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resiliency.tex
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\hypersetup{
pdftitle={A utility-based approach to modeling systemic resilience of highway networks with an application in Utah},
pdfauthor={Gregory S. Macfarlane; Max Barnes; Natalie M. Gray},
pdfkeywords={Accessibility,, Location Choice,, Resiliency},
colorlinks=true,
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\title{A utility-based approach to modeling systemic resilience of
highway networks with an application in Utah}
\author[1*]{Gregory S. Macfarlane}%
\affil[1*]{
Brigham Young University, Civil and Construction Engineering
Department;
Email: gregmacfarlane@byu.edu
; Corresponding author}
\author[2]{Max Barnes}%
\affil[2]{
Kimley-Horn;
Email: maxbarnes@kha.com
}
\author[3]{Natalie M. Gray}%
\affil[3]{
WSP;
Email: nat.gray2000@gmail.com
}
\NameTag{Macfarlane, \today}
\begin{document}
\maketitle
\begin{abstract}
The resilience of transportation networks is an important consideration
in policy, management and planning, but practical techniques to identify
systemically critical links are limited. Further, current practical
techniques ignore that when transportation networks are damaged or
degraded, people potentially change destinations and modes as well as
travel routes. In this research, we develop a model to examine network
highway resilience based on changes to mode and destination choice
logsums, and apply this model to 41 scenarios representing the loss of
links on the statewide highway network in Utah. The results of the
analysis suggest a fundamentally different prioritization scheme than
would be identified solely through a methodology based on increased
travel times. Beyond this, the comparable user costs of the logsum
method are generally lower than those considering only the value of
increased travel times.
\end{abstract}
\KeyWords{Accessibility,Location Choice,Resiliency}
\par
\vspace{1em}
\bookmarksetup{startatroot}
\section{Introduction}\label{intro}
Transportation agencies are tasked with maintaining effective transport
networks connecting a seemingly infinite variety of activities and
destinations. These networks are under constant obvious and non-obvious
threats, while the agencies possess finite resources with which to guard
against the threats. Identifying which facilities in a transportation
network are most \emph{critical} --- which would cause the most
disruption if they were to be degraded --- however, is not trivial.
State of the practice techniques typically rely on traffic volumes
represented in terms of vehicles, trips, or freight value (e.g.
\citeproc{ref-aem2020}{AEM 2020}). But these methods ignore the fact
that some networks have alternate routes readily available, have
multiple well developed modes of transportation, or have redundant
destination locations. When a network link does break, routes, mode
choice, and destination choice often change as well. These responses
have been observed in real-world crisis events like the I-35 W bridge
collapse in Minneapolis and the I-85 bridge fire and collapse in Atlanta
(\citeproc{ref-hamedi2018}{Hamedi et al. 2018};
\citeproc{ref-xie2011}{Xie and Levinson 2011};
\citeproc{ref-zhu2010}{Zhu et al. 2010a};
\citeproc{ref-levinson2010}{b}).
In this research, we apply a destination choice accessibility model to
identify critical highway links in a statewide highway context. This
model is designed to capture the utility lost to individuals operating
on a degraded network who may choose a longer route, a different travel
mode, or a different destination. We then apply the model to a highway
network representing the state of Utah. The model structure permits a
more nuanced evaluation of link criticality than using traffic volume
alone or in conjunction with an increased travel time measure.
The paper proceeds as follows. First, a \hyperref[litreview]{literature
review} discusses previous attempts to identify critical links in
transportation networks. A \hyperref[methodology]{methodology} section
presents the model developed for this research and describes the
implementation process in Utah. A \hyperref[results]{results} section
describes the model output in detail for one scenario and then compares
and ranks the model outputs for an array of several dozen independent
scenarios. The paper \hyperref[conclusion]{concludes} with a discussion
of limitations and associated avenues for future research.
\bookmarksetup{startatroot}
\section{Literature}\label{litreview}
Systemic resilience is an important consideration for transportation
agencies, though specific definitions of ``resilience'' might vary under
different contexts. Some agencies and researchers see resiliency as
facility-level design and engineering that hardens the system against
failure (\citeproc{ref-bradley2007}{Bradley 2007};
\citeproc{ref-peeta2010}{Peeta et al. 2010}); others as an ability for
maintenance staff to rapidly restore service following catastrophe
(\citeproc{ref-zhang2016}{Zhang and Wang 2016}); and others as an
ability for a system to continue operating in degraded state
(\citeproc{ref-berdica2002}{Berdica 2002}; \citeproc{ref-ip2011}{Ip and
Wang 2011}). Regardless of the definition used, assessing the resilience
of a transportation network --- and addressing any potential shortfalls
--- requires a method to identify which links or facilities are most
critical to the smooth operation of the network.
