investigation of speed-flow relations and estimation of volume delay functions for travel demand...

Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions for Travel Demand Models in Virginia TRB Planning Applications Conference - May 19, 2009Presented by:Jaesup Lee, Virginia Department of TransportationDean Munn, The Corradino Group

Investigation of Speed-Flow Relations and Estimation of Volume Delay Functions for Travel Demand Models in Virginia TRB Planning Applications Conference, May 19, 2009

IntroductionTraffic Data used in basic analysis and model estimationData Development and DefinitionFree Flow SpeedTraffic Flow (Uninterrupted vs. Interrupted)Link Capacity Various Curve Fittings by Functional ClassFindings and Further ResearchOutline


IntroductionProject Goals

Use empirical data obtained from Virginia facilities to evaluate speed-flow relationships

Test various volume-delay functional forms for each facility type and determine which provides the best performance

Calibrate volume delay function parameters for each facility type

Outcome should be suitable for implementation in Virginia urban travel models


IntroductionFundamental Elements of Volume-Delay Estimation

Converting spot speeds to space-mean speed

Characteristics of free-flow

Identifying boundary between uninterrupted and interrupted flow

Using knowledge of this boundary to estimate the maximum sustainable flow rate (Capacity)

Use empirical observations to fit VDF curve parameters


Traffic Monitoring System (TSM) Data5,848 locations from 17,400 detector locations availableThree locations per classification selected


Traffic DataData records are a summary of each 15 minute period Speed bins are in 5 mph incrementsData records are organized by lane and vehicle classCUBE/Voyager script simplifies dataSpot speeds are converted to Space Mean Speeds


Processed DataSpeed vs DensitySpeed vs FlowSpeed by Time of Day


Estimating Free Flow SpeedHCM recommends using mean value for low volume conditionsStandard practice also includes using 85th Percentile speed71.1 mph73.7 mph


Defining Interrupted FlowPlots of flow vs density and speed vs density show two flow states

Others have defined the transition point as the maximum flow or the density at maximum speed, but this is not representative of typical conditions

Statistical techniques can define the transition between the two statesFlow vs. DensitySpeed vs. DensityInterrupted FlowInterrupted Flow


Defining Interrupted FlowWe define interrupted flow as: Any speed below the threshold where there is 0.0001% probability that it is the same as freeflow.


Defining Interrupted FlowRural Freeway example, with flow states identified


Interrupted FlowHistogram Percent with Interrupted Flow vs. Flow Density


Estimating CapacityOur data shows a classic logistic distributionWe estimated parameters (using density as the only variable) to create a probability function that best fits the data

Capacity corresponds to flow density with a 50% probability of being interrupted PI = 1/[1 + e(b1D+ b0)], where D = Density (veh/mi)


99.5% Probability of Interrupted Flow0.50% Probability of Interrupted Flow50.0% Probability of Interrupted FlowCapacity EstimatesThis example gives a 39.7 pc/mi Density Threshold or a 2384 pc/hr Max Flow Rate


Fitting Volume Delay FunctionsVolume-Delay Functions - Using the computed capacity, the following volume delay functions were estimated based on speeds during uninterrupted flow


Curve Fitting - non-linear regression

Goodness of Fit R-squared Root Mean Square ErrorNon-Parametric tests e.g. Chi-Square

Other Criteria - suitability for model applicationsFitting Volume Delay Functions


Fitting Volume Delay FunctionsUrban Interstate


Fitting Volume Delay FunctionsRural Interstate


Fitting Volume Delay FunctionsUrban Expressway


Fitting Volume Delay FunctionsRural Principal Arterial


Fitting Volume Delay FunctionsUrban Other Principal Arterials


Fitting Volume Delay FunctionsRural Minor Arterial


Fitting Volume Delay FunctionsUrban Minor Arterial


Fitting Volume Delay FunctionsRural Collector


Fitting Volume Delay FunctionsUrban Collector


Fitting Volume Delay FunctionsRural Local


Fitting Volume Delay FunctionsSummary of calibrated inputs to VDF fitting process


Fitting Volume Delay FunctionsSummarized results from VDF fitting process


Initial FindingsStandard VDF functions are all capable of performing adequately across road classes

For a given road class, VDF parameters fitted for one location, seem to be transferable to other locations

Goodness of fit measures do not strongly differentiate between functions

The Akcelik function, with its more rigorous theoretical underpinnings, seems to work very well


Next StepsAdditional facility types

Check model transferability to other facilities

Compare HCM capacity, planning capacity, and empirical capacity

Continue to automate analysis process

Test functions in urban models (assignment convergence, average travel speeds)

New VDF functional forms and calibrated parameters will become part VDOT modeling standards


Q & A

Thank you !

Contact pointsJaesup Lee: [email protected] Munn: [email protected] Raw : [email protected]

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investigation of speed-flow relations and estimation of volume delay functions for travel demand...

Documents

travel demand models

virginia facilities

mphinvestigation of

free flow speedhcm

minute period speed

mean value

traffic datadata records

functional classfindings