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Optimal Adaptive Signal Control for Diamond Interchanges Using Dynamic Programming. FALL 2005 UMASS Amherst Operations Research / Management Science Seminar Series Fang (Clara) Fang, Ph.D. Assistant Professor The University of Hartford. Outline of Presentation. Background Methodology

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Optimal adaptive signal control for diamond interchanges using dynamic programming

Optimal Adaptive Signal Control

for Diamond Interchanges Using

Dynamic Programming

FALL 2005 UMASS AmherstOperations Research / Management Science Seminar Series

Fang (Clara) Fang, Ph.D.

Assistant Professor

The University of Hartford


Outline of presentation

Outline of Presentation

  • Background

  • Methodology

    • Dynamic Programming Formulation

    • Vehicle Arrival-Discharge Projection Model

    • Algorithm Implementation

  • Using Simulation for Evaluation

  • Sensitivity Analysis and Comparisons

  • Conclusions and Recommendations


Diamond interchanges

Diamond Interchanges

D = 400 – 800 ft or less

Freeway

Surface Street

Freeway


Optimal adaptive signal control for diamond interchanges using dynamic programming

Geometric Layout of a Diamond Interchange

Freeway

On-Ramp

Freeway

Off-Ramp

Arterial

Freeway

On-Ramp

Freeway

Off-Ramp


Optimal adaptive signal control for diamond interchanges using dynamic programming

Common Signalization Schemes

  • Three-phase Plan

  • Four-phase Plan

Freeway

Off-Ramp

Freeway

On-Ramp

Arterial

Freeway

On-Ramp

Freeway

Off-Ramp


Optimal adaptive signal control for diamond interchanges using dynamic programming

Common Signalization Schemes

Phase - part of cycle (sum of green, yellow and red times) allocated to any combination of traffic movements receiving the right-of-way simultaneously.


Optimal adaptive signal control for diamond interchanges using dynamic programming

4

6

6

6

1

1

5

5

2

2

2

8

Common Signalization Schemes

  • Three-phase Plan

  • Four-phase Plan

Freeway

Off-Ramp

Freeway

On-Ramp

Arterial

Freeway

On-Ramp

Freeway

Off-Ramp


Background

Background

  • PASSER III (Signal Optimization Tool for Diamond Interchanges)

    • Off-line and pre-timed

    • Search: three-phase or four-phase plan


Background1

Background

  • Adaptive Control

    • Generates and implements the signal plan dynamically based on real time traffic conditions that are measured through a traffic detection system


Objectives

Objectives

  • To develop a methodology for real-time signal optimization of diamond interchanges

  • To evaluate the developed optimal signal control using micro-simulation


Optimization method dynamic programming dp

Optimization MethodDynamic Programming (DP)

  • To optimize a sequence of inter-related decisions

  • Global optimal solution

Optimal signal switch sequence

Time

Decision Tree


Optimal adaptive signal control for diamond interchanges using dynamic programming

DP Formulation - Decision Network

Optimization Horizon (10 seconds)

State

Stage 1

Stage 2

Stage 3

Stage 4

Input:

Initial Phase & Queue Length

Arrivals from t0 – t4

Output:

Optimal

Decision Path

Three-Phase Ring Structure


Optimization objective

Optimization Objective

  • Performance Measure Index (PMI)

Weights

Queue Length, Storage Ratio, Delay, etc.


Optimal adaptive signal control for diamond interchanges using dynamic programming

Fixed Weights vs.Dynamic Weights

Dynamic Values:

Fixed Values


Dp formulation forward recurrence relation

DP FormulationForward Recurrence Relation

Minimal PMI from stage 0 to stage n-1

Minimal PMI from

stage 0 to stage n

Immediate Return

over stage n, due to decision k,

state (n-1,j) changing to state (n,i), given initial queue lengths at stage n-1

Minimal PMI over

all decisions


Optimal adaptive signal control for diamond interchanges using dynamic programming

Vehicle Projection Model

Distance, ft

DP Horizon

Implement Optimal Signal Plan

0 2.5 5 7.5 10 20

Stop-line

Time, sec

Queue

Detection Period

DP Calculation

Detector

Time, sec

-16 -15 -12 -2 0

-8.5 -2 5.5

Detection

Overlap


Optimal adaptive signal control for diamond interchanges using dynamic programming

Detectors PlacementLayout


Optimal adaptive signal control for diamond interchanges using dynamic programming

