02-literature.qmd

# Literature {#litreview}

```{r setup, file = "R/chapter_start.R", include = FALSE, cache = FALSE}
# a number of commands need to run at the beginning of each chapter. This
# includes loading libraries that I always use, as well as options for 
# displaying numbers and text.
library(readxl)
```

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 [@bradley2007; @peeta2010];
others as an ability for maintenance staff to rapidly restore service following
catastrophe [@zhang2016]; and others as an ability for a system to continue
operating in degraded state [@berdica2002; @ip2011]. 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, @berdica2002 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
@tbl-authortable) based on the overall technique applied in the study. These
groups include:

-   *Network connectivity*: How does damage to a network diminish the
    connectivity between network nodes?

-   *Travel time analysis*: How much do shortest path travel times between
    origins and destinations increase on a damaged network?

-   *Accessibility analysis* How easily can the population using the damaged
    network complete their daily activities?

```{r authortable, echo = FALSE, cache = FALSE}
#| label: tbl-authortable
#| tbl-cap: Attempts to Evaluate Systemic Resiliency
readxl::read_xlsx("images/author_summary.xlsx") %>%
  kbl(booktabs = TRUE) %>%
  kable_styling()
```

The purpose of transportation networks is to connect locations to each other;
presumably damage to a network would diminish the network's *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 [@abdel2007]. More advanced measures have included
heirarchical clustering of node paths [@agarwal2011; @zhang2015], a count of
independent paths [@vodak2019], the reduction of total network capacity
[@ip2011], and special applications of the knapsack and traveling salesman
problems [@guze2014; @osei2014]. 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 [@berdica2007; @jenelius2012; @jaller2015; @ganin2017] as well as the
allocation of emergency resources [@peeta2010]. 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 [@scott2006; @ibrahim2011;
@balijepalli2014; @serulle2011; @xu2015], and others attempt to model a shift in
departure time or mode [@omer2013].

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 [@ben-akiva1985;
@geurs2004].

Accessibility is an abstract concept with multiple methods of quantification
[@handy1997]. 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 @xie2011 in an analysis of the impact of the I-35 W
bridge collapse in Minneapolis, and in a theoretical context in Australia by
@taylor2012. 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
[@dong2006]. These measures can even be weighted by a cost coefficient to
translate the lost utility in monetary terms [@geurs2004; @geurs2010].

Logsum-derived accessibility meaures have been used before to evaluate network
resiliency [@taylor2008; @masiero2012; @winkler2016]. @miller2015 and
@gecchele2019, 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.