Analysis of speed disturbances in empirical single vehicle probe data before traffic breakdown
2017; Institution of Engineering and Technology; Volume: 11; Issue: 9 Linguagem: Inglês
10.1049/iet-its.2016.0315
ISSN1751-9578
AutoresSven‐Eric Molzahn, Boris S. Kerner, Hubert Rehborn, Sergey L. Klenov, Micha Koller,
Tópico(s)Traffic and Road Safety
ResumoIET Intelligent Transport SystemsVolume 11, Issue 9 p. 604-612 Research ArticleFree Access Analysis of speed disturbances in empirical single vehicle probe data before traffic breakdown Sven-Eric Molzahn, Corresponding Author Sven-Eric Molzahn sven-eric.molzahn@daimler.com Daimler AG, HPC: X901, 71063 Sindelfingen, GermanySearch for more papers by this authorBoris S. Kerner, Boris S. Kerner University of Duisburg-Essen, Lotharstr. 1, 47057 Duisburg, GermanySearch for more papers by this authorHubert Rehborn, Hubert Rehborn Daimler AG, HPC: X901, 71063 Sindelfingen, GermanySearch for more papers by this authorSergey L. Klenov, Sergey L. Klenov Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Moscow Region, RussiaSearch for more papers by this authorMicha Koller, Micha Koller Daimler AG, HPC: X901, 71063 Sindelfingen, GermanySearch for more papers by this author Sven-Eric Molzahn, Corresponding Author Sven-Eric Molzahn sven-eric.molzahn@daimler.com Daimler AG, HPC: X901, 71063 Sindelfingen, GermanySearch for more papers by this authorBoris S. Kerner, Boris S. Kerner University of Duisburg-Essen, Lotharstr. 1, 47057 Duisburg, GermanySearch for more papers by this authorHubert Rehborn, Hubert Rehborn Daimler AG, HPC: X901, 71063 Sindelfingen, GermanySearch for more papers by this authorSergey L. Klenov, Sergey L. Klenov Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Moscow Region, RussiaSearch for more papers by this authorMicha Koller, Micha Koller Daimler AG, HPC: X901, 71063 Sindelfingen, GermanySearch for more papers by this author First published: 20 September 2017 https://doi.org/10.1049/iet-its.2016.0315Citations: 11AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract In single vehicle probe data measured on German freeways the authors have revealed free flow→synchronised flow→free flow transitions that occur before traffic breakdown at a bottleneck occurs. Thus resulting in the formation of a congested pattern. The empirical findings of these phase transitions confirm a recent microscopic stochastic theory of traffic breakdown developed by Kerner. Only because of the recently introduced possibility of gathering larger amounts of anonymised vehicle data – including a sequence of positions of each car – the authors are able to show the phenomenon of these phase transitions in measured floating car data. This contribution reveals empirical findings in microscopic data which support and prove some of the recent theoretical findings of the nature of traffic breakdown. 1 Introduction 1.1 Problem background One of the main objectives of intelligent transport systems (ITS) is to prevent or decrease traffic congestion in traffic networks. One of the main problems of the development of ITS that can improve traffic is the lack of understanding of real microscopic features of traffic breakdown at a highway bottleneck. To study microscopic features of traffic breakdown, single vehicle data should be measured. We study the anonymised global positioning system (GPS) data from vehicles driving on the entire road network. The vehicles provide the location data in a five- or ten-second interval which enables precise microscopic reconstruction and analyses of some microscopic empirical features of traffic breakdown at the bottleneck. 1.2 Literature review Two empirical phenomena can be distinguished in highway traffic: (i) traffic breakdown at a bottleneck, i.e. a transition from free flow to congested traffic and (ii) moving jams emergence in congested traffic resulting from the breakdown (see, e.g. references in reviews and books [1-5]). In particular, moving jams (called also freeway traffic oscillations) have been studied empirically in classical works by Koshi et al. [6], Edie et al. [7] and Treiterer [8]. These traffic flow phenomena can be explained in the framework of the classical traffic flow instability introduced in 1958–1961 by Herman et al. [9] and Gazis et al. [10] that leads to the development of a wave of a local speed reduction in free flow (Fig. 1a) (called often as the traffic flow instability of traffic flow models of the General Motors (GM) model class). The empirical characteristic features of moving jam propagation (see references in [4, 5]) have been used in many ITS applications, in particular, for the development of