Signal ImplementationMajority Rolling Concept

For each horizon of 10s, a majority signal phase is implemented for

Either 7.5s green if this majority phase is the same as the previous one,

Or otherwise 2.5s yellow-and-all-red clearance timefollowed by 5s green


Using simulation to evaluate the dp algorithm

Using Simulation to Evaluate the DP Algorithm

Select one diamond interchange, Collect field data

Select a simulation model from AIMSUN, CORSIM & VISSIM

Calibrate the model

Simulate the DP algorithm by the calibrated simulation model

Sensitivity Analysis

Simulate three signal plans by the calibrated simulation model

Comparisons

DP Algorithm

PASSER III

TRANSYT-7F


Diamond interchange field data

Diamond InterchangeField Data


Aimsun and the dp algorithm

AIMSUN Simulation

GETRAM Extension Module

Detection Information

Signal Timing

DP Algorithm

Coded in C++ Generate *.DLL

AIMSUN and the DP Algorithm


Code flow structure and time logic

Code Flow Structure and Time Logic

GetExtLoad

idprolling=0

isimustep=-1

idp=0

GetExtManage

GetExtInit

Detecting over every 0.5 seconds for all lane groups.

  • . Discharging headway

  • . Arrival vehicles traveling speed

  • . Arrival vehicle number

If time >=284

If isimustep<27

Block 1

isimustep=isimustep+1

If isimustep=27, isumstep=0

Detection Overlapping

Estimating the initial queue at t=300+idprollong*10, based on the queue and signal at t=298, and the averaged number of arrival vehicles every 0.5 second

If time =298

Arrival Projection and discharge dynamics calculation

DP value forward iteration

DP optimal signal backward declaration

Block 2 & Block 3

If 298<time <300

Layer 0 to 4

i=0~3

Disable the current fixed control plan

If time = 300

Block 4

idp=idp+1

If idp=4, then idp=0

Idprolling=0

Implement the DP optimal signal, rolling 2.5 sec forward, for a total of 4 DP intervals

If time=300+idp*2.5

Step-wise simulation is finished

Time = time + 0.5

No

If time=7200, Switch to fixed control

Yes

GetExtFinish

GetExtUnLoad


Sensitivity analysis

Sensitivity Analysis

  • Delay vs. PMI

    • Sum of Average Queue Length Per Lane for All Approaches

    • Sum of Average Delay Per Lane for All Approaches

    • Sum of Total Delays for All Approaches

    • Sum of Storage Ratio Per Lane for All Approaches

  • Delay vs. Weights

    • Ramp Weights

    • Arterial Weights

    • Internal Link Left Turning Weights

Weights


Comparisons dynamic weights fixed weights

ComparisonsDynamic Weights & Fixed Weights

System Delays (sec/veh)

Saving 36% - 49%


Summary fixed weights and dynamic weights

Summary Fixed Weights and Dynamic Weights

  • When the demand varies unpredictably every 15 minutes and is unbalanced, using dynamic weights can reduce the system delay up to 49%, compared to using fixed weights.

  • With dynamic weights, operations remain under-saturated for higher demands than with fixed weights.

  • With dynamic weights, users do not need to manually adjusting the weights.

  • The performance of dynamic weights also depends on how their values are defined.


Comparisons dp passer iii transyt 7f

ComparisonsDP, PASSER III & TRANSYT-7F

System Delays (sec/veh)


Conclusions

Conclusions

  • Developed a methodology and the corresponding algorithm for optimal and adaptive signal control of diamond interchanges

    • Various performance measures

    • Dynamic weights

  • Built a vehicle arrival-discharge projection model at the microscopic level

  • Simulated the algorithm using AIMSUN

  • Studied the algorithm performance


  • Conclusions for the algorithm performance

    Conclusionsfor the Algorithm Performance

    • Optimize both phase sequence and phase duration

    • The real-time DP signal algorithm is superior to PASSER III and TRANSYT-7F in handling demand fluctuations

    • The dynamic weighted algorithm is appropriate to be applied in special events or incidents when high demands are unexpected and varying


    Future research

    Future Research

    • Expand the decision network of signal control

    • When it is not possible or practical to place detectors far enough

    • Results compared to other adaptive signal systems and/or actuated control systems

    • Apply the method for urban arterials and small networks


    Optimal adaptive signal control for diamond interchanges using dynamic programming

    Questions and Comments?


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