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Comparing Speed Data from Stationary Detectors Against Floating-Car Data⁎
15th IFAC Symposium on Control in Transportation Systems 15th IFAC Symposium on Control in Transportation Systems JuneIFAC 6-8, 2018. Savona,on Italy 15th Symposium Control in Transportation Systems June 6-8, 2018. Savona, Italy Available online at www.sciencedirect.com 15th Symposium Control in Transportation Systems JuneIFAC 6-8, 2018. Savona,on Italy June 6-8, 2018. Savona, Italy
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IFAC PapersOnLine 51-9 (2018) 299–304
Comparing Speed Data from Stationary Comparing Speed Data from Stationary Comparing Speed Data from Stationary Detectors Against Floating-Car Data Comparing Speed Data from Stationary Detectors Against Floating-Car Data Detectors Against Floating-Car Data Detectors Against Floating-Car Data Lisa Kessler ∗∗ Gerhard Huber ∗∗ Arne Kesting ∗∗ ∗∗
Lisa Kessler ∗∗ Gerhard Huber ∗∗ Arne Kesting ∗∗ ∗ Bogenberger Lisa Kessler ∗ Klaus Gerhard Huber ∗ Arne Kesting ∗∗ ∗ ∗ Klaus Bogenberger ∗ Lisa Kessler Klaus Gerhard Huber Arne Kesting ∗∗ Bogenberger ∗ Klaus Bogenberger ∗ ∗ ∗ Munich University of the Federal Armed Forces, Germany of the Federal Armed Forces, Germany ∗ Munich University (e-mail: Munich University of [email protected]) the Federal Armed Forces, Germany ∗ ∗∗ (e-mail: Munich University of [email protected]) the Federal Armed Forces, Germany TomTom Development Germany [email protected]) ∗∗ ∗∗ (e-mail: [email protected]) Development Germany ∗∗ (e-mail: TomTom Development Germany ∗∗ TomTom Development Germany Abstract: This paper compares speed data measured by induction loops of stationary detectors Abstract: This paper compares speed data measured by induction loops of stationary detectors with reported speeds floating-car data,measured which arebybased on most recent GPS observations Abstract: This paperfrom compares speed data induction loops of stationary detectors with reported speeds from floating-car data,measured which arebybased on most recent GPS observations Abstract: This paper compares speed data induction loops of stationary detectors of probe vehicles. Detector data are aggregated over aa one minute time interval and that means with reported speeds from floating-car data, which are based on most recent GPS observations of probe vehicles. Detector data are aggregated over one minute time interval and that means with speeds floating-car data, which based on most recent GPS observations a 30 sreported delay occurs on from average. delay issues respect to floating-car data aremeans quite of probe vehicles. Detector dataThe are time aggregated overare awith one minute time interval and that a 30 s delay occurs on average. The time delay issues with respect to floating-car data are quite of probe vehicles. Detector dataThe are aggregated over awith one respect minute time interval and that means with many influences: (i) the update frequencies from vehicles to the backend server, aconvoluted 30 s delay occurs on average. time delay issues to floating-car data are quite (i)time the update frequencies from vehicles to the backend convoluted with many influences: a 30the s delay occurs average. The delay issues withflow, respect to floating-car datatreatment. areserver, quite (ii) fleetwith sizemany ofon floating cars, (iii)the theupdate current traffic and (iv) the convoluted influences: (i) frequencies from vehicles to provider the backend server, (ii) the fleet size of floating cars, (iii) the current traffic flow, and (iv) the provider treatment. convoluted with many influences: (i) the update frequencies from vehicles to provider the length backend server, The floating-car dataset has a high spatial resolution with an average segment of 100 (ii) the fleet size of floating cars, (iii) the current traffic flow, and (iv) the treatment. Thethe floating-car dataset has a high spatial resolution with an and average segment length of 100 m m (ii) fleet size dataset of floating (iii) theand current traffic flow, (iv) segment the provider treatment. suited for large-scale traffic observation management. The spatial dimension of detector The floating-car has cars, a high spatial resolution with an average length of 100 m suited for large-scale traffic observation and management. The spatial dimension of detector The has observation a high spatial resolution with an average segment length 100 m data floating-car can be dataset reconstructed ex-post from spotty positions (mean detector positions distance suited foronly large-scale traffic and management. The spatial dimension of of detector data can only be reconstructed ex-post from spotty positionsThe (mean detector positions distance suited for large-scale traffic observation and management. spatial dimension of detector approx. 