In a groundbreaking theoretical article, Berdica
(\citeproc{ref-berdica2002}{2002}) attempted to identify, define and
conceptualize network ``vulnerability'' --- the complement of resilience
--- by envisioning analyses conducted with several vulnerability
performance measures including travel time, delay, congestion,
serviceability, and accessibility. She then defined vulnerability as the
level of reduced accessibility due to unfavorable operating conditions
on the network. A network vulnerability is therefore a critical link
whose loss would have the largest negative impacts on the people using
the network. In particular, the author identified a need for further
research toward developing a framework capable of investigating
reliability and critical links in transportation networks.
In this section we examine several attempts by numerous researchers to
do precisely this using various measures of network performance. It is
helpful to categorize the existing literature into three groups
(summarized in Table~\ref{tbl-authortable}) based on the overall
technique applied in the study. These groups include:
\begin{itemize}
\item
\emph{Network connectivity}: How does damage to a network diminish the
connectivity between network nodes?
\item
\emph{Travel time analysis}: How much do shortest path travel times
between origins and destinations increase on a damaged network?
\item
\emph{Accessibility analysis} How easily can the population using the
damaged network complete their daily activities?
\end{itemize}
\begin{table}
\caption{\label{tbl-authortable}Attempts to Evaluate Systemic
Resiliency}
\centering{
\centering
\begin{tabular}[t]{rll}
\toprule
Year & Author & Performance Metric\\
\midrule
2004 & Geurs and van Wee & Accessibility (isochrone, gravity, logsum)\\
2006 & Scott et al. & Travel time and cost\\
2007 & Abdel-Rahim et al. & Network Connectivity\\
2008 & Taylor, M & Accessibility (logsum)\\
2010 & Peeta et al. & Travel time and cost\\
\addlinespace
2010 & Geurs et al. & Accessibility (logsum)\\
2010 & Levinson and Zhu & Travel time and cost\\
2010 & Zhu et al. & Travel time and cost\\
2011 & Agarwal et al. & Network connectivity\\
2011 & Ip and Wang & Network connectivity\\
\addlinespace
2011 & Serulle et al. & Travel time and cost\\
2011 & Ibrahim, S & Travel time and cost\\
2011 & Xie and Levinson & Accessibility (isochrone)\\
2012 & Jenelius and Mattson & Travel time and cost\\
2012 & Taylor and Susilawati & Accessibility (gravity)\\
\addlinespace
2013 & Omer et al. & Travel time and cost\\
2014 & Balijepalli and Oppong & Travel time and cost\\
2014 & Osei-Asamoah and Lownes & Network connectivity\\
2014 & Guze & Network connectivity\\
2015 & Zhang et al. & Network connectivity\\
\addlinespace
2015 & Jaller et al. & Travel time and cost\\
2015 & Xu et al. & Network connectivity\\
2016 & Winkler, C. & Accessibility (gravity)\\
2017 & Ganin et al. & Accessibility (gravity)\\
2019 & Vodak et al. & Network connectivity\\
\addlinespace
2019 & Hackl and Adey & Network connectivity\\
2019 & Gecchele et al. & Accessibility (logsum)\\
\bottomrule
\end{tabular}
}
\end{table}%
The purpose of transportation networks is to connect locations to each
other; presumably damage to a network would diminish the network's
\emph{connectivity}, or the number of paths between node pairs. It may
even leave nodes or groups of nodes completely isolated. In studies
using connectivity as the primary performance measure, researchers
typically apply methods and concepts from graph theory. These measures
may include elementary measures such as the isolation of nodes in a
network (\citeproc{ref-abdel2007}{Abdel-Rahim et al. 2007}). More
advanced measures have included heirarchical clustering of node paths
(\citeproc{ref-agarwal2011}{Agarwal et al. 2011};
\citeproc{ref-zhang2015}{Zhang et al. 2015}), a count of independent
paths (\citeproc{ref-vodak2019}{Vodák et al. 2019}), the reduction of
total network capacity (\citeproc{ref-ip2011}{Ip and Wang 2011}), and
special applications of the knapsack and traveling salesman problems
(\citeproc{ref-guze2014}{Guze 2014};
\citeproc{ref-osei2014}{Osei-Asamoah and Lownes 2014}). Though useful
from a theoretical perspective, many of these authors reported that
their approaches tend to break down to some degree on large, real-world
networks where the number of nodes and links numbers in the tens of
thousands, and the degree of connectivity between any arbitrary node
pair is high. They also do not typically account for how network users
may react to the new topology or capacity constraints of the degraded
network.