ASDA/FOTO methods (ASDA: A utomatische S taud ynamika nalyse (automatic analysis of traffic jams), FOTO: Fo recasting of t raffic o bjects) for tracing and forecasting of congested traffic patterns [11]. Up to now there are many studies of freeway traffic oscillations (moving jams) in which new microscopic features of the classical traffic flow instability have been found [12-18]. Fig. 1Open in figure viewerPowerPoint Simulations of classic traffic flow instability of Herman et al. [9] and Gazis et al. [10] in free flow in a traffic flow model (a) GM model class (b, c) S→F instability in synchronised flow introduced in Kerner's three-phase theory (adapted from [27]) Users of traffic and transportation networks would expect that through the use of ITS applications free flow can be maintained in the network. This is because due to traffic breakdown congested traffic occurs in which travel time, fuel consumption as well as other travel costs increased considerably in comparison with travel costs in free flow. During the last 30 years significant achievements in a study of empirical features of traffic breakdown and highway capacity have been made, in particular, by Hall and Agyemang-Duah [19], Banks [20], Elefteriadou et al. [21], Persaud et al. [22], and Brilon et al. [23] (see other references in review [1] as well as in a recent book by Elefteriadou [3] and a paper [24]). Nevertheless, traffic breakdown has not been sufficiently studied empirically up to now. In 1996–1999, Kerner found that traffic breakdown in real highway traffic at a highway bottleneck is a phase transition from free flow to synchronised flow (F→S transition) that occurs in a metastable state of free flow with respect to the F→S transition. This means that small enough speed disturbances in free flow at the bottleneck decay; however, when a large enough speed disturbance appears at the bottleneck, traffic breakdown (F→S transition) does occur (for reviews, see [4, 5, 25, 26]). This large enough speed disturbance is called a nucleus for traffic breakdown. Respectively, we can state that empirical traffic breakdown (F→S transition) exhibits the nucleation nature. To explain the empirical nucleation nature of traffic breakdown Kerner has introduced the three-phase traffic theory in which there are three traffic phases: 1. Free flow (F). 2. Synchronised flow (S). 3. Wide moving jam (J) [4, 5, 25, 26]. In Kerner's three-phase traffic theory [4, 5, 25, 26], there are two types of traffic flow instabilities: (i) The instability of synchronised flow with respect to moving jam emergence called an S→J instability. The S→J instability is associated with the classical traffic flow instability of Herman et al. [9] and Gazis et al. [10]. (ii) The instability of synchronised flow with respect to free flow emergence within an initial synchronised flow called an S→F instability. The S→F instability has been introduced in the three-phase theory [4, 5, 25, 26]. The difference between the S→J instability and the S→F instability is as follows: the S→J instability is a growing wave of local speed reduction in synchronised flow leading to moving jam formation in the synchronised flow (Fig. 1a). In contrast, the S→F instability is a growing wave of local speed increase in synchronised flow leading to the formation of free flow (Figs. 1b and c). Recently, Kerner has developed a microscopic theory of the S→F instability [27]. It turns out that the S→F instability governs the nucleation nature of traffic breakdown (F→S transition) at a highway bottleneck. 1.3 F→S→F transitions and S→F instability of three-phase theory In accordance with the three-phase theory, Kerner's S→F instability should govern traffic breakdown (F→S transition) at freeway bottlenecks [27]. In the theory of the S→F instability it has also been found that before the traffic breakdown (F→S transition) occurs with the resulting congested pattern formation, there can be a series of random F→S transitions that are all followed by S→F transitions caused by the S→F instability. The F→S transition with the subsequent S→F transition have been called a sequence of F→S→F transitions in [27]. From the theory of Kerner's F→S→F transitions [27], it follows that only microscopic empirical studies of single vehicle data can show and confirm the F→S→F transitions that have been found in the three-phase traffic theory. Simulations made in [27] show a random time delay before the breakdown ( in Figs. 2a and b). In accordance with [27], the random time delay of the breakdown is associated with the nucleation features of the S→F instability found in numerical simulations (Fig. 2). In particular, it