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An Optimal Control Model for Traffic Corridor ManagementPowerPoint Presentation

An Optimal Control Model for Traffic Corridor Management

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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
- Research Framework
- Model Formulation
- Optimization Process

- Numerical Experiments
- A test network
- A real city network

- Concluding Comments

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- Introduction
- Literature Review
- Methodology
- Numerical Experiment
- Concluding Remarks

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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

- 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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- 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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- 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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- Introduction
- Literature Review
- Methodology
- Numerical Experiment
- Concluding Remarks

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- 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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- 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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- Introduction
- Literature Review
- Methodology
- Numerical Experiment
- Concluding Remarks

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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

- 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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- 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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- 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

- Flow conservation

qi(k):inflow

ui(k):outflow

qi(k):inflow

ui(k):outflow

xi(k):queue length

βHi :length of section

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- 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

- ALINEA

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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- 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

- Cycle, Green time, Lost time

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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Optimization Process

- Formulation Construction
- Use CPLEX to optimize the problem

- Introduction
- Literature Review
- Methodology
- Numerical Experiments
- Concluding Remarks

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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

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Change of Objective Values

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

High Level

under saturation

Median Level

low

Level

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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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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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Low iterations

medium

high

Vehicles accessing airport also cause traffic congestion

The interchange is a critical point in the network

- Introduction iterations
- Literature Review
- Methodology
- Numerical Experiment
- Concluding Remarks

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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 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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- Thank You for Your Attention. iterations

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