Highway system network failures --- in most imaginable cases --- degrade
the shortest or least cost path, but typically do not eliminate all
paths. The degree to which travel time increases when a particular link
is damaged, however, could provide an estimate of the criticality of
that link or node. This general method has been used to evaluate
potential choke points in various networks
(\citeproc{ref-berdica2007}{Berdica and Mattsson 2007};
\citeproc{ref-ganin2017}{Ganin et al. 2017};
\citeproc{ref-jaller2015}{Jaller et al. 2015};
\citeproc{ref-jenelius2012}{Jenelius and Mattsson 2012}) as well as the
allocation of emergency resources (\citeproc{ref-peeta2010}{Peeta et al.
2010}). Though many applications only consider the increase in travel
time, some authors consider how the users of the network will respond to
the decreased capacity (\citeproc{ref-balijepalli2014}{Balijepalli and
Oppong 2014}; \citeproc{ref-ibrahim2011}{Ibrahim et al. 2011};
\citeproc{ref-scott2006}{Scott et al. 2006};
\citeproc{ref-serulle2011}{Serulle et al. 2011};
\citeproc{ref-xu2015}{Xu et al. 2015}), and others attempt to model a
shift in departure time or mode (\citeproc{ref-omer2013}{Omer et al.
2013}).
A primary limitation with increased travel time methodologies is that
they ignore other possible ways a population might adapt its travel to a
damaged network. Aside from shifting routes and modes, people may choose
other destinations and it is possible that some previously planned trips
might be canceled entirely. Travel time-based methods do not account for
the costs of these changes in plans, when people select (presumably
worse) activity locations and modes of travel in addition to seeing
their travel costs increase because of the additional travel time. But
accessibility methods --- in particular the accessibility calculations
embedded within many existing regional transport models ---- provide a
framework for evaluating these costs
(\citeproc{ref-ben-akiva1985}{Ben-Akiva and Lerman 1985};
\citeproc{ref-geurs2004}{Geurs and van Wee 2004}).
Accessibility is an abstract concept with multiple methods of
quantification (\citeproc{ref-handy1997}{Handy and Niemeier 1997}).
Perhaps the most popular method is the cumulative opportunities measure:
e.g., the number of jobs within a specified travel time threshold. This
is the method employed by Xie and Levinson
(\citeproc{ref-xie2011}{2011}) in an analysis of the impact of the I-35
W bridge collapse in Minneapolis, and in a theoretical context in
Australia by Taylor and Susilawati (\citeproc{ref-taylor2012}{2012}).
But cumulative opportunities measures require the analyst to assert a
travel time threshold, a mode, and an opportunity of interest. Some of
these assumptions can be relaxed with a gravity-style access model, but
the logsum of a destination choice model has several benefits as an
accessibility term including its grounding in choice framework, ability
to weigh multiple attributes of an alternative, and include travel
impedances by all modes (\citeproc{ref-dong2006}{Dong et al. 2006}).
These measures can even be weighted by a cost coefficient to translate
the lost utility in monetary terms (\citeproc{ref-geurs2010}{Geurs et
al. 2010}; \citeproc{ref-geurs2004}{Geurs and van Wee 2004}).
Logsum-derived accessibility meaures have been used before to evaluate
network resiliency (\citeproc{ref-masiero2012}{Masiero and Maggi 2012};
\citeproc{ref-taylor2008}{Taylor 2008};
\citeproc{ref-winkler2016}{Winkler 2016}). Miller et al.
(\citeproc{ref-miller2015}{2015}) and Gecchele et al.
(\citeproc{ref-gecchele2019}{2019}), for example, each employ an
activity-based model to evaluate the change travel demand related to a
highway link --- implicitly using the log sums of a trip and destination
choice model --- but only evaluate the change in observed choices rather
than the implied costs of those choices at the utility level. But beyond
this, these research efforts have not yet entered the mainstream in
practical application. Though previous researchers have shown that
logsum-derived accessibility measures are feasible and informative,
their use in actual resilience analysis efforts by state departments of
transportation and other relevant agencies appears limited. This limited
practical application is unfortunate, given the important theoretical
steps described to this point.