1.3 km). data can1.3 only be reconstructed ex-post from spotty positions (mean detector positions distance approx. km). data can1.3 only be reconstructed ex-post from spotty positions (mean detecting detector positions distance The paper analyzes which approx. km). The paper analyzes which source source is is more more advantageous advantageous in in terms terms of of detecting traffic traffic jams, jams, high high approx. 1.3 km). temporal of detector data or advantageous detailed spatial resolution of floating-car data.high An The paperavailability analyzes which source is more in terms of detecting traffic jams, temporal availability of detector data or detailed spatial resolution of floating-car data. An The paperavailability which source is more advantageous in terms of detecting traffic jams, high algorithm isanalyzes presented compute the orjam detection duration, which means we are able to temporal oftodetector data detailed spatial resolution of floating-car data. An detection duration, which we aredata. ableAn to algorithm is presentedoftodetector compute the orjam temporal availability data detailed spatial resolution of means floating-car recognize which data source detects the earliest. The results demonstrate that there exist algorithm is presented to compute the jam detection duration, which means we are able to recognize which data source detects the jam earliest. The results demonstrate that there exist algorithm is presented to compute the jam detection duration, which means we are able to regions along certain road stretches where floating-car data clearly outperform stationary data. recognize which data source detects the jam earliest. The results demonstrate that there exist regions along certain road stretches where floating-car dataresults clearlydemonstrate outperform stationary data. recognize which data source detects the jam earliest. The that there exist However, in regions detectorswhere are densely placed,data stationary sensor data stationary recognize adata. jam regions along certainwhere road stretches floating-car clearly outperform However, in regions where detectorswhere are densely placed,data stationary sensor data stationary recognize a jam regions certain road stretches floating-car clearly situationalong approx. 2 min earlier than floating-car based data. outperform However, in regions where detectors are densely placed,speed stationary sensor data recognize adata. jam situation approx. 2 min earlier than floating-car based speed data. sensor data recognize a jam However, in regions where detectors are densely placed, stationary The cover a of 80 days for driving situation approx. 2 min earlier based speed data. directions The datasets datasets cover a period period ofthan 80 floating-car days in in 2015 2015 for both both driving directions on on the the German German situation approx. 2 min earlier than floating-car based speed data. directions autobahn A9 in the north of Munich. The datasets cover a period of 80 days in 2015 for both driving on the German autobahn A9 in the north of Munich. The datasets cover a period of 80 days in 2015 for both driving directions on the German autobahn A9 in the north of Munich. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. autobahn A9 in the north of Munich. Keywords: Information displays/system, Automotive sensors and actuators, Navigation, Keywords: Information displays/system, Automotive sensors and actuators, Navigation, System integration and displays/system, supervision, Floating-car data, Inductive detector data, Speed Keywords: Information Automotive sensors and loop actuators, Navigation, System integration and displays/system, supervision, Floating-car data, Inductive detector data, Speed Keywords: Information Automotive sensors and loop actuators, Navigation, measurements System integration and supervision, Floating-car data, Inductive loop detector data, Speed measurements System integration and supervision, Floating-car data, Inductive loop detector data, Speed measurements measurements 1. These 1. INTRODUCTION INTRODUCTION These two two approaches, approaches, stationary stationary and and floating-car floating-car based based traffic measurements, be compared towards different 1. INTRODUCTION These two approaches,can stationary and floating-car based traffic measurements, can be compared towards different 1. INTRODUCTION These two stationary and floating-car based data,approaches, e.g. speedcan values. Stationary counted traftraffic measurements, be compared towards different Traffic data measurements from stationary devices have data, e.g. speedcan values. Stationary counted trafTraffic data measurements from stationary devices have traffic traffic measurements, be compared towards different fic data have the advantage of registering every passing traffic data, e.g. speed values. Stationary counted trafplayed adata dominant role in traffic over the last Traffic measurements fromobservations stationary devices have fic datadata, havee.g. the speed advantage of Stationary registering every passing over the last played a dominant role in traffic observations traffic values. counted trafTraffic measurements from stationary devices have vehicle frequency) but with aa low