has been found that during the random time period S→F instability can happen and lead to the dissolution of the former F→S transition. At a random time instant an F→S transition occurs that cannot be affected by S→F instability. This F→S transition is traffic breakdown resulting in the formation of a congested traffic pattern at the bottleneck [27]. It is of high interest if these simulated results can be seen in measured traffic data, e.g. by the analyses of vehicle probe data. Fig. 2Open in figure viewerPowerPoint Simulations of Kerner's F→S→F transitions within a permanent speed disturbance at on-ramp bottleneck [27] (a) One of the simulation realisations (b) Fragment of from (a) in a larger scale in space and time; dashed-dotted lines mark regions of dissolving synchronised flow caused by F→S→F transitions (c) Fragment of (b) that shows one of the regions of dissolving synchronised flow (d) Vehicle trajectories related to (c) (e) Arrows F→S and S→F show, respectively, F→S and S→F transitions along with vehicle trajectories labelled by numbers (f) Vehicle trajectories are labelled by using the same numbers as in (e) The theoretical findings of [27] include the microscopic features of sequence of Kerner's F→S→F transitions at a bottleneck, which are as follows. During the time period (Figs. 2a and b) a permanent spatiotemporal competition between the speed adaption effect supporting an F→S transition and the over acceleration effect supporting an S→F instability is observed. These effects result in a permanent average speed decrease in the neighbourhood of the bottleneck that is called 'permanent speed disturbance'. The F→S→F transitions are indicated in Figs. 2c and d as the dash-dotted lines and single trajectories for these transitions are shown in Fig. 2e. In Fig. 2f it has also been indicated where the F→S transition and S→F transition happen leading to the F→S→F transition. 1.4 The objective and outline of this paper Thus, in accordance with the nucleation theory of traffic breakdown of the three-phase theory, F→S→F transitions should determine a random character and random time delay of traffic breakdown [27]. However, up to now Kerner's F→S→F transitions have not been found in empirical data measured in real traffic flow. The empirical findings of the F→S→F transitions are the main objectives of this paper. The paper is organised as follows. In Section 2 we discuss the empirical environment and how the single vehicle data has been collected. In Section 3, microscopic empirical features of F→S→F transitions are presented. A discussion about whether empirical F→S→F transitions can be identified, resolved and studied based on the standard methodology of data measurements with road detectors is made in Section 4. In Section 5 we discuss the possible future ITS-applications of empirical findings of this paper. Conclusions and future research of F→S→F transitions are the subjects of Section 6. 2 Study empirical environment We study empirical F→S→F transitions with the use of single vehicle data measured by probe vehicles in traffic flow. 2.1 Problem of study of F→S→F transitions based on empirical single vehicle data Handheld personal navigations devices and factory-installed navigation devices in vehicles allow microscopic gathering and analysis of GPS data for a big fleet of vehicles. Probably a first analysis of randomly distributed anonymised probe vehicle data that has confirmed the existence of three distinct traffic phases with the traffic breakdown being an F→S transition of the three-phase theory [4, 5] has been done in [28]. However, in [28] the share of randomly distributed probe vehicles has been only about or less than (mean time distance between cars has been about 10 min). With it has not been possible to reconstruct the traffic dynamics in space and time with an accuracy that is sufficient to observe F→S→F transitions. Empirical data available from the next generation simulation (NGSIM) dataset [29] is not suitable for this particular investigation due to the limited distance covered on the road with this data. Moreover, the transition from free flow to synchronised flow (traffic breakdown) cannot be observed in the compiled NGSIM data for highway traffic [29]. There are two main features of the data used for this work in comparison with known data up to now: (i) In contrast with NGSIM data for highway traffic [29], traffic breakdown (F→S transition) can be observed in real traffic. (ii) In contrast with data of [28] in which the mean time distance between cars has been about 10 min, in our single vehicle data a time distance throughout the examined time span 25 s on average between cars has been observed. With this data we show empirically Kerner's F→S→F transitions [27] that emerge before the traffic breakdown. 