\bookmarksetup{startatroot}
\section{Methodology}\label{methodology}
In this section we describe a model framework designed to evaluate
resilience using a logit-based choice metric. This framework is heavily
based on tools and methods in existing statewide travel models, with a
few necessary extensions. We then describe the implementation of this
model framework to a prioritization exercise on the Utah Statewide
Travel Model (USTM).
\subsection{Model Design}\label{model-design}
The overall model framework is presented in Fig.~\ref{fig-framework},
and is designed to capture the utility-based accessibility for a
particular origin zone \(i\) and trip purpose \(m\). The model begins
with a travel time skim procedure, to determine the congested travel
time from zone \(i\) to zone \(j\) by auto as well as the shortest
network distance for non-motorized modes. The transit travel time skim
is fixed, assuming that transit infrastructure would not be affected by
changes to the highway network. Throughout this section, lower-cased
index variables \(k\) belong to a set of all indices described by the
corresponding capital letter \(K\).
\begin{figure}
\centering{
\includegraphics[width=1\textwidth,height=\textheight]{03-methods_files/figure-pdf/fig-framework-1.png}
}
\caption{\label{fig-framework}Model framework with feedback cycle. Blue
boxes are calculated after the second feedback loop.}
\end{figure}%
With the travel time \(t_{ijk}\) for all modes \(k \in K\), the model
computes mode choice utility values. The multinomial logit mode choice
model describes the probability of a person at origin \(i\) choosing
mode \(k\) for a trip to destination \(j\):
\begin{equation}\phantomsection\label{eq-mcp}{
\mathcal{P}_{ijm}(k) = \frac{\exp(f(\beta_{m}, t_{ijk}))}{\sum_{K}\exp(f(\beta_{m}, t_{ijk}))}
}\end{equation} The log of the denominator of the this equation is
called the mode choice logsum, \(MCLS_{ijm}\) and is a measure of the
travel cost by all modes, weighted by utility parameters \(\beta_m\)
that may vary by trip purpose.
The \(MCLS\) is then used as a travel impedance term in the multinomial
logit destination choice model, where the probability of a person at
origin \(i\) choosing destination \(j \in J\) is
\begin{equation}\phantomsection\label{eq-dcp}{
\mathcal{P}_{im}(j) = \frac{\exp(f(\gamma_{m}, MCLS_{ijm}, A_j))}{\sum_{J}\exp(f(\gamma_{m}, MCLS_{ijm}, A_j))}
}\end{equation} where \(A_j\) is the attractiveness --- represented in
terms of socioeconomic activity --- of zone \(j\). As with mode choice,
the log of the denominator of this model is the destination choice
logsum, \(DCLS_{im}\). This quantity represents the value access to all
destinations by all modes of travel, and varies by trip purpose.
The \(DCLS_{im}\) measure is relative, but can be compared across
scenarios. The difference between the measures of two scenarios
\begin{equation}\phantomsection\label{eq-deltas}{
\Delta_{im} = DCLS_{im}^{\mathrm{Base}} - DCLS_{im}^{\mathrm{Scenario}}
}\end{equation} provides an estimate of the accessibility lost when
\(t_{ij\mathrm{drive}}\) changes due to a damaged highway link. This
accessibility change is \emph{per trip}, meaning that the total lost
accessibility is \(P_{im} * \Delta_{im}\) where \(P\) is the number of
trip productions at zone \(i\) for purpose \(m\). This measure is given
in units of dimensionless utility, but the mode choice cost coefficient
\(\beta_{\mathrm{cost}}\) provides a conversion factor between utility
and cost. The total financial cost of a damaged link for the entire
region for all trip purposes is
\begin{equation}\phantomsection\label{eq-totalcost}{
\mathrm{Cost} = \sum_{I}\sum_{M} -1 / \beta_{\mathrm{cost},m} * P_{im} \Delta_{im}
}\end{equation}
For comparison to a common method that only includes the increased
travel time between origins and destinations (and not the cost and
opportunities of changing modes and destinations), we compute the change
in congested travel time between \(\delta t_{ij}\) and multiply the
number of trips by this change and a value of time coefficient derived
from the cost and vehicle time coefficients of the mode choice model,
\begin{equation}\phantomsection\label{eq-ttmethod}{
\mathrm{Cost}' = \sum_I \sum_J \sum_M \frac{\beta_{\mathrm{time}, m} }{\beta_{\mathrm{cost}, m}} T_{ijm} \delta t_{ijm}
}\end{equation}
\subsection{Model Implementation in
Utah}\label{model-implementation-in-utah}
The Utah Department of Transportation (UDOT) manages an extensive
highway network consisting of interstate freeways (I-15, I-80, I-70, and
I-84), intraurban expressways along the Wasatch Front, and rural
highways throughout the state. The rugged mountain and canyon topography
throughout the state places severe constraints on possible redundant
paths in the highway network. A landslide or rock fall in any single
canyon may isolate a community or force a redirection of traffic that
could be several hours longer than the preferred route; understanding
which of these many possible choke points is most critical is a key and
ongoing objective of the agency.
