi(k+1) = xUi(k) + τ[(1-tij)qUi(k) + dUi(k) - uUi(k)]

      0 ≦ xUi(k) ≦ xmax,Ui

    • Inflow & Outflow

      qUi(k) = Σ tUi,UjuUj(k)

      uUi(k) = Sui × gUi(k) / c

c:cycle time

g:green time

L:lost time

qi(k):inflow

si(k):exit flow

tij :exit rate

qi(k):inflow

ui(k):outflow

xi(k):queue length

di(k):demand

qi(k):inflow

ui(k):outflow

tuiuj :turning rate

S :saturation flow rate

g:green time

c:cycle time

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An optimal control model for traffic corridor management

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Optimization process
Optimization Process

  • Formulation Construction

  • Use CPLEX to optimize the problem


An optimal control model for traffic corridor management

  • Introduction

  • Literature Review

  • Methodology

  • Numerical Experiments

  • Concluding Remarks

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The test network
The Test Network

  • includes a mainstream of freeway, ramps,and urban networks

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Experimental design
Experimental Design

  • Objectives:

    • To observe the system performance in terms of objective values

    • To observe the variation of decision variables, such as green time and ramp metering rates

  • Experimental factor

    • Demand levels: 11

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The virtual network experiment
The Virtual Network Experiment

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Change of objective values
Change of Objective Values

  • It is obvious that objective values increase with respect to the demand level.


An optimal control model for traffic corridor management

High Level

under saturation

Median Level

low

Level

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Comparisons of different demand level
Comparisons of Different demand level. iterations

  • Low demand level (case 1)

    • Number of vehicles 2400 vehicles

    • Total delay : 218vehs-min

    • Average values 0.091min

  • Median demand level (case 5)

    • Number of vehicles 4320 vehicles

    • Total delay : 14290 vehs-min

    • Average values 3.308 min

  • High demand level (case 8)

    • Number of vehicles 5760 vehicles

    • Total delay : 29636 vehs-min

    • Average values 5.145 min

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An optimal control model for traffic corridor management

Low Level iterations

Median Level

High Level

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Results of green time allocations
Results of Green Time Allocations iterations

low

Level

In low and median level, more green time is allocated for the E-W.

Median Level

High Level

In high level, more green time is allocated for the S-N.

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Results of metering rates
Results of Metering rates iterations

low

Level

Median Level

High Level

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A real network taoyuan network
A Real Network – Taoyuan Network iterations

No. 31

No. 4

Freeway No. 2

Freeway No. 1



An optimal control model for traffic corridor management

Low iterations

medium

high

Vehicles accessing airport also cause traffic congestion

The interchange is a critical point in the network


An optimal control model for traffic corridor management

  • Introduction iterations

  • Literature Review

  • Methodology

  • Numerical Experiment

  • Concluding Remarks

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Concluding comments
Concluding Comments iterations

  • The optimal control model is developed based on the concept of the store-and-forward, thus a linear model could be formulated to solve the problem.

  • The total queue length increases with respect to demand levels.

  • As the traffic is getting congested, the ramp metering rate drops dramatically

  • For the VMS applications, acceptance percentages need to be determined in advance.

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Future developments
Future Developments iterations

  • Evaluate the optimal strategies through simulation models

  • Relax the cycle time constraints in the formulation

    • More variables

    • More constraints

    • Difficult to solve for the signal optimization problems

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An optimal control model for traffic corridor management

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