ITE Journal – December 2019 - 34

datasets contained 20 percent and 80 percent of the intersections,
respectively. The model was estimated using the training dataset
and evaluated on testing data. A binary variable was used to indicate
the presence of an RLC at signalized intersections. The relationship
between traffic flow and crashes followed a non-linear pattern, which
is commonly used for highway safety models. The spillover effect of
RLC was examined using specially weighted variables.
Table 3 summarizes the modeling results. The term represents
the decay rate of the exponential correlation function. According
to the value of the exponential correlation function parameter,
the spatial dependency between intersections dissipates within 3
kilometers (calculated with equation 5). As expected, the coefficient
of AADT was positive which implies that the more vehicles passing
through the intersection, the more crashes will occur, although at
a decreasing rate. A 1 percent increase in traffic on each lane was
associated with a 0.5 percent increase in the probability of a crash.
The results show that the more lanes are linked to an intersection,
the higher the risk of injury crashes would be. According to the
model, the presence of a median in the minor approach improves
intersection safety by 8 percent. The effectiveness of RLC is shown
by capturing a 6 percent lesser chance of crash for intersections
equipped with a camera, which is in line with the previous study on
same dataset.5 Not only do RLCs improve intersections safety but
also reduces the risk of crash by 2 percent within a 1 kilometer (km)
(.62 miles) network distance. Respectively, the presence of enforcing
cameras with a 2-km (1.24 miles) distance could reduce the crash
occurrence probability by 1 percent (statistically significant at the 10
percent level - posterior value). In spite of observing a statistically
significant effect of the alcohol-serving POI density (in a 1,000
m-buffer) on crash frequency in modeling process, we did not include
this variable to avoid multicollinearity and instead, the variables with
a dominant effect on crashes (intersection AADT) was used.

To find the optimal locations for RLCs across the intersections,
we specified an optimization problem with an objective function
that seeks to maximize the safety benefits of RLC. The objective
function in this problem aims to maximize the reduction in the
total number of injury crashes at intersections as a function of the
RLC location. In addition to the RLC impacts on intersection safety,
the spillover effect of RLC is taken into account. The objective
function was defined as:

Σ (c y l + Σ c y l d
n

c i i

i=1

j=1

-1
s i j i, j

(12)

subject to:
li =
34

{

1
0

if camera located at i
otherwise

D ecem ber 2019

Covariance
Function
Parameters

Process
Model Mean
(μ)

i t e jo u rn al

(13)

Variables

Estimate

0.88

0.53

Variables

Posterior Mean
(Posterior Standard
Deviation)

Intercept

-3.12***
(0.77)

Log of the AADT per lane

0.51 *
(0.14)

Number of lanes linked
the intersection

0.02 *
(0.00)

Median presence in minor -0.08 ***
approach
(0.03)

Goodnessof-Fit

RLC presence

-0.06 **
(0.02)

Inverse distance of RLC to
intersection (1/km)

-0.02 **
(0.00)

MAD

3.15

MPSE

25.41

DIC

1107.61

- Asterisks *, **, and *** correspond with statistical significance levels at 5 percent, 10 percent, and
15 percent, respectively.
- Standard deviations in parenthesis.

lj =

{

1
0

if camera located at j
otherwise

(14)

Σl =R

iЄI

(15)

Σl =R

jЄJ

(16)

i=1

RLC allocation

max

Table 3. Modeling results

j=1

where li and lj indicate whether a camera is located at intersection i and j. The rate of decrease in crash risk after RLC installation
is shown by cc and the spillover effect is cs. yi and yj represent the
injury crash frequencies at the intersections i and j, respectively.
R represents the total number of cameras in the system. For
comparison purposes, the total number of RLC is constrained to 90
(number of cameras in 2010).
We compared the predicted number of injury crashes in
2010-2012 for the optimal distribution of intersections and the
existing locations in 2010 using the proposed model. The optimized
solution yielded to reduce the total number of injury crashes at
intersections. The optimal RLC locations are depicted in Figure 2.
The total number of crashes in the system was reduced by 13 percent
after relocating the cameras. Twenty-four cameras are needed to be

ITE Journal – December 2019

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