Several data elements for the model described above were obtained from
the Utah Statewide Travel Model (USTM). USTM is a trip-based statewide
model that is focused exclusively on long-distance and rural trips:
intraurban trips within existing Metropolitan Planning Organization
(MPO) model regions are pre-loaded onto the USTM highway network. This
means that USTM as currently constituted can be used for infrastructure
planning purposes, but would be inadequate to evaluate the systemic
resiliency of the highway network given the disparate methodologies of
the MPO models. USTM can, however, provide the following data elements
\begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\tightlist
\item
\emph{Highway Network}: including free flow and congested travel
speeds, link length, link capacity estimates, etc.
\item
\emph{Zonal Productions} \(P_{im}\): available for all zones by
purpose, including those in the MPO region areas.
\item
\emph{Zonal Socioeconomic Data}: the destination choice model
described in Eq.~\ref{eq-dcp} calculates attractions \(A_{jm}\) from
the USTM zonal socioeconomic data based on the utility coefficients in
Table~\ref{tbl-coeffs}.
\item
\emph{Calibration Targets}: USTM base scenario estimates of mode split
and trip length were used to calibrate the utility coefficients as
described below.
\end{enumerate}
Among MPO models in Utah, only the model jointly operated by the Wasatch
Front Regional Council (WFRC, Salt Lake area MPO) and the Mountainland
Association of Governments (MAG, Provo area MPO) model includes a
substantive transit forecasting component. The transit travel time skim
from the WFRC / MAG model was used for the mode choice model in
Eq.~\ref{eq-mcp}; the zonal travel time between the smaller WFRC / MAG
model zones was averaged to the larger USTM zones, and the minimum time
among the several modes available (commuter rail, light rail, bus rapid
transit, local bus) was taken as the travel time for a single transit
mode in this implementation.
\begin{table}
\caption{\label{tbl-coeffs}Choice Model Coefficients}
\centering{
\centering
\begin{tabular}[t]{llrrr}
\toprule
& Variable & HBW & HBO & NHB\\
\midrule
\addlinespace[0.3em]
\multicolumn{5}{l}{\textbf{Destination Choice}}\\
\hspace{1em} & Households & 0.0000 & 1.0187 & 0.2077\\
\hspace{1em} & Office Employment & 0.4568 & 0.4032 & 0.2816\\
\hspace{1em} & Other Employment & 1.6827 & 0.4032 & 0.2816\\
\hspace{1em} & Retail Employment & 0.6087 & 3.8138 & 5.1186\\
\hspace{1em} & Distance & -0.0801 & -0.1728 & -0.1157\\
\hspace{1em} & Distance\textasciicircum{}2 & 0.0026 & 0.0034 & 0.0035\\
\hspace{1em} & Distance\textasciicircum{}3 & 0.0000 & 0.0000 & 0.0000\\
\cmidrule{1-5}
\addlinespace[0.3em]
\multicolumn{5}{l}{\textbf{Mode Choice}}\\
\hspace{1em} & Shared & -1.1703 & 0.0164 & -0.0336\\
\hspace{1em} & Transit & -0.3903 & -1.9811 & -2.2714\\
\hspace{1em} & Non-Motorized & -1.2258 & -0.3834 & -0.8655\\
\hspace{1em} & Travel Time [minutes] & -0.0450 & -0.0350 & -0.0400\\
\hspace{1em} & Travel Cost [dollars] & -0.0016 & -0.0016 & -0.0016\\
\hspace{1em} & Walk Distance (less than 1 mile) [miles] & -0.0900 & -0.0700 & -0.0800\\
\hspace{1em} & Walk Distance (1 mile or more) [miles] & -0.1350 & -0.1050 & -0.1200\\
\bottomrule
\end{tabular}
}
\end{table}%
The utility coefficients for the destination and mode choice models are
presented in Table~\ref{tbl-coeffs}. The mode choice coefficients were
adapted from USTM and supplemented with coefficients from the Roanoke
(Virginia) Valley Transportation Planning Organization (RVTPO) travel
model (\citeproc{ref-wang2016}{Virginia Department of Transportation
2016}). This model was selected for its simplicity and analogous data
elements to the proposed model. The alternative-specific constants were
calibrated to regional mode choice targets developed from the 2012 Utah
Household Travel Survey (UHTS) using methods described by Koppelman and
Bhat (\citeproc{ref-koppelman2006}{2006}).
The destination choice utility equation consists of three parts: a size
term, a travel impedance term, and a calibration polynomial.
Coefficients for the size term and travel impedance terms were adapted
from the Oregon Statewide Integrated Model (SWIM)
(\citeproc{ref-donnelly2017}{Donnelly 2017}) for all purposes except
HBW, which coefficients were adapted from the RVTPO model as the SWIM
uses a different methodology for selecting work locations. The distance
polynomial coefficients were calibrated to targets developed from the
2012 UHTS.
\subsubsection{Vulnerable Link
Identification}\label{vulnerable-link-identification}
To develop evaluation scenarios on which to apply the model, we used
information contained in the UDOT Risk Priority Analysis online map
(\citeproc{ref-UDOT2020}{UDOT 2020}). This map considers the probability
of various events that could impact road performance including rock
falls, avalanches, landslides, and other similar occurrences. Using this
tool, combined with information gathered from the research team and UDOT
officials, 41 locations of interest were identified for analysis, at the
locations shown in Fig.~\ref{fig-linksmap}. Each link was identified due
to its location in relation to population centers, remote geographic
location, and proximity to other highway facilities, or because the link
was known to be at risk due to geologic or geographic features, or
because it was a suspected choke point in the network.
\bookmarksetup{startatroot}
\section{Results}\label{sec-results}
In this section we apply the model to scenarios where critical highway
links are removed from the model network. This includes first a detailed
analysis of a single scenario, where I-80 between Salt Lake and Tooele
Counties is severed. We compare the model output to an alternative
method that measures only the change in travel time and does not allow
for mode or destination choice. The model was then applied to 40
additional link closure scenarios throughout the state.
\subsection{Detailed Scenario
Analysis}\label{detailed-scenario-analysis}
To illustrate how the logsum-based model framework captures the costs of
losing a link, we conducted a scenario where I-80 between Tooele and
Salt Lake Counties west of the Salt Lake City International Airport
becomes unavailable. Tooele is a largely rural county with increasing
numbers of residents who commute to jobs in the Salt Lake Valley. I-80
is the only realistic path between the two counties, as alternate routes
involve mountain canyons and many additional miles of travel.
The costs obtained by the logsum and travel time based methods for this
scenario are shown in Table~\ref{tbl-tooeletable}.
Fig.~\ref{fig-tooelemap} presents the lost HBW utility in each TAZ
associated with removing the interstate link between Tooele and Salt
Lake Counties. Multiplying these values by the population in each
production TAZ, summing based on whether the TAZ is inside or outside
Tooele County, and then multiplying by the cost coefficient yields the
HBW values for the Utility Logsum in Table~\ref{tbl-tooeletable}.
In both the logsum and travel time analyses, we separate the costs
spatially, though the definitions of the two are slightly different. In
the logsum-based method, ``Inside Tooele'' are costs associated with
decreased accessibility for trips produced in Tooele County. The
increased costs in this case capture the loss in utility by measuring
increased multi-model travel impedances to destinations with high
attractiveness. In the travel-time method, by contrast, the ``Inside
Tooele'' costs are those for trips with an origin in Tooele County and a
destination in Salt Lake County, and are the increase in travel time
multiplied by a value of time and the number of vehicles making the
trip. The difference in definition is required by the difference in
framework construction.
In general, the logsum-based method arrives at cost estimates that are
less than half of the comparable estimates of the travel time-based
method. This is not unexpected, as the travel time-based method assumes
that all the preexisting trips would still occur, but on a longer path.
