Optimal Adaptive Signal Control for Diamond Interchanges Using

Dynamic Programming

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 HartfordThe University of Hartford

FALL 2005 UMASS Amherst

Operations Research / Management Science Seminar Series

Fang (Clara) Fang, Ph.D.Assistant Professor

The University of HartfordThe University of Hartford

Outline of PresentationOutline of Presentation

Background

MethodologyDynamic Programming FormulationVehicle Arrival-Discharge Projection ModelAlgorithm Implementation

Using Simulation for Evaluation

Sensitivity Analysis and Comparisons

Conclusions and Recommendations

Diamond InterchangesDiamond Interchanges

FreewayD = 400 – 800 ft or less

Surface StreetFreeway

Geometric Layout of a Diamond Interchange

Arterial

Freeway Off-Ramp

Freeway On-Ramp

Freeway Off-Ramp

Freeway On-Ramp

Arterial

Freeway On-Ramp

Freeway On-Ramp

Freeway Off-Ramp

Freeway Off-Ramp

Common Signalization SchemesThree-phase Plan

Four-phase Plan

Common Signalization Schemes

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

Arterial

Freeway On-Ramp

Freeway On-Ramp

Freeway Off-Ramp

Freeway Off-Ramp

Common Signalization SchemesThree-phase Plan

Four-phase Plan

2

652

6

4

1

8

2

615

Background Background

PASSER III (Signal Optimization Tool for

Diamond Interchanges)

Off-line and pre-timed

Search: three-phase or four-phase plan

BackgroundBackground Adaptive Control

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

ObjectivesObjectives

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

To evaluate the developed optimal signal control using micro-simulation

Optimization MethodDynamic Programming (DP)

Decision Tree

To optimize a sequence of inter-related decisions

Global optimal solution

Time

Optimal signal switch sequence

DP Formulation - Decision Network

Three-Phase Ring Structure

Optimization Horizon (10 seconds)

Input:

Initial Phase & Queue Length

Arrivals from t0 – t4Output:

Optimal

Decision Path

Stage 1 Stage 2 Stage 3 Stage 4State

Optimization Objective

Performance Measure Index (PMI)

jj i

iQfinaliwPMI

4

1

8

1

][*][

Weights

Queue Length, Storage Ratio, Delay, etc.

jj i

iQfinaliwPMI

4

1

8

1

][*][

9][,9.0][

......

2][,2.0][

1,1.0][

iwtheniRatioStorageQueueIf

iwtheniRatioStorageQueueIf

iwtheniRatioStorageQueueIf

Fixed Weights vs.Dynamic WeightsFixed Weights vs.Dynamic Weights

Fixed Values Dynamic Values:

Length Storage Queue

Length Vehicles Queued

Ratio Storage Queue

DP FormulationForward Recurrence Relation

Minimal PMI from

stage 0 to stage n

Minimal PMI from stage 0 to stage n-1

Immediate Returnover 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

)},1(),,,({),( ** jnfqkinPMIMininf iKk i

Vehicle Projection ModelDistance, ft

Stop-line

Detector

Time, sec

Time, sec

0 2.5 5 7.5 10 20

-16 -15 -12 -2 0

DP Horizon

Queue

-8.5 -2 5.5

Detection Overlap

DP Calculation

Implement Optimal Signal Plan

Detection Period

Detectors Placement Layout

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 time followed by 5s green

Using Simulation to Evaluate the Using Simulation to Evaluate the DP AlgorithmDP Algorithm

Select one diamond interchange, Collect field data

Select a simulation model from AIMSUN, CORSIM & VISSIM

Calibrate the model

Simulate three signal plans by the calibrated simulation model

Comparisons

PASSER III TRANSYT-7FDP Algorithm

Simulate the DP algorithm by the calibrated simulation model

Sensitivity Analysis

Diamond InterchangeDiamond InterchangeField DataField Data

AIMSUN and the DP AlgorithmAIMSUN and the DP Algorithm

Signal Timing

DP Algorithm

Coded in C++ Generate *.DLL

GETRAM Extension Module

Detection Information

AIMSUN Simulation

Code Flow Structure and Time LogicCode Flow Structure and Time Logic

Detection OverlappingIf time >=284 If isimustep<27

GetExtLoad

GetExtInit

Detecting over every 0.5 seconds for all lane groups.1. Discharging headway2. Arrival vehicles traveling speed3. Arrival vehicle number

If time =298Estimating 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 298<time <300Arrival Projection and discharge dynamics calculationDP value forward iterationDP optimal signal backward declaration

If time = 300 Disable the current fixed control plan

If time=300+idp*2.5Implement the DP optimal signal, rolling 2.5 sec forward, for a total of 4 DP intervals

If time=7200, Switch to fixed control

Time = time + 0.5

Step-wise simulation is finished

GetExtFinish

GetExtUnLoad

GetExtManageidprolling=0isimustep=-1idp=0

isimustep=isimustep+1If isimustep=27, isumstep=0

Layer 0 to 4i=0~3

idp=idp+1If idp=4, then idp=0Idprolling=0

No

Yes

Block 1

Block 2 & Block 3

Block 4

Sensitivity AnalysisSensitivity Analysis

Delay vs. PMISum of Average Queue Length Per Lane for All ApproachesSum of Average Delay Per Lane for All ApproachesSum of Total Delays for All ApproachesSum of Storage Ratio Per Lane for All Approaches

Delay vs. WeightsRamp WeightsArterial Weights Internal Link Left Turning Weights

jj i

iQfinaliwPMI

4

1

8

1

][*][

Weights

ComparisonsComparisonsDynamic Weights & Fixed WeightsDynamic Weights & Fixed Weights

System Delays (sec/veh)

Demand Scenario Dynamic FixedHigh EB Demand 30s 52sHigh SB Demand 23s 36s

High EB & WB Demand 39s 1m17sHigh EB & SB Demand 29s 51sHigh EB & NB Demand 29s 48s

Saving 36% - 49%

Summary Summary Fixed Weights and Dynamic WeightsFixed 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.

ComparisonsComparisonsDP, PASSER III & TRANSYT-7FDP, PASSER III & TRANSYT-7F

System Delays (sec/veh)

Fixed Dynamic PASSER III TRANSYT-7FArterial L: 400 TH: 2000 R: 250Ramp L: 750 TH: 300 R: 750Arterial L: 400 TH: 2300 R: 250Ramp L: 750 TH: 300 R: 750Arterial L: 400 TH: 2500 R: 250Ramp L: 750 TH: 300 R: 750Arterial L: 400 TH: 2700 R: 250Ramp L: 750 TH: 300 R: 750Arterial L: 400 TH: 3000 R: 250Ramp L: 750 TH: 300 R: 750Arterial L: 400 TH: 3300 R: 250Ramp L: 750 TH: 300 R: 750

Off-LineReal-Time DP Algorithm

4

5

43

26

26

29

23

24

24

21

26

32 51

6134

40 76

81

21

33

67

86

82

92

19

38

6

# Varying Demand

1

2

3

ConclusionsConclusionsDeveloped 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

ConclusionsConclusionsfor the Algorithm Performancefor 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 ResearchFuture 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

Questions and Comments?