2.2 Features of empirical single vehicle data used in the paper The data was collected from a large fleet of connected vehicles of more than 1 million cars in Europe. To find and analyse the F→S→F transitions in empirical data made, we have chosen the German Autobahn A8 south of Stuttgart on a 10 km distance from the off-ramp 'Moehringen' to the interchange Stuttgart (Fig. 3). The data is anonymously gathered by means of a vehicle backend that the fleet vehicles are permanently connected to while driving. The data used was collected from a fleet of connected vehicles measured on 7 December 2015 and 15 December 2015 during rush hours. Fig. 3Open in figure viewerPowerPoint Examined freeway section with on- and off-ramps and the automatic release of the hard shoulder One of the unique characteristics of this segment is the automatic release of the hard shoulder in-between these two junctions. In the case of high traffic density the hard shoulder can be released for vehicles resulting in a four-lane freeway. Due to the many vehicles leaving the freeway A8 at 30.7 km at off-ramp Stuttgart, there are many lane changes and overtaking manoeuvres shortly upstream. At about 29.3 km in Fig. 3 the effective location of the bottleneck at which traffic breakdown occurs usually in real traffic data is marked. In a probe vehicle, GPS locations are measured and stored in a 5 or 10 s interval. The vehicle computer builds 'pearl chain' of 2 min time length that contains the GPS locations with related timestamps (e.g. for 10 s data, there are 12 'pearls' in the pearl chain). The 'pearl chains' are sent to the vehicle backend. The backend server calculates the speed of the probe vehicle along each of the pearl chains. After the map-matching process trajectories of individual vehicles for this particular section are extracted. The map-matching was done with an optimised process and the trajectory data is then stored in a relational database. Extracting the data is based on an on road network and is done via link ids for particular road sections. This allows us for a precise extraction of any street regardless of functional road class and length. The analyses and plotting were mainly done with python scripts using build in libraries, functions and plotting library matplotlib. Errors of collected data GPS data are mostly related to the error in determination of the GPS vehicle position. This error is <10 m. Therefore, for 10 s interval data the error in the speed is <2 m/s. Thus, this error does not prevent to resolve free flow from synchronised flow, i.e. to resolve F→S transitions and S→F transitions along vehicle trajectories. F→S transitions and S→F transitions along vehicle trajectories have been determined through the use of the procedure explained in detail in Section 4 of [28]. 3 Microscopic empirical features of F→S→F transitions before traffic breakdown For the empirical studies of the microscopic feature of traffic breakdown, trajectories for the observed freeway section have been extracted and analysed. Fig. 4a shows vehicle trajectories from 'Moehringen' to 'Stuttgart' on a 5 km span. The time interval in the shown section between two cars is on average 54 s. The effective location of the bottleneck at which traffic breakdown has occurred at time instant about 06:46am is labelled by 'Bottleneck'. Fig. 4Open in figure viewerPowerPoint Real empirical single vehicle data on a typical weekday (data was measured on 15 December 2015) (a) Vehicle trajectories in space and time in which only parts of vehicle trajectories with the vehicular speed that is <85 km/h are shown; bottleneck is labelled by horizontal dashed line 'Bottleneck' (b) Subset of data within a time interval marked in (a) as (A) (c–i) Microscopic vehicle speeds over time along vehicle trajectories in (b); vehicle trajectories are marked by the same numbers in (b) and (c–i). Arrows F→S and S→F in (e) and (f) are related, respectively, to F→S and S→F transitions on vehicle trajectories In the three-phase theory [4, 5], during the time delay of traffic breakdown ( in Figs. 2a and b) a permanent spatiotemporal competition between the driver speed adaption effect supporting an F→S transition and the driver over acceleration effect supporting an S→F instability have been found [27]. In empirical single vehicle data studied, we have found the following traffic phenomena: Fig. 4b shows a subset of the trajectories of Fig. 4a with a time interval before traffic breakdown has occurred. To illustrate speed