Optimal Adaptive Signal Control for Diamond Interchanges Using Dynamic Programming

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Optimal Adaptive Signal Control for Diamond Interchanges Using Dynamic Programming

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Optimal Adaptive Signal Control for Diamond Interchanges Using Dynamic Programming

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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

- Background
- Methodology
- Dynamic Programming Formulation
- Vehicle Arrival-Discharge Projection Model
- Algorithm Implementation

- Using Simulation for Evaluation
- Sensitivity Analysis and Comparisons
- Conclusions and Recommendations

D = 400 – 800 ft or less

Freeway

Surface Street

Freeway

Geometric Layout of a Diamond Interchange

Freeway

On-Ramp

Freeway

Off-Ramp

Arterial

Freeway

On-Ramp

Freeway

Off-Ramp

Common Signalization Schemes

- Three-phase Plan
- Four-phase Plan

Freeway

Off-Ramp

Freeway

On-Ramp

Arterial

Freeway

On-Ramp

Freeway

Off-Ramp

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.

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

- PASSER III (Signal Optimization Tool for Diamond Interchanges)
- Off-line and pre-timed
- Search: three-phase or four-phase plan

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

- To develop a methodology for real-time signal optimization of diamond interchanges
- To evaluate the developed optimal signal control using micro-simulation

- To optimize a sequence of inter-related decisions
- Global optimal solution

Optimal signal switch sequence

Time

Decision Tree

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

- Performance Measure Index (PMI)

Weights

Queue Length, Storage Ratio, Delay, etc.

Fixed Weights vs.Dynamic Weights

Dynamic Values:

Fixed Values

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

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

Detectors PlacementLayout

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

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

AIMSUN Simulation

GETRAM Extension Module

Detection Information

Signal Timing

DP Algorithm

Coded in C++ Generate *.DLL

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

- 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

System Delays (sec/veh)

Saving 36% - 49%

- 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.

System Delays (sec/veh)

- Developed a methodology and the corresponding algorithm for optimal and adaptive signal control of diamond interchanges
- Various performance measures
- Dynamic weights

- 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

- 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

Questions and Comments?