roshan kumar, peter vovsha, pb petya maneva, vladimir livshits, kyunghwi jeon, mag

Using Detailed Navigation Networks for Modeling Transit Access and Non-Motorized Modes: Application to MAG CT-RAMP ABM

Roshan Kumar, Peter Vovsha, PBPetya Maneva, Vladimir Livshits, Kyunghwi Jeon, MAG

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TPAC, Columbus, OH, May 5-9, 2013

All location choices implemented at a finer level of spatial resolution in recent CT-RAMP ABMs 20,000-40,000 Micro-Analysis Zones (MAZs) -- instead of

2,000-4,000 Traffic Analysis Zones (TAZs)

Full advantage of MAZs not taken in most ABMs because of a simplified path building procedure straight line Euclidian distance skims (multiplied by a

correction factor) used for MAZ-to-MAZ walk and MAZ-to-Stop transit access

Some distances substantially overestimated, some distances underestimated

Introduction

Enhanced Spatial Resolution MAZs nested in TAZs:

CT-RAMP handles all location choices at MAZ level Assignment & skimming cannot handle MAZ-to-MAZ

matrices Virtual Path (VP) building:

Access and egress time pre-calculated for MAZ-to-station matrices using detailed navigation network (NavTeq)

Station-to-station time/cost matrices skimmed MAZ-station-station-MAZ path calculated on the fly

TPAC, Columbus, OH, May 5-9, 2013 3

Fine-Grain LOS (1=Pre-fixed VP)


Origin 2 TAZ/TAP

Destination 1 TAZ/TAP

Origin 1 TAZ/TAP

Origin 3 TAZ/TAP



23

1

56

4

89

7

23

1

56

4

89

7

Access EgressMain In-Vehicle

Fine-Grain LOS (2=On Fly VP/CT-RAMP)


Origin 2 Stop

Destination 1 Stop

Origin 1 Stop

Origin 3 Stop

Destination 2 Stop

Destination 3 Stop

23

1

56

4

89

7

23

1

56

4

89

7

Access EgressStop-to-Stop LOS

TPAC, Columbus, OH, May 5-9, 2013

Transit Path-Building

Boarding stop requires bus transfer to

rail

Longer walk but no bus transfer

Different Origin MAZ (same TAZ) has different walk &

transit times

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Eliminate “across the board” predetermined correction factors for straight-line distance

1. Use detailed navigation networks to compute shortest path skims for walk and walk-to-transit access in built areas implementing Dijkstra’s shortest path algorithm.

2. Develop a regression model to estimate ratio of shortest path to Euclidian distance for non-built MAZs for future scenarios

3. Extract non-motorized LOS skims using a hash table

Objective

Objective: Find MAZ-to-MAZ Walk Paths (less than 3 miles) Inputs : NavTeq Network, MAZ Layer Outputs : MAZ-to-MAZ Walk Cloud (cloud[I,J] = walk dist (I,J))

MAZ to MAZ Shortest Paths

Higher level facilities removed (Functional Classes 1 and 2)

Centroid connectors updated (no connectors to highways; 4 per MAZ)

Nodes close (within 0.5 miles) to highways tagged

MAZ “walkability” identified

All MAZ to MAZ shortest paths less than 3 miles found

Estimating Pedestrian Shortest Paths

MAZ to MAZ Shortest Paths All MAZ to MAZ shortest paths less

than 3 miles found Dijkstra’s shortest path with a heap

structure implemented Code written in Python Network data structures modified and code

parallelized: Finding all MAZ-to-MAZ shortest paths takes only

20 minutes Being implemented to utilize MAZ_8 IDs

Compression Factor =

For 3 mile threshold, compression factor = 1.16% (6.25 million paths)

For 1 mile threshold, compression factor = 0.2% (1.08 million paths)

pathsshortest #reshold within thpathsshortest #

Density/Land Use

Hyperbolic Function

Benchmarking tests for Hash Tables Results:

Distances checked for first 10,000 MAZs 3.7 million out of 100 million MAZ pairs within 3 miles Space required to store 10,000 X 10,000 matrix was 780 MB

Benchmarking tests for accessing Rectangular Matrix and Hash TableVariable Type Data Structure Memory Used (GB)* Access Time (sec)**

Short Rectangular Matrix 2.18 1

Float Rectangular Matrix 4.36 1

Java Float Hash Table 0.78 35

**Times reported for accessing each data structure 100 times*Total Memory = 8 GB

Storing MAZ Walk metrics as Nested Hash Tables

Distances within 3 miles

Distances within 3 miles

Out of Range

Out of Range

0 mi to 0.1 miMAZ 1 to MAZ 20.1 mi to 0.2 miMAZ 1 to MAZ 3 0.2 mi to 0.3 mi

MAZ 1 to MAZ 4 0.3 mi to 0.4 miMAZ 1 to MAZ 5

00010203

MAZ-to-M

AZ within 3 m

i

Hash Function

BucketsKeys

Distance

MAZ-to-MAZ Distance Matrix

Hash Table

Future Scenarios Exact navigation network not available Certain zones not build yet but expected to be

built Certain zones planned to change the LU

substantially In both cases, LU development plans are

available The method has to be adjusted:

Predict pedestrian conditions and walk-ability for new/changed zones

Integrate built and no-built zones in one procedure seamlessly

Estimating Shortest Paths Regression model to estimate shortest path

cost

Hyperbolic Function

DensityLand Use

Ws = Weighted cost for every land use for every pathWalk = 1 if Origin and Destination MAZs are “walkable”

Procedure to calculate Ws

For node j within MAZ m in path p, calculate: wjm = (cij + cjk )/2

Weighted Path cost for land use type ‘s’ is:

Single family high density is assumed as base, since

Estimating Shortest Paths

Pathpi j k

cij cjk

cij = Cost of link (i,j)wsm = Share of Land use type ‘s’ in MAZ ‘m’wjm = Weight of node j within MAZ m in path p.Ws = Weighted Path cost for land use type ‘s’

MAZ m

Regression Results

28.02 R

Predicted Observed

Regression ResultsVariable Estimate Std. Error t-value Variable Estimate Std. Error t-value

(Intercept) 0.04580 0.00379 12.07200 Industrial -0.9299 0.0072 -129.2140

Euclidian Distance 0.00037 0.00000 1443.61800 Medical/Nursing Home -0.1488 0.0185 -8.0600

Density (OD) 2181.00000 9.63600 226.37300 Mixed Use 2.8000 0.3749 7.4700

Walk 0.17180 0.00453 37.89200 Multi Family - Apartment/Condo 0.0259 0.0068 3.8310

Near Highway -0.33440 0.00170 -197.13600 Office -0.0065 0.0150 -0.4370

Active Open Space -0.69330 0.01783 -38.88300 Other Employment - Landfill/Proving Grounds/Sand and Gravel/etc. -1.4320 0.0581 -24.6400

Agriculture -1.27200 0.01461 -87.04300 Passive/Restricted Open Space/Undevelopable -1.3520 0.0343 -39.3760

Airport -2.60000 0.06870 -37.85200 Public/Special Event/Military 0.7408 0.0145 51.1660

Business Park -2.30200 0.11310 -20.35300 Religious/Institutional 1.3960 0.0253 55.2810

Cemetery -1.31000 0.05637 -23.23200 Single Family High Density - Greater than 4 du/ac - Includes Mobile Homes 0.0000 -- --

Commercial High - Community Retail/Regional Retail -0.46510 0.01787 -26.02800 Single Family Low Density - Less than 1

du/ac -0.6788 0.0122 -55.6450

Commercial Low - Amusement/Movie Theatre/Specialty Retail/Neighborhood Retail

1.37900 0.01086 127.00100 Single Family Medium Density - 1 to 4 du/ac -0.1119 0.0059 -18.8680

Developing Employment Generating 1.21800 0.11010 11.06700 Tourist Accomodations - Motel/Hotel/Resort 0.0976 0.0429 2.2730

Developing Residential -0.63660 0.02819 -22.58200 Transportation 1.5270 0.0182 83.8840

Educational/Religious -0.45030 0.01328 -33.90700 Vacant -0.4920 0.0116 -42.5280

Golf Course -1.98800 0.02332 -85.23100 Water -4.6650 0.0410 -113.6880

*Residual standard error: 1.82 on 6304527 degrees of freedom**Multiple R-squared: 0.2807, Adjusted R-squared: 0.2807***F-statistic: 8.2e+04 on 28 and 6304527 DF, p-value: < 2.2e-16

Regression Results (Most Walkable LU)Variable Estimate Std. Error t-value Variable Estimate Std. Error t-value












du/ac -0.6788 0.0122 -55.6450








Regression Results (Least Walkable LU)Variable Estimate Std. Error t-value Variable Estimate Std. Error t-value












du/ac -0.6788 0.0122 -55.6450








Estimating Shortest Paths for Green Zones

Three types of paths

Brown Zone

Brown Zone

Green Zone

Brown Zone

Green Zone

Green Zone

Actual Shortest Path

Estimate of Shortest

Path

Actual Shortest Path

Replace simplified path building procedure with shortest path algorithm using detailed navigation networks

Algorithm implemented in Python and parallelized 6.25 million paths less than 3 miles found in 20 minutes Applied as network processing step in CT-RAMP ABMs

developed for MAG, PAG, and CMAP

Regression model that uses land use variables developed to estimate shortest path costs for future built MAZs

Summary

roshan kumar, peter vovsha, pb petya maneva, vladimir livshits, kyunghwi jeon, mag

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