spatial data (number have theand advantage of registering every passing decades. In recent years, measurements derived played adata dominant role inspeed traffic observations over thefrom last fic vehicle (number and frequency) but with low spatial decades. In recent years, speed measurements derived from fic data have the advantage of registering every passing played dominant role inspeed traffic observations over thefrom last vehicle availability. The amount of floating-car data a(FCD) obser(number and frequency) but with low spatial frequenta In uploads GPS datameasurements from probe vehicles have decades. recent of years, derived The amount of floating-car data a(FCD) obserfrequent In uploads of GPSspeed datameasurements from probe vehicles have availability. vehicle andthe frequency) with low spatial decades. recent of years, derived from vations (number depends on number ofbut passing This availability. The amount of floating-car data vehicles. (FCD) obserbecome a serious alternative to the infrastructural-based frequent uploads GPS data from probe vehicles have vations depends on the number of passing vehicles. This become a serious alternative to the infrastructural-based availability. The amount of floating-car data vehicles. (FCD) obserfrequent of GPS data probe vehicles have becomes and more with sample vations depends on more the number of irrelevant passing This approachauploads for traffic monitoring. Traffic observation with limitation become serious alternative to from the infrastructural-based limitation becomes more and more irrelevant with sample approach for traffic monitoring. Traffic observation with vations depends on the number of passing vehicles. This become a for serious alternative to whole the infrastructural-based rates of some percent of the volume. addibecomes more andtotal moretraffic irrelevant withIn sample floating cars istraffic possible over the road network while approach monitoring. Traffic observation with limitation rates of some percent of the total traffic volume. In addifloating cars is possible over the whole road network while limitation becomes more and more irrelevant with sample approach forage monitoring. Trafficroad observation with rates tion, the main advantage is of of some of the totalscalability traffic volume. In addithe average of the speedthe observations used in traffic floating cars istraffic possible over whole network while tion, the mainpercent advantage is the the scalability of floating-car floating-car the average age of the over speedthe observations used in traffic rates of some percent ofcan the total trafficwherever volume. In addifloating cars is possible whole road used network while based technology: data be collected traffic tion, the main advantage is the scalability of floating-car services depends on both the probe sample and the total the average age of the speed observations in traffic technology: data canisbe collected wherever traffic is is services depends onthe both the probe sampleused and in thetraffic total based tion, the mainallows advantage the scalability ofnetwork-wide floating-car the average age of speed observations flowing. This for new applications in based technology: data can be collected wherever traffic is traffic flow. services depends on both the probe sample and the total flowing. This allows for new applications in network-wide traffic flow. based technology: data can be collected wherever traffic is services depends on both the probe sample and the total traffic monitoring and management applications. flowing. This allows for new applications in network-wide traffic flow. traffic monitoring and management applications. flowing. This allows for new applications in network-wide Nowadays, all traffic providers like TomTom, Google, Intraffic flow. all traffic providers like TomTom, Google, In- traffic monitoring and management applications. Nowadays, aspect the time both trafficmain monitoring and applications. rix, and Here floating-car technology on a big Nowadays, all use traffic providers based like TomTom, Google, In- One One main aspect is is themanagement time delay delay of of both measurement measurement rix, and Here use floating-car based technology on a big Nowadays, all traffic providers like TomTom, Google, Inapproaches to capture the current real-world traffic One main aspect is the time delay of both measurement scaleand to offer ‘live’ or ‘real-time’ traffic services re- approaches to capture the current real-world rix, Hereso-called use floating-car based technology on a big traffic sitsitscaleand to offer so-called ‘live’ or ‘real-time’ traffic services re- One main aspect is the timestate delayestimation of both measurement rix, Hereso-called use floating-car based technology onspeeds. a big uation. FCD-based traffic depends on approaches to capture the current real-world traffic sitporting delays for detected traffic incidents or link scale to offer ‘live’ or ‘real-time’ traffic services reuation. FCD-based traffic state estimation depends on porting