In this section, the sensor-based assessment of traffic flows and travel times are shown in the first subsection. The second subsection presents the estimation results of the proposed MLR models and compares performances with the defined performance metrics.
6.1. Traffic State Representation and Sensor-Based Assessment
The traffic flow results are derived by determining the vehicle counts from (a) the installed thermal cameras (b) the detected vehicles from the ALPR algorithm, and (c) the empirical measurement, i.e., the ground-truth data set. Note that the Google Distance Matrix does not allow the derivation of traffic flow. We derive all data sets and calculate the 10 min moving average of all time series
–
, i.e., the window size
.
Figure 5a,b present the derived flow time series
and
for all data sets. In addition,
Figure 5c denotes the matching rate of the ALPR algorithm. The matching rate is calculated by the fraction of detected vehicles by ALPR and the actually vehicle count from the ground-truth data set.
A comparison
and
of the ground-truth (in gray) and the data from the thermal cameras (in blue) T4 and T1 show a high correlation between the time series. Only small deviations of the thermal cameras’ detection are noticeable. A quantitative analysis of the correlation coefficient
and the
show a coefficient result of 0.91 and an error rate of 4.83% for
and
,
for
(
Table 1). Further, the ALPR results are depicted in orange. The ALPR algorithm shows a good fit for
until the flow drops around timestamp 17:00 significantly. This can also be seen in the matching rate of C1 that drops below 50%. After 17:30, the performance increases again with a matching rate around 70% to 75%. The average matching rate of C1 is 70%,
, and
(
Table 1).
For
, the ALPR shows a lower performance compared to
. Several significant deviations from the ground-truth data can be observed throughout the investigated period. The matching rate of C2 shows an average rate of 59%. Nevertheless, it is observed that the matching rate around 17:30 is below 10%. The error metrics show a performance of
, and
.
Figure 6 depicts the results for all data sources of
and
, respectively.
Again, a good fit of
’s ground-truth data and the thermal camera data from T3 can be observed (
,
). The ALPR results show significant deviations from the ground truth over time. Especially around 16:20, a drop in the flow is observed. In addition, from 16:45 until 17:30, deviations are observed and are supported by the matching rate (
Figure 6c) dropping below 50%. The average matching rate is calculated with 59%,
, and
.
Figure 6b shows a high deviation from the ground-truth of the data set derived from T3. No correlation between the ground-truth and the thermal camera data is determined, i.e.,
and
. The reason for the high deviation is that T3 observes both traffic directions with one camera. Due to the high lane width (two lanes for individual transport and two additional lanes for public transportation), T3 cannot observe the traffic flow in this direction. A re-positioning of the camera or installing a second thermal camera could help improve the results. The ALPR shows a correlation of
and
. The average matching rate is calculated with 76%. The performance metrics are collected in
Table 1.
Figure 7 shows the results for
and
.
The thermal cameras of T4 and T1 show good results for
and
. Note that two thermal cameras are installed due to a tram line between the two traffic lanes. For the flow
, the correlation
and
; for
,
and
. The ALPR algorithm shows deviations for both quantities. For
, the average matching rate is 70%,
and
. The results for
show decreased ALPR algorithm performance over time. An inspection of the ground-truth video material showed that this is caused by increasing light reflections over time. The average detection rate is equal to 57%,
and
. Again, the quantitative results are collected in
Table 1.
The travel time results are derived by determining the timestamp when a vehicle enters and exits the system. As data sources (a) the installed thermal cameras, (b) the detected license plates from the ALPR algorithm (c) tracked data from the Google Distance Matrix API, and (d) the empirical measurement, i.e., the ground-truth data set are used. We derive all travel time data sets and calculate the 10 min weighted moving average (the window size ) of the routes , , , and ; consequently, , , , and . Note that for and , the ground-truth data set showed low traffic volume (7 and 19 vehicles for the measurement period, respectively). Thus, data gaps occur, and a comparison of different data sources would not lead to a representative result. Therefore, these two routes are excluded from the analysis.
Figure 8a,b presents the derived travel time series
and
for all data sets. The travel time results for
and
are depicted in
Figure 8c,d.
The performance metrics are compiled in
Table 2. One can note that the quantity
increases over time, peaks around 17:45, and decreases again afterward. Results computed from the ALPR detections (orange time series) replicate this trend with small deviations. The time series correlate with
and an
. Contrary results are shown by the set of thermal cameras T2 and T3 that are utilized for travel time derivation of
. The time series only shows small variations and does not capture the trend of the ground-truth data (
). Potential reasons for the modest performance can be (a) a low penetration rate, i.e., a small number of WiFi devices are detected, or (b) the data are strongly post-processed. The time series computed from the Google Distance Matrix API shows a higher variance than the thermal camera data and fails to show the variation of the ground-truth data. Especially around 17:30, when travel time continues to rise, the Google Data (green time series) does not react to this system behavior. The correlation with the ground-truth results in
and the
. The results show a similar trend for the travel time results of
. The ALPR results replicate the ground-truth data with some small over- and underestimations. Nevertheless, one can note a data gap from 17:30 to 17:45, where no vehicles were detected. This results in a correlation of
and
. Again the time series of the thermal camera data and the Google Distance Matrix API under- and overestimate the travel time, respectively. Both methods do not allow a reaction to a travel time change from, e.g., 180 sec to 250 sec at 16:45, as the peak is not covered. Additionally, the Google data does not show any variance, i.e., the standard deviation is zero. This also does not allow the determination of a correlation coefficient. Hence,
Table 2 denotes such observations with ’NA’. For the thermal camera data, the computed performance metrics are
, and for the Google data
. For
, similar results as for
are derived. The ALPR algorithm allows the derivation of travel times that show a good fit to the ground-truth (
,
), and the thermal camera data and Google data under- and overestimate the travel time with performance metrics of
and
,
, respectively. For the travel times on
, i.e.,
, the ALPR algorithm allows an accurate representation of the ground-truth data with
and
. The thermal camera data shows a correlation of
with an
and the Google data allows the computation of
and
.