ITE Journal - July 2021 - 44

the stop bar). Since the intersection approach is assumed to be
under-saturated, the vehicle approaching the intersection is passing
through it within the same cycle.
Step 2 - Critical Points Extraction and State Identification
As introduced earlier, eight traffic states are considered in this study.
They are plotted in the space time diagram in Figure 1 below. A shock
wave (i.e., dash lines in Figure 1) separates one state from its next
state in traffic flow; and a critical point indicates the changing point
between states for each vehicle's trajectory. In the previous research
on vehicle trajectory, the critical point extraction is based on speed
and acceleration.20
However, speed and acceleration are sensitive to
change in driving. For instance, when a driver slightly accelerates
during a deceleration process, such change in acceleration may cause
a false critical point extraction. To overcome such difficulty in critical
point extraction from vehicle trajectory data, previous literature
added thresholds or ranges around identified critical point for verification.
For instance, Cheng et al. introduced a method to identify
the data points representing the changes in vehicle dynamics by
establishing thresholds on speed, and acceleration to extract critical
points.20
The authors adopted a similar approach in this study.
Figure 2. A schematic diagram of the Fundamental Diagram formed by
shock waves at a signalized intersection.
to compare the estimated fundamental diagram with the one
built from (assumed) ground truth values (i.e., outputs from link
performance evaluation in VISSIM).
In order to obtain the individual vehicle's trajectory, a signalized
intersection located between Kensington Avenue and Bailey Avenue
in Buffalo, NY, USA is coded in VISSIM as shown in Figure 3.
The traffic counts for this signalized intersection are in Table 1
and were based on PM peak (5:00 p.m. to 6:00 p.m.) provided by the
Modern Traffic Analytics and Greater Buffalo Niagara Regional Transportation
Council through the open-source Traffic Count Database
System. The intersection was with a ν/c ratio of 0.76 for the northbound
approach of the intersection. The intersection implemented a
two-phase pre-timed signal timing plan with permitted left turns.
The cycle length was set at 80 seconds. The green time for Kensington
Avenue (minor street) was 28 seconds, and 42 seconds for Bailey
Avenue (major street). The yellow and all-red intervals were 3 seconds
and 2 seconds. The timing plan was recorded from a field study.
With this established VISSIM simulation network, a composition
Figure 1. Eight traffic states at a signalized intersection identified by CV
trajectory data.
Step 3 - Shock Wave Formation and Structure Formation of FD
After extracting critical points and identifying traffic states, backward
forming shock wave (ωBE
recovery shock wave (ωGB
), frontal stationary shock wave (ωB
), and forward forming shock waves (ωF
ωH, ωC, ωG, ωE) are illustrated by different colors in Figure 2.
Simulation Design
The proposed method in this study was then evaluated using CV
trajectory data generated with VISSIM. This allowed the authors
44 July 2021 ite journal
,
of regular vehicles and CV in different MPRs (i.e., 10% and 100%)
Table 1. Volume Inputs of Kensington Ave. & Bailey Ave.
Number of Vehicle (veh)
), backward
, ωA
Duration
5:00-5:15 p.m.
5:15-5:30 p.m.
5:30-5:45 p.m.
5:45-6:00 p.m.
139
164
146
137
94
83
118
81
223
224
188
191
82
65
82
69
Northbound
Eastbound
Southbound
Westbound

ITE Journal - July 2021

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