Evaluación y análisis de la información

As mentioned earlier, the general framework of the algorithm to identify some phase change points, such as SRST and RST, were adopted with some enhancements from the earlier algorithm developed by Kwon [2]. Also, another type of phase change points, such as PSR and NPR were newly added by enhancing in defining phases in the speed variations during snow events. The enhancement efforts on the existing algorithm will be described in this section. It will be introduced in the order of the process of algorithm, i.e., SRST, NPR, RST, and PSR. It should be mentioned that LST remained same with the previous algorithm.

SRST (Speed Reduction Starting Time)

The algorithm to find SRST was enhanced by employing the dry normal speed variations to compare with the snow-affected patterns, while the existing pattern only examine the snow-affected pattern itself. The enhancement allows to distinguish the normal traffic variations due to the traffic congestion from the speed reduction resulted by the snow precipitations. The step-by-step is as followings:

Step i) Retrieve the smoothed speed variations both of snow event and dry-normal day.

Step ii) Starting from the snow event start time to the snow event end time plus 8hrs, find the point where the snow-affected speed deviates the dry-normal speed for n time intervals (n = 20), i.e., the first point which after Equation 14 remain true to determine it as SRST.

𝑈_𝑑𝑟𝑦− 𝑈_{𝑠𝑛𝑜𝑤} > 0

Equation 14

Step iii) If none of points were found satisfying Equation 14, find the first point of speed reduction in the quantized speed variations.

Step iv) Refine the point by searching back the smoothed speed to find the first point to start speed reduction.

NPR (Normal Pattern Recovery Time)

For the similar reasons with SRST, the process to identify NPR employs the corresponding dry-normal speed variations in identifying NPR. The step-by-step to identify NPR is as following:

Step i) Retrieve the smoothed speed variations both of snow event and dry-normal day.

Step ii) Starting from SRST to the end of data (8 hours after the snow event end time), find the point where the snow-affected speed returns to the dry-normal speed even one time interval, i.e., the point where Equation 15 satisfies.

𝑈𝑑𝑟𝑦− 𝑈𝑠𝑛𝑜𝑤 = 0

Equation 15

Figure 50: Flow Chart of Identification of NPR

RST (Recovery Starting Time)

RST is defined as the point which after the speed starts to increase continuously until reaching NPR. The previous algorithm locate the RST at the point where the lowest speed starts to increase significantly. The enhanced algorithm assumed that the speed variations can experience the significant speed reduction due to the recurring snow precipitations. In such cases, RST does not necessarily found near the LST, but more reasonable to identify it at the lastly located starting point of speed increase.

The automatic process to identify RST was designed to find the lastly located significant speed reduction before the dry-normal speed is recovered. The detail step-by- step is as followings:

Step i) To determine the range of RST, examine if the traffic is congested during road recovery period using Equation 16.

𝑈𝑠𝑛𝑜𝑤(𝑆𝑅𝑆𝑇) − 𝑈𝑠𝑛𝑜𝑤(𝑡) ≥ 𝛼 𝑚𝑝ℎ (𝑤ℎ𝑒𝑟𝑒 𝛼 = 30)

Equation 16

Step ii) If traffic is uncongested, the boundary of RST is determined as from LST to NPR. If traffic is congested, the boundary of RST is determined as from LST to the congestion starting time.

Step iii) Starting from LST, identify if speed turns to decrease in the quantized speed variations using Equation 17.

𝑈𝑞𝑢𝑎𝑛𝑡(𝑡 − 1) − 𝑈𝑞𝑢𝑎𝑛𝑡(𝑡) ≤ 0

Equation 17

Step iv) If speed reduction is identified in Step (iii), determine if speed reduction amount is significant in the smoothed speed variations. If the speed reduction amount is greater than the pre-determined threshold, define the lowest speed point as RST which after the speed continue to increase to NPR.

Step v) If none of significant speed reduction is found within the boundary of RST, define LST as RST.

The process for identifying the congestion starting point is as follows:

Step i) Identify if traffic is congested by determining if speed was reduced up to 𝞪 mph (𝞪=30) after snow event ended.

Step ii) If traffic is assumed congested, find the minimum speed point after snow event ended.

Step iii) Starting from the minimum speed point, search back the speed variations to find the starting point where after speed continuously decreases to define it as “Congestion Starting Point.”

Figure 51: Flow Chart of Identification of RST

PSR (Posted Speed Limit Recovery Time)

PSR defines the point where the speed reaches the posted speed limit of the current snow section. PST was newly identified in this study with the need to locate the point where

the traffic flow recovers the minimum level of stability, which the traffic system operators are interested in. The automatic algorithm is as following:

Step i) Starting from RST to the end of traffic data, find the point where the speed reaches the level of Posted speed limit – 𝞪 mph (𝞪=3) to identify it as PSR. The threshold of 𝞪 was given to allow flexibility in determining the desired time.

5.4. Development of a Process for Identifying the Newly Identified Phase Change