delays for detected traffic incidents or link speeds. to capture the current real-world traffic sitscale to offer so-called ‘live’ or ‘real-time’ traffic services re- approaches the rate of observations, which, in turn, depends on the uation. FCD-based traffic state estimation depends on This data-driven technology is established itself as stateporting delays for detected traffic incidents or link speeds. the rate of observations, which, in turn, depends on the This data-driven technology is established itself as stateuation. trafficwhich, state inestimation depends on porting delays for technology detected traffic incidents or linkasspeeds. penetration rate of probe vehicles and on the traffic rate FCD-based of observations, turn, depends onflow. the of-the-art for routing applications. With increasing per- the This data-driven is established itself statepenetration rate of probe vehicles and on the traffic flow. of-the-art for routing applications. With increasing per- the rate of detector observations, which, in turn, depends onflow. the This data-driven technology is established itself as stateStationary data (SDD) can be used for spatial penetration rate of probe vehicles and on the traffic centage of for probe vehicles, this technology becomes more of-the-art routing applications. With increasing per- Stationary detector data (SDD) can be used for spatial centage of for probe vehicles, this technology becomes more rate ofwhen probe vehicles andbe ondetectors the traffic flow. of-the-art routing applications. With increasing per- penetration speed estimations double-loop not Stationary detector datathe (SDD) can used for are spatial and more also for traffic management applicacentage of attractive probe vehicles, this technology becomes more speed estimations when the double-loop detectors are not and more attractive also for traffic management applicaStationary detector data (SDD) can be used for spatial centage of probe vehicles, this technology becomes more too far apart. On the considered autobahn A9 the mean estimations when the double-loop detectors are not tions.more attractive also for traffic management applica- speed and too far apart. On the considered autobahn A9 the mean tions. speed the double-loop detectors not and distance of detector is just 1.3 Therefarestimations apart. On when thecross-sections considered autobahn A9km. theare mean tions.more attractive also for traffic management applica- too distance of detector cross-sections is just 1.3 km. Theretoo apart. On thecan considered autobahn A9km. theTheremean tions. fore,far detector speeds be considered as benchmark. On distance of detector cross-sections is just 1.3 This work was supported by the German Federal Ministry for the This work was supported by the German Federal Ministry for the fore, detector speeds can be considered as benchmark. On distance of detector cross-sections is just 1.3be km.theTherea road with less detectors the contrary could case. fore, detector speeds can be considered as benchmark. On Environment, Nature Conservation, Building and Nuclear Safety. This work was supported by the German Federal Ministry for the a road with less detectors the contrary could be the case. Environment, Nature Conservation, Building and Nuclear Safety. fore, detector speeds can bethe considered benchmark. On a road with less detectors contrary as could be the case. This work was supported by the German Ministry for the Environment, Nature Conservation, BuildingFederal and Nuclear Safety. a road with less detectors the contrary could be the case. Environment, Nature Conservation, Building and Nuclear Safety.
2405-8963 © © 2018 2018, IFAC IFAC (International Federation of Automatic Control) Copyright 299 Hosting by Elsevier Ltd. All rights reserved. Copyright © under 2018 IFAC 299 Control. Peer review responsibility of International Federation of Automatic Copyright © 2018 IFAC 299 10.1016/j.ifacol.2018.07.049 Copyright © 2018 IFAC 299
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The main disadvantage of SDD are the high installation and maintenance costs, therefore the infrastructural-based measurement technology remains limited to just a few corridors. It is obvious that floating-car based technology does not require any measurement infrastructure except the telecommunication network. This paper is structured as follows. After the state of the art the datasets of SDD and of FCD are described in sec. 3. Section 4 treats the question which of both data sources detects a jam event earlier. An algorithm to find reliable congestion cluster matchings and the results of the analysis are presented. Finally, a conclusion and an outlook on further research are given. 2. STATE OF THE ART