The logsum-based method on the other hand attempts to capture the fact
that when a path changes, people may shift their destination or their
mode of travel. To be clear, the framework we have developed for this
exercise does not explicitly model the selection of a new alternative
destination; rather, we calculate instead the value of a destination
choice set before and after the link is removed. But the implication is
that the availability of alternative destinations still provide some
benefit to the choice maker, a proposition that the travel time method
ignores.
\begin{table}
\caption{\label{tbl-tooeletable}Comparison of Logsum-based and
Time-based costs for I-80 at Tooele}
\centering{
\centering
\resizebox{\linewidth}{!}{
\begin{tabular}[t]{lrrrrrr}
\toprule
\multicolumn{1}{c}{ } & \multicolumn{3}{c}{Utility Logsum} & \multicolumn{3}{c}{Travel Time} \\
\cmidrule(l{3pt}r{3pt}){2-4} \cmidrule(l{3pt}r{3pt}){5-7}
Purpose & Other Counties & Inside Tooele & Total & Other Counties & Inside Tooele & Total\\
\midrule
\addlinespace[0.3em]
\multicolumn{7}{l}{\textbf{Passenger}}\\
\hspace{1em}HBO & \$2,637 & \$28,290 & \$30,927 & \$8,595 & \$75,862 & \$84,457\\
\hspace{1em}HBW & \$4,039 & \$113,660 & \$117,699 & \$7,868 & \$234,009 & \$241,877\\
\hspace{1em}NHB & \$2,141 & \$44,911 & \$47,051 & \$5,875 & \$100,245 & \$106,120\\
\addlinespace[0.3em]
\multicolumn{7}{l}{\textbf{External / Freight}}\\
\hspace{1em}Internal Freight & & & & \$24,617 & \$26,083 & \$50,700\\
\hspace{1em}Inbound / Outbound Freight & & & & \$59,758 & \$1,190 & \$60,948\\
\hspace{1em}Recreation & & & & \$176 & \$190 & \$366\\
\hspace{1em}Through Freight & & & & \$251,508 & & \$251,508\\
\hspace{1em}Through Passenger & & & & \$56,103 & & \$56,103\\
Comparable Total & \$8,817 & \$186,860 & \$195,677 & \$22,338 & \$410,116 & \$432,454\\
Total & \$8,817 & \$186,860 & \$195,677 & \$414,499 & \$437,580 & \$852,079\\
\bottomrule
\end{tabular}}
}
\end{table}%
\begin{figure}
\centering{
\includegraphics{04-results_files/figure-pdf/fig-tooelemap-1.pdf}
}
\caption{\label{fig-tooelemap}Tooele county HBW utility loss. Basemap
from OpenStreetMap via Dunnington (\citeproc{ref-ggspatial}{2023}).}
\end{figure}%
Another key element of Table~\ref{tbl-tooeletable} is that the largest
single element of costs in the scenario is associated with through
freight, as well as contributions from other purposes for which the
logsum model developed in this study did not include a corresponding
methodology. This was due to data limitations and the modeling approach
of the existing USTM, but it is obvious that a choice-based framework
for examining the costs of through and inbound / outbound traffic is an
important limitation in this scenario and potentially many others.
\subsection{Prioritization Scenario
Results}\label{prioritization-scenario-results}
We now apply the model to compare 40 additional scenarios where
individual highway facilities are removed from the model highway
network. Fig.~\ref{fig-traveltimerank} presents the logsum and travel
time results for all 41 scenarios, ordered by decreasing logsum costs.
In other words, I-15 at the boundary between Utah and Salt Lake Counties
is the most ``critical'' link analyzed in this exercise as determined by
the logsum method. Were this link to be cut, the people of Utah would
have the highest costs per day in lost destination and travel access of
any other link. Each of the highest-ranking roads in this analysis is an
interstate facility in northern Utah, which is more heavily populated
than the remote areas in the south. A map showing the locations of these
scenarios is given in Fig.~\ref{fig-linksmap}. The concentration of the
highest cost links in the Salt Lake City metropolitan area is obvious,
though the links with the highest cost are not \emph{in} Salt Lake City
where multiple parallel routes exist. Rather, they are in mountain
canyons surrounding the main urban area.
\begin{figure}
\begin{minipage}{\linewidth}
\centering{
\includegraphics{04-results_files/figure-pdf/fig-linksmap-1.pdf}
}
\subcaption{\label{fig-linksmap-1}Statewide}
\end{minipage}%
\newline
\begin{minipage}{\linewidth}
\centering{
\includegraphics{04-results_files/figure-pdf/fig-linksmap-2.pdf}
}
\subcaption{\label{fig-linksmap-2}Wasatch Front}
\end{minipage}%
\caption{\label{fig-linksmap}Total cost of link closure for each
scenario by the logsum method. Basemap from OpenStreetMap via Dunnington
(\citeproc{ref-ggspatial}{2023}).}
\end{figure}%
Perhaps strangely, many scenarios in the analysis show a \emph{benefit}
from loss of the link. Investigating these scenarios showed that for
many paths, the shortest automobile travel time in the complete network
is \emph{not} the shortest path by distance. When the shortest time path
is disrupted, the new shortest time path may be only a few minutes
longer by time but dozens of miles shorter (on a slower road). Because
the automobile operating costs are calculated per mile and not per
minute, this means that the new path actually produces a benefit. This
challenge is exacerbated by the apparent agency practice of placing
artificial time penalties on the network links in some canyons during
calibration. This exercise reveals one reason why such a practice should
be discouraged, and also highlights the importance of using consistent
functions for impedance calculation at all stages of the model.