disturbances before traffic breakdown has occurred, only parts of vehicle trajectories with a vehicular speed <85 km/h are shown in Fig. 4a. Single vehicle trajectories shown in Fig. 4b have been extracted (Figs. 4c –i) that show the following traffic phenomenon: vehicle 4 is driving at a constant velocity and passes the bottleneck with no disturbance. As vehicle 6 approaches the effective location of the bottleneck (about 4 min after vehicle 4, the driver has to reduce the speed of the vehicle (as marked symbolically as F→S in Fig. 4d). The same behaviour can be seen for vehicles 12, 13 and 16. While vehicle 12 does not experience a drop in velocity, but an S→F transition, vehicle 13 shows a drop in velocity. Thus, we observe a sequence of F→S→F transitions. The F→S→F transitions prevent traffic breakdown with the subsequent development of a congested traffic pattern at the bottleneck. Due to F→S→F transitions, a region of dissolving synchronised flow appears that has been labelled by dashed-dotted lines in Fig. 4b. This is in accordance with the theoretical findings of Kerner [27] (see dashed-dotted lines in Figs. 2b –d). Qualitatively the same empirical F→S→F transitions occur in this data once more later as shown in Fig. 5. Sequences of F→S→F transitions, just before breakdown has occurred, are indicated by the dash-dotted lines in Figs. 5a and b. The microscopic vehicle speed on trajectories show the characteristic features of sequences of F→S→F transitions with the disturbance and speed increase at the bottleneck preventing the development of a congested flow pattern (these transitions are shown as dash-dotted lines in Figs. 5a and b. The upstream and downstream fronts of these regions of empirical dissolving synchronised flow are very similar to the theoretical findings presented by the dash-dotted lines in Figs. 2b and d. As in theory (Fig. 2b), our empirical data shows that such sequences of F→S→F transitions continue as time progresses up until a certain point where no S→F transition can be observed that could be able to destroy a former F→S transition. This results in traffic breakdown (F→S transition) at the bottleneck with resulting congested pattern formation (Fig. 5b). In this case, the congested pattern is a widening synchronised flow pattern (WSP) (Figs. 4a and 5b). As seen in Fig. 5a (cut-out from Fig. 4a for a time interval labelled by (B)) the same section as previously described is shown at a later time between 06:40am and 07:20am. The traffic breakdown occurs at roughly 06:56am clearly seen in Fig. 5b by means of the localised downstream front of synchronised flow at the bottleneck. Fig. 5Open in figure viewerPowerPoint Continuation of Fig. 4 (data measured on 15 December 2015) (a) Vehicle trajectories in space and time; subset of data within a time interval marked in Fig. 4a as (B) (b) Same data as in (a), however, only parts of vehicle trajectories with the vehicular speed that is <85 km/h are shown (c–g) Microscopic vehicle speeds over time along vehicle trajectories in (a); vehicle trajectories are marked by the same numbers in (a) and (c–g). Arrows F→S and S→F in (e) and (f) are related, respectively, to F→S and S→F transitions on vehicle trajectories We have observed the same phenomenon of the F→S→F transitions occurring before traffic breakdown on several days and briefly illustrate results of these observations for data measured on 7 December 2015 on the same freeway section (Figs. 6 and 7). On 7 December 2015 traffic breakdown has occurred at 06:28am (Fig. 6a). Empirical F→S→F transitions that occur before traffic breakdown (Figs. 6 and 7) exhibit qualitatively the same empirical features as those discussed for 15 December 2015 (Figs. 4 and 5). Fig. 6Open in figure viewerPowerPoint Real empirical single vehicle data on a second typical weekday (7 December 2015) (a) Vehicle trajectories in space and time in which only parts of vehicle trajectories with a vehicular speed <85 km/h are shown; bottleneck is labelled by horizontal dashed line 'Bottleneck' (b) Subset of vehicle trajectories within a time interval marked in (a) as (A) (c–g) Microscopic vehicle speeds over time along vehicle trajectories in (b); vehicle trajectories are marked by the same numbers in (b) and (c–g). Arrows F→S and S→F in (e) and (f) are related, respectively, to F→S and S→F transitions on vehicle trajectories Fig. 7Open in figure viewerPowerPoint Continuation of Fig. 6 (data measured on 7 December 2015) (a) Subset of vehicle trajectories within a time interval marked in Fig. 6a as (A) (b) Same vehicle trajectories as in (a), however, only parts of vehicle trajectories with a vehicular speed <85 km/h are shown (c–g) Microscopic vehicle speeds over time along vehicle trajectories in (b); arrows F → S and S → F are related, respectively, to F → S and S → F transitions along vehicle trajectories In Figs. 6c –g, vehicles 2 and 4 experience disturbances where the driver has to brake. In contrast, following cars (vehicles 6 and 7) do not experience any disturbance but pass the bottleneck at a nearly constant speed. Vehicle 13 on the other hand does experience a significant drop in speed. Empirical F→S→F transitions found here lead also to a region of dissolving synchronised flow marked by dashed-dotted lines in Fig. 6b. Qualitatively the same phenomena of empirical F→S→F transitions leading to a region of dissolving synchronised flow occur also later in this data set (Fig. 7). Two different sequences empirical F→S→F transitions leading to associated regions of dissolving synchronised flow have been marked by dashed-dotted lines in Figs. 7a and b. An example of empirical F→S→F transitions is shown in Figs. 7c –g. Vehicle 7 experiences a significant drop in speed to a degree that an F→S transition happens. On the other hand, vehicle 36 (Fig. 7g) does not have to brake in order to pass the bottleneck but rather drives with little to no disturbance: this means that F→S→F transitions occur. The occurrence of a bottleneck leading to traffic breakdown shown in Figs. 6 and 7 can be explained as follows: traffic flow is heavily influenced by the layout of the freeway and the automatic release of the hard shoulder. As seen in Fig. 4 right after the release of the shoulder, the off-ramp 'Stuttgart' begins. Vehicles that want to stay on the A8 are driving on the hard shoulder need to merge on the left lane, while vehicles driving to Stuttgart city either stay on the hard shoulder or merge from one of the three left lanes onto the off-ramp lane. The effective location of the bottleneck is, therefore, located at about 29 km where most of the lane changes happen. It should be noted that the distribution of these speeds presented in Figs. 4-7 can show more meanings about traffic. However, such a study is out of scope of this paper in which we limit a study of empirical F→S→F transitions only. In accordance with simulations made in [27], Kerner's F→S→F transitions are random phase transitions. This means that both the time instant of a F→S transition and the time instant of a return S→F transition within F→S→F transitions and, therefore, the duration of the dissolving synchronised flow resulting are random events. In simulations (Fig. 2b), the mean time interval between the F→S transition and return S→F transition is several minutes. The mean time interval depends on flow rates and the bottleneck [25]. In empirical data, the time interval between the F→S transition and return S→F transition in F→S→F transitions is of the same order of magnitude as in the theory [27]. Moreover, in the data sets the time instant of an F→S transition and the time instant of a return S→F transition within F→S→F transitions seem to be random values (see totally different time intervals between sequences of empirical F→S→F transitions in Figs. 4-7). However, we still have not enough data for different days and types of bottlenecks to study statistical (probabilistic) characteristics of empirical F→S→F transitions. 4 Single probe vehicle data versus vehicle detector data for empirical study of F→S→F transitions Traffic breakdown has usually been studied with the use of road detectors installed in a neighbourhood at a bottleneck (see reviews and books [1, 3-6] as well as recent papers [19-24, 28, 30]). In [29], measurements both of road detectors and single-vehicle probe data have been used. It turns out that if the mean time distance between probe vehicles is large (about 10 min in [28]), then there is no considerable benefit of the use of single vehicle data in comparison with detector data. The situation changes drastically when the mean time distance between probe vehicles decreases considerably (Figs. 5-8). This is because the probe vehicles provide the speed as a function of time and space whereas detectors measure the time function of the speed at detector locations only. Therefore, the information about the speed distribution between detector locations is lost through detector measurements. When traffic breakdown with the resulting congested pattern formation is studied, as made in [1, 3-6, 19-24, 28, 30], road detector measurements are sufficient to detect the breakdown at the bottleneck as well as to study the most important features of traffic breakdown (see the book [26]). However, F→S→F transitions are a fine