(lat, long) = (48.1787, 11.5955)) and triangle Holledau (at (48.5841, 11.5801)). Data are available for both driving directions, in northbound direction (NB) comprising 47.7 km, in southbound direction (SB) 31.4 km. Data are collected within April to June 2015 (80 days). The A9 is one of Germany’s most used freeways. In 2013, more than 150, 000 vehicles per day have been counted on average at interchange Munich-Nord for both directions (ABDSB (2017)). This freeway is equipped with variable message signs and the shoulder is in part-time use. The number of lanes is typically 3 − 4 in each direction. Together with the part-time use of hard shoulder the number of available lanes goes up to 5. 3.2 Stationary Detector Data
In literature many studies investigate up to which degree broadcasted traffic information is able to mirror real traffic situations accurately. Some of these studies focus on specific aspects of traffic information services such as the latency with which traffic related incidents are reported. In Rainer (2011), it is stated that for traffic messages broadcasted in Austria, via the traffic message channel, the average time of delay was about 10 min. In Kim and Coifman (2014) traffic information provided by Inrix is assessed. The results of this analysis indicate that the reported Inrix speeds tended to lag those stationary detector data by almost 6 min on average. The authors of Rakha et al. (2013) also assess Inrix data and compare them to stationary sensor data but rather focus on travel time and travel time reliability. Other studies such as Bogenberger (2003), Bogenberger and Hauschild (2009), Lux (2011), Rehborn et al. (2011), Huber et al. (2014) discuss quality of traffic information via indices (see Bogenberger and Weikl (2012) for an overview of these studies). The fundamental idea of all these approaches is to interpret ‘quality’ as the level of similarity between the broadcasted traffic information and a ground truth representing the real traffic situation adequately. It is either generated by tracking test vehicles (Bogenberger and Hauschild (2009), Lux (2011)) or by applying traffic state reconstruction methods on the basis of stationary detector data (Bogenberger (2003), Rehborn et al. (2011), Huber et al. (2014)). Those approaches significantly differ from the idea presented here and in our preceding work (Kessler et al. (2018)) where neither the detector data nor the floating-car data are considered as a reference. Furthermore, jam event messages are compared directly and without regarding one of the sources as ground truth. Both types of data show strengths and weaknesses when being compared to each other. One of the central objectives of the described research is to identify these strengths and weaknesses in order to obtain a comprehensive understanding which of the data types are suited for which purposes. 3. DESCRIPTION OF THE DATA 3.1 Test Site: Autobahn A9, Germany The following analysis considers autobahn A9 in the north of Munich between intersection Munich-Schwabing (at 300
Stationary detector data (SDD) are available from 33 (NB) respectively 27 (SB) cross-sections. The inductive double-loop detectors allow for direct speed measurements. Aggregated data have a resolution of one minute. The flowweighted mean speed over all car and truck lanes is given as one combined speed data value per minute. The average distance of 1.3 km between cross-sections allows for interpolating the time-series data. For this purpose, the Adaptive Smoothing Method (ASM) (Treiber and Helbing (2002), Treiber et al. (2011)) has been applied to derive (smoothed) speed values also for the space between detector positions. The ASM algorithm uses two smoothing kernels, one for free-flow conditions with a downstream propagation and another one for congested flow in upstream direction. Both kernels are weighted combined depending on the speed. The spatiotemporal smoothing kernels interpolate spatially between detector positions but also in time at one detector position. Therefore, ASM compensates for gaps in the original time series (Fig. 1), for example due to a system break down.
Fig. 1. SDD time series at location 494.84 km (NB) for April 1. In the night hours speed = 0 is provided at some minutes due to no vehicles passing in those minutes (flow = 0 ⇒ speed = 0). Note that smoothing preserves the jam fronts during the morning peak. Since the ASM interpolation uses forward and backward times at different locations this method can only be applied in a post-processing analysis (ex-post), in contrast to FCD. See table 1 for used ASM parameters.
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Table 1. ASM parameters used for smoothing the detector data Parameter Spatial grid distance Temporal grid distance Speed in congestion Free-flow speed Crossover from free to congested traffic Width of the transition region
301
single probe measurement is known (determined by the upload frequency (typically 1-3 min) and the time needed for the map-matching process (in general a few seconds)). Since the reported speed is based on several latest probe observations, the average age may vary. Here, the focus is on delays in capturing speeds due to the underlying data collection methodology. For a better comparison, SDD have also been capped above the TomTom free-flow speed values.
