Figure 9.1: Evolution in average speed on Hillerødmotorvejen on Wednesday 28-02-2007
9.3 Results
9.3.1 Example: the aggregated travel times
Figure 9.2 shows the aggregated travel times for motorway segment 10051006 for a number of Mondays from October 2006 to March 2007. Days with miss-ing values in the examined time interval have been discarded. The aggregated travel times fluctuate quite considerably over very short periods of time. This is mainly due to the fact that traffic is processed in a ”stop-go” manner, meaning that localized queuing of short duration occurs very often. Furthermore, the ag-gregated travel times are not true travel times per se, but are rather the results of an aggregation - first, an accumulation of values of speed for all cars passing between two detectors over a period of 60 seconds; second, an aggregation of the accumulated values of speed across detectors and subsequently across cross sections. Both are a cause for considerable variations in speed which, in turn, is reflected in the aggregated travel times.
Figure 9.2: Aggregated travel times for different Mondays - motorway segment 10051006
9.3.2 Smoothing
The very stochastic nature of the aggregated travel time data could make the modeling process ineffective and in the worst case scenario, impact on the accu-racy of the forecasts to an extent that would render them useless for the end user.
To remedy this problem, it was decided to apply a simple moving average func-tion, even if this would probably result in the loss of information. The purpose for this is to diminish the erratic minute-to-minute fluctuations in the aggre-gated travel times, which in overall terms have little significance, and allow the major trends in traffic flow to be made more visible. Erratic minute-to-minute fluctuations in the aggregated travel times were also deemed unacceptable by the Road Directorate in that these times would also be reported to the pub-lic through the website. The interpretation of minute-to-minute variations in the travel times would be confusing for the ordinary user. The fluctuations reflect the variations in cross section speed, not in segment travel time. Due to these reasons, a 10-minute moving average function was applied. For exam-ple, the calculation for travel time at time 06:45:00 consists of the average of travel times from 10 consecutive minutes preceding and including time point 06:45:00. This number is scientifically unsubstantiated per se; however, the inspection of the aggregated travel times, 1-minute (1 minute preceding and including the current travel time), 5-minute (5 minutes preceding and including the current travel time) and 10-minute moving average travel times indicated that the best results were obtained by choosing the 10-minute moving average
9.3 Results 41
window function. The 1-minute and 5-minute moving average travel times were too responsive to the recent variations in the aggregated travel times, with the result that the minute-to-minute fluctuations in the travel times were still quite substantial. The 10-minute moving average function seemed to produce the desired results. A larger smoothing interval, however, would give a mislead-ing picture of the current travel time times as it, from a theoretical viewpoint, would produce a more pronounced lag in the smoothed sequence. It can be dis-cussed whether the proposed smoothing interval is already too large. This has, however, not been tested out in practice. Figure 9.3,9.4 and9.5 show the ag-gregated travel times after application of the 1-minute, 5-minute and 10-minute moving average function. It can be seen in Figure 9.5 that the course of the traffic flow is now illustrated more clearly. A number of traffic flow patterns have emerged, suggesting that the traffic flow might be grouped into a number of clusters. The disadvantage of using this smoothing technique is that all
Figure 9.3: 1 - minute moving average travel time data for a number of Mondays - motorway segment 10051006
past observations are given the same weight, in which case, the resulting travel times might be downright misleading, especially as the size of the smoothing interval gets bigger. This applies also for congestion build-up and phase-out.
Other smoothing techniques could have been used to diminish the fluctuations in the aggregated travel time values, such as the weighted moving average or the exponential smoothing functions. Both give more weight to recent observa-tions and less weight to older observaobserva-tions [13]. However, these funcobserva-tions are only useful when there are trends. And there are no well-defined trends in the
Figure 9.4: 5 - minute moving average travel time data for a number of Mondays - motorway segment 10051006
Figure 9.5: 10 - minute moving average travel time data for a number of Mon-days - motorway segment 10051006
evolution in the aggregated travel times per se. Visual inspection of Figure9.2 supports this claim. The aggregated travel times shift considerably throughout the rush hour period, even during congestion build-up and phase-out.
9.3 Results 43
9.3.3 Application of the aggregated travel time data
As a starting point, the aggregated travel times can be used to form a general view of the traffic patterns that govern the examined motorway segment. The 15-minute forecast model developed in connection with the extension of the M3 motorway assumed that the traffic followed a weekly pattern, which meant that the traffic pattern on any Monday morning resembled those of the other Mondays; the traffic pattern on any Tuesday morning resembled those of the other Tuesdays etc [3]. It is of interest to find out whether this assumption also applies to this motorway segment. Examination of the 10-min moving average travel times from October 2006 though March 2007 immediately disproves this assumption, as shown in Figure 9.6.
Figure 9.6: 10-min moving average travel times for motorway segment 100510006. Mondays: blue lines, Tuesdays: green lines, Wednesdays: red lines, Thursdays: light blue lines, Fridays: pink lines
It can be seen that congestion build-up intervals range from 07:15:00 and 07:30:00 and congestion phase-out intervals range from 09:00:00 to 09:30:00. The 10-minute moving average travel times range on average from 8 10-minutes up to 14 minutes. Some days reach peak travel times that are as high as 18 minutes. The travel time on the majority of days is, however, around 8 minutes. It can be concluded that the travel times do not follow a distinct weekly pattern, but are rather governed by the location of congestion build-up, the length of the rush hour, the travel times and the location of congestion phase-out.