Measuring accessibility in infrastructure-poor regions

Antonio Paez
School of Geography and Earth Sciences
McMaster University

ETH Zurich July 1, 2019

Accessibility

A commonly used concept in transportation planning and research.

Commonly implemented as a combination of:

The number of opportunities available
The cost of reaching opportunities

Infrastructure-poor regions

There are decades-worth of accessibility research, but mostly for motorized travel in infrastructure-rich regions.

However, interest in accessibility in regions where infrastructure is not well-developed. Consequently:

Few or no network constraints
Active travel

Infrastructure-rich and -poor regions

Infrastructure-rich

Infrastructure-poor

Active Accessibility

Some key research challenges in active accessibility research (Vale, Saraiva, and Pereira, 2016):

Limited consideration of topography
Data and analytical limitations
An almost exclusive focus on time and distance
Conceptual and analytical limitations
Focus on accessibility at the point of origin but not at the destination
An implicit assumption of symmetry

Topography

According to Saelens, Sallis, and Frank (2003), topography is likely related to active travel but remains largely unstudied.

By 2016, the situation remains for the most part unchanged (Vale, Saraiva, and Pereira, 2016).

Why?

Topography

Data limitations are now largely moot.

Digital Elevation Model at 30 m resolution (Kenya): plot of chunk unnamed-chunk-1

Topography

Montreal Digital Elevation Data at 1 m resolution: plot of chunk unnamed-chunk-2

Topography

But how to relate topography to movement?

Analytically, the cost of movement has been measured using (horizontal) distance and time.

Distance
Straight line distance
Network distance
Time
Obtained from distance and speed

Cost Functions: Surface Distance

\[ d = \delta \sqrt{1 + m^2} \] Where $ \delta $ is the horizontal distance and $ m $ is the slope. plot of chunk unnamed-chunk-3

Cost Functions

Other alternatives have existed for decades, but have not been widely used:

Tobler (1993) relates speed (and indirectly time) to the slope of the terrain
Minetti et al. (2002) relate metabolic energy for walking to the slope of the terrain

Cost Functions: Tobler's Hiking Function

\[ t = \frac{1}{100}\delta \cdot e^{3.5|m + 0.05|} \] Where $ t $ is travel time in seconds. plot of chunk unnamed-chunk-4

Cost Functions: Metabolic Energy Equation

\[ C_w = 280.5m^5 - 58.7m^4 - 76.8m^3 + 51.9m^2 + 19.6m + 2.5 \] Where $ C_w $ is energy in $ J\cdot kg^{-1}\cdot m^{-1} $. plot of chunk unnamed-chunk-5

Cost Functions

plot of chunk unnamed-chunk-6

Cost Functions

Different assumptions
Are there differences in the implied behavior?

Example: Simulated Landscape

plot of chunk simulated-landscape

Example: Origins and Destinations

plot of chunk unnamed-chunk-7

Example: Shortest Paths

$\label{fig:figure-paths-1-simulation}Examples of shortest paths using different definitions of resistance, sample pairs 1 and 2 (blue path is origin-destination, red path is destination-origin, i.e., return trip)$

Highlights

Surface distance and travel time are more similar between them than either is to metabolic energy.

Cost on the return trip is not necessarily the same as on the original trip.

Empirical Example: Accessibility to Water in Kenya

plot of chunk figure-study-area

Empirical Example: Shortest Path Analysis

$\label{fig:figure-shortest-paths-kenya}Examples of shortest paths using different definitions of resistance, case study (blue path is origin-destination, red path is destination-origin, i.e., return trip)$

Empirical Example: Comparison of costs on shortest paths for O-D pair

$\label{fig:figure-scatterplots-kenya}Scatterplots of shortest path costs for different definitions of resistance: empirical example$

Empirical Example: Comparison of equivalent costs for O-D pair

$\label{fig:figure-scatterplots-equivalent-cost-kenya}Scatterplots of shortest path costs and equivalent cost for different definitions of resistance$

Empirical Example: Accessibility

$\label{fig:figure-accessibility-cumulative-opportunities-kenya}Cumulative opportunities accessibility maps in empirical example using different measures of resistance (Red = 0 water sources; Orange = 1 water source; Green = 2 water sources; Light Blue = 3 water sources; Dark Blue = 4 water sources)$

Empirical Example: Summary of Accessibility Results by Cost Criterion

\begin{table}[t]

\caption{\label{tab:table-summary-accessibility}\label{tab:table-summary-accessibility}Summary of accessibility analysis in case study: number of bomas with different levels of accessibility to water sources by cost criteria} \centering \begin{tabular}{lcccc} \toprule \multicolumn{1}{c}{} & \multicolumn{4}{c}{Cost Criterion} \ \cmidrule(l{3pt}r{3pt}){2-5} Water Sources & Euclidean Distance & Surface Distance & Time & Energy\ \midrule 0 & 41 & 42 & 38 & 40\ 1 & 22 & 24 & 24 & 17\ 2 & 7 & 4 & 5 & 6\ 3 & 3 & 3 & 6 & 7\ 4 & 0 & 0 & 0 & 3\ \bottomrule \end{tabular} \end{table}

Conclusions

Progress in data and analytics make it possible to model active accessibility using criteria that have hitherto been ignored.
Results suggest that use of different criteria can lead to more realistic and possibly more accurate results.
Example is in an infrastructure-poor region: relatively simple situation.

Directions for Future Research

Incorporate network constraints.
What is actual behavior?
Time minimization?
Distance minimization?
Energy minimization?
A combination of the above?
Calibrate cost functions for a range of travelers
Older adults
Cycling
Identify other elements of the environment that may affect routing
Zebra crossings
Parks