value 100 m 30 s -18 km/h 80 km/h 70 km/h 10 km/h
3.3 TomTom Speed Data TomTom offers a product called TomTom Flow, which is a live data feed reporting current speeds for links in the road network with a time update of 1 min. The level of spatial resolution can be customized. The dataset used in this academic study uses a link aggregation defined by segments with an average link length of about 100 m (maximum of 198 m). The reported speed is calculated in a ‘fusion engine’, which determines a consistent speed for each link in each update cycle from various input sources. The speed estimation is basically driven by a weighted average over the last observations from individual probes plus some blackbox refinements, which are in the scope of data interpretation and control of the provider. The probe speed measurements are derived from mapmatched GPS positions. These floating-car data are a permanent input stream in TomTom’s live processing chain depicted in Fig. 2. Probes Providing GPS Data
Asynchronous Upload (typical frequencies of 1-3 min)
Other Sources than GPS
Fusion Engine: Periodic Updates of 30 sec
Map Matching
Data Delivery: Conversion, Filtering Client Sessions
Data Formats and Feeds
Fig. 2. Processing chain of TomTom’s live traffic service In the dataset, a free-flow speed is provided for each link. This speed is defined by the minimum of the map speed limit and the free-flow speed measured from historic floating-car data. This free-flow speed is used to define an upper bound for the reported speeds. Thus, there is no higher speed in the FCD than the free-flow speed (although individual probe speeds may be higher). 3.4 Combination of Datasets The spatial resolution of FCD is high (100 m on average; traffic information per segment) compared to SDD with typical spacings of 1-3 km between detector positions (traffic information per location point). Therefore, FCD can be plotted directly to illustrate the spatiotemporal traffic dynamics while SDD need to be interpolated for reconstructing the spatiotemporal dynamics in a postprocessing step (ASM data), cf. Fig. 3. The temporal resolution of both datasets is 1 min, which is sufficient for most traffic-management related applications. All times mentioned here are local times (UTC+02:00). The SDD timestamps refer to the end of each 1-minute measurement interval. Subsequently, the aggregated data are 30 s old on average. For a floatingcar based speed measurement method only the age of a 301
Fig. 3. Spatiotemporal speed contour plots from April 30 in NB direction (decreasing kilometrage). Speeds are visualized in different colors. The light green horizontal bars indicate general speed limits of 80 km/h. A qualitative comparison of speed colors in Fig. 3 indicates that both sources report very similar speeds in both freeflow and congested regimes. The FCD contour plot shows the spatiotemporal dynamics at a higher level of detail compared to the situation derived from SDD. For example, the reduced speeds during the night hours at KM 515 (probably a speed limit effective at night) as well as the traffic jam fronts are spatially more precisely pictured in the FCD. The traffic jam at KM 490 (downstream front) is a separate structure in FCD while it becomes conjoined with the congestion pattern at KM 494 due to the interpolation of SDD. 4. PRIMARY CONGESTION DETECTION ANALYSIS In the following, an approach is described to systematically compare which of the data sources allows for detecting
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congestion earlier. The ability to detect emerging traffic congestion promptly is essential for the provision of advance congestion warnings to drivers. FCD profit from not being bound to discrete positions along the considered road corridors. Contrarily, SDD may profit from temporal latencies of FCD due to the data processing. Which of the effects is dominating will be analyzed in the following. The algorithm works in three steps. First single congestion events (‘congestion clusters’) are identified based on SDD as well as on FCD. In a second step, SDD and FCD congestion clusters are associated with each other. The third step comprises the comparison between the temporal starts of the resulting pairs of congestion clusters. Hence, it can be decided on the basis of which data source a congestion warning could have been provided earlier in the respective situation. 4.1 Associating SDD Jams and FCD Jams Let FCD be available for a road corridor X and a time period T . A spatiotemporal speed function vF CD returns the speed value where the FCD are reported for any location x ∈ X and any time t ∈ T . Furthermore, let X be separated into a set of links {Li }i=1,...,I , the spatial resolution of FCD. Similarly, let T be separated into a set of time intervals {Tj }j=1,...,J . Sets {Li } and {Tj } separate the spatiotemporal area X × T into a grid, and function vF CD is constant within each cell Li × Tj of this grid (see part 1 of Fig. 4). Space
1. Speed function 𝒗𝒗𝑭𝑭𝑭𝑭𝑭𝑭 :
2. Identification of congested areas: Space
Cluster A Cluster C
Time
Time
Speed
Jam
𝒗𝒗𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄
3. Trajectory computation: Space
𝒗𝒗𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄
4. Merge clusters: Space
Cluster A
Cluster C
𝑡𝑡𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚
Time
Time