spatiotemporal effect occurring within a relatively short road stretch (about 1–3 km) during several minutes (about 3–10 min). For this reason, it is very difficult to resolve and to study F→S→F transitions with the use of detector data only. Fig. 8Open in figure viewerPowerPoint Single probe vehicle data versus vehicle detector data for empirical study of F→S→F transitions (a, b) Vehicle trajectories and time-dependence of the 1 min averaged speed at two detector locations with the use of probe vehicle data measured on 15 December 2015 (see Figs. 4 and 5); road locations of detectors and are 29.25 and 28 km, respectively (c, d) Vehicle trajectories and time-dependence of the 1 min averaged speed at two detector locations with the use of probe vehicle data measured on 7 December 2015 (see Figs. 6 and 7). In (a, d), dashed-dotted lines mark regions of dissolving synchronised flow caused by F→S→F transitions This is illustrated in Fig. 8, in which we have used two virtual road detectors and that measure the time function of the 1 min averaged speed of probe vehicles passing detector locations (measurements of the average speed of all vehicles with road detectors are not available for the highway section under consideration, Fig. 3). Probe vehicle data provides information about the regions of dissolving synchronised flow occurring through F→S→F transitions (dashed-dotted regions in Figs. 8a and d). In contrast with probe vehicle data, this fine microscopic spatiotemporal structure of the speed distribution in space and time is considerably lost through measurements with road detectors. Although we can see an indication about the appearance of a short-time synchronised flow at detectors and in Figs. 8b and c and detector in Fig. 8f. However, we cannot make a clear statement about the spatial distribution of the synchronised flow. This is because the information about the speed distribution of synchronised flow on the road that vehicle trajectories of probe vehicles exhibit is lost between detector locations when measurements are made through the use of road detectors only. For this reason, no clear empirical proof of the F→S→F transitions can be made through measurements with road detectors. There is, however, an advantage of measurements with detector data in comparison with our approach, in which single vehicle data of probe vehicles have been studied only: a road detector measures the flow rate. In contrast, single vehicle data of probe vehicles that are currently available do not allow us to find the flow rate. The flow rate could give more information about the empirical features of F→S→F transitions. Thus, empirical studies of single vehicle data of probe vehicles together with detector data could be very interesting for future empirical investigations of F→S→F transitions. 5 Possible ITS applications of empirical findings The empirical findings of F→S→F transitions of this paper can be useful for future ITS applications, especially for traffic control. One aim of future control methods that take into account the empirical features of F→S→F transitions could be to suppress local traffic disturbances or even to prevent the development of traffic breakdown at a highway bottleneck. Further application can be found in the regulation of automated and autonomous vehicles: with an adapted trajectory planning and driving strategy such vehicles can be used to influence and govern the traffic breakdown. 6 Conclusions Based on an analysis of single vehicle probe data measured on German freeways, we have found empirical F→S→F transitions occurring before traffic breakdown at the bottleneck. Empirical data shows during a relatively long time interval before traffic breakdown occurs at the bottleneck many local regions of synchronised flow appear (F→S transition) which follows by an S→F transition. The empirical F→S→F transitions lead to the emergence of local regions of synchronised flow (due to F→S transition) propagating upstream that dissolves over time (due to a subsequent S→F transition). This phenomenon leads to regions of dissolving synchronised flow looking as similar triangles of space and time (regions of dissolving synchronised flow are labelled by dashed-dotted lines in Figs. 5-8). The empirical phenomena of the occurrence of F→S→F transitions with the formation of regions of dissolving synchronised flow revealed in this article prove the empirical evidence of Kerner's F→S→F transitions found recently in the three-phase theory [27]. Future empirical works include a study of probabilistic features of the F→S→F transitions in empirical data. 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