\begin{figure}
\centering{
\includegraphics{04-results_files/figure-pdf/fig-traveltimerank-1.pdf}
}
\caption{\label{fig-traveltimerank}Scenario results of travel time and
logsum methods in comparison.}
\end{figure}%
Fig.~\ref{fig-traveltimerank} also presents the costs associated with
link closure based on the travel time method for comparable purposes and
also for freight. Many of the most costly scenarios in the logsum model
also appear to be costly in the comparable elements of the travel time
method. That is, the scenario breaking the interstate link between Salt
Lake and Utah counties is the most costly scenario in both methods, and
underscores the significance of this link to Utah's economy and people.
But while many of the largest and most impactful scenarios have similar
rankings and scales, there are also drastic differences between the two
methods down the line. To put it simply, the choice of analysis method
would change the priority that UDOT places on its roads in terms of
preparing for incidents and hardening assets.
\subsection{Sensitivity Analysis}\label{sensitivity-analysis}
A primary limitation of the model framework presented to this point is
that the input parameters used for the mode and destination choice
utilities were gathered from several different sources including a
statewide trip-based model, a statewide activity-based model, and an
urban model for a small region. These models were transferred without a
knowledge of the individual parameter estimation statistics or overall
goodness of fit. How much would the findings presented to this point
change if the parameters in Table~\ref{tbl-coeffs} were to change
modestly?
To examine this possibility, we construct 25 independent draws of the
parameter coefficients using Latin Hypercube Sampling
(\citeproc{ref-helton2003}{Helton and Davis 2003}). The coefficient of
variation for each parameter was assumed to be 0.1; originally, a value
of 0.3 was selected based on the uncertainty research of Zhao and
Kockelman (\citeproc{ref-zhao2002}{2002}), but this resulted in an
unreasonable range of implied values of time in many parameter draws.
Using each of the 25 draws, we ran the base scenario and three
large-impact scenarios and calculated the logsum-based costs.
Fig.~\ref{fig-saplot} presents the estimated monetary costs for each of
these three scenarios under each of the 25 parameter draws. The results
are ordered in the figure by the estimated cost for the highest-impact
scenario. Two observations can be made from this figure. First,
different parameter values do not affect the scenarios uniformly. The
second observation is that despite the within-scenario variation, the
overall scale of the three scenarios is maintained regardless of the
drawn parameter values. Indeed, the three scenarios remain in their
priority ranking across all 25 draws of the choice model parameters. We
therefore do not expect that the selection of parameters is a major
element in the relative ranking of scenarios.
\begin{figure}
\centering{
\includegraphics{04-results_files/figure-pdf/fig-saplot-1.pdf}
}
\caption{\label{fig-saplot}Estimated logsum-based scenario costs in 25
different draws of the choice model parameters.}
\end{figure}%
\bookmarksetup{startatroot}
\section{Limitations and Discussion}\label{limitations-and-discussion}
The issue of systemic resilience to natural and other hazards is an
important question for transportation agencies in the United States and
around the world, given the precarious situation of many of its
transportation assets. Flash floods, rockfalls, avalanches, earthquakes,
and other incidents pose threats to the network of independent
transportation facilities. This research did not consider risk
assessment directly at any level, but rather took as a given that 41
facilities were at some level of risk and played a potentially large
systemic role. A well-conceived approach to systemic resilience should
involve all three elements of resilience: hardening assets from failure
through high-quality engineering and construction; locating maintenance
resources in areas where they can most quickly resolve issues and return
facilities to optimal conditions; and understanding how the system could
work effectively in a damaged or degraded state for medium to long
periods of time if necessary.
This research focused on the systemic criticality of 41 facilities that
were assumed to fail independently. Some of the disaster scenarios most
likely to affect highway facilities -- especially a major earthquake --
are likely to damage multiple highway assets simultaneously. This
research might be extended to consider what would happen if a set of
highway facilities failed; is there a facility that is not critical were
it to fail by itself, but ends up being a critical component of several