Fig. 4. Computation of congestion clusters for FCD Also let SDD be available for the aforementioned road corridor X and time period T . The detector position locations along X are denoted with x1 , . . . , xD , D ∈ N. A spatiotemporal speed function vSDD returns for any location x ∈ {x1 , . . . , xD } and any time t ∈ T the latest speed value measured by the corresponding detector. Cells of interest for this analysis are only those which contain a speed value below vcrit since they are congested. Two cells Li1 ×Tj1 and Li2 ×Tj2 are denoted as ‘connected’ if the following two conditions hold: 302
i1 ∈ {i2 − 1, i2 , i2 + 1} (1) (2) j1 ∈ {j2 − 1, j2 , j2 + 1} This definition of congestion clusters leads to many very small clusters. Furthermore, it can be observed that these clusters frequently are located closely to each other. In order to achieve a smoothing effect clusters which are located closely to each other are merged into one single cluster. ‘Closely’ means that a driver needs not more than tmerge ∈ R≥0 to get from one cluster to the other. For the merging it is iterated over all clusters located in X × T . For each of these clusters a set of virtual driving trajectories is computed. This set consists of one driving trajectory starting from each corner of a cell belonging to the considered cluster (see part 3 of Fig. 4, illustrated with tmerge = 2 for cluster A). This can be done for some starting point (xS , tS ) ∈ X × T by solving the ordinary differential equation dx = vF CD (x(t), t) (3) dt with initial condition x(tS ) = xS (x as function returning a location in dependency of time). For each virtual trajectory the computation is terminated as soon as time tS + tmerge is reached. All clusters touched by one of the generated trajectories are assigned to the original cluster. This means that all congested cells belonging to one of these clusters to be part of the same cluster (part 4). Congestion clusters are also computed for SDD. Analogously to FCD, jam clusters are identified for detector data. In order to identify one coherent cluster for discrete detector positions, the ASM is again used as the smoothing method. Clusters are found iterating the ASM data applying the methodology described in Fig. 4. For the resulting ASM congestion clusters the jammed times from the original detector data positions x1 , . . . , xD are taken to compare the first congested timestamps instead of the smoothed speed values, again with the threshold vcrit . For all detector positions in the spatial range of one found ASM congestion cluster, the first temporal occurrences are computed and the detector position with the least time value is taken as reference to compare the SDD speeds to the FCD congestion cluster. In order to associate FCD and SDD congestion clusters, it iterates over the set of all congestion clusters. All FCD congestion clusters, which show any intersection with an SDD congestion cluster, are assigned to the SDD cluster with the earliest beginning. However, to reduce the risk of incorrectly matched clusters, the identified pairs of clusters need to fulfill additional conditions: Let CF CD ⊆ X × T denote the spatiotemporal area of an FCD cluster, CSDD ⊆ X × T of an SDD cluster. Furthermore, let | A | denote the size of an area A ⊆ X × T . CF CD can only be assigned to CSDD if they fulfill (4)–(6): | CSDD ∩ CF CD | ≥ Pmin (4) | CSDD | | CSDD ∩ CF CD | ≥ Pmin (5) | CF CD | (6) | CSDD ∩ CF CD | ≥ Amin Pmin ∈ [0, 1] denotes the minimum percentage of the area of the FCD and the SDD cluster that has to be covered by both clusters. Amin ∈ R≥0 denotes the minimum area that
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needs to be covered by the intersection of both clusters. Conditions (4) and (5) ensure that significant parts of clusters are congested according to both data types, (6) ensures that small clusters are ignored. Finally, the earliest time at which a congestion warning could have been made on the basis of FCD is denoted by tmin (CF CD ) with (7) tmin (CF CD ) := min{t ∈ T : t ∈ CF CD }. Time tmin (CSDD ) is defined analogously. Both data sources yield to jam areas with a different level of detail: ASM data result in more coherent clusters due to the smoothing (fewer clusters in total), FCD in more separate small clusters due to the direct measurements (more clusters in total). Therefore, it can happen that one congestion of one source is matched to an area with several congestions of the other source. The algorithm preserves the different number of jam clusters in an 1:n matching, otherwise (4)–(6) would not hold, especially (4) and (5) would yield to wrong first timestamps. The described approach presents one reliable possibility to compare FCD and SDD with regard to their ability to provide advance congestion warnings. One main drawback of the proposed procedure is the high parameter number. However, the findings of the computational analysis indicate that different parameter sets only have little influence. 4.2 Results of Primary Jam Detection Analysis The algorithm described in the previous section has been tested with several parameterizations (vcrit ∈ {40 km/h, 60 km/h}, Pmin ∈ {0.1, 0.3, 0.5}) while tmerge = 4 min and Amin = 2 km·min have been kept constant. The jam clusters have been determined for both FCD and SDD and these clusters have been matched. For a match, the deviation between the start times can be calculated. Figure 6 shows the probability distributions for the time differences tdiff = tmin (CF CD ) − tmin (CSDD ) for all matchable jam events. Median and quartile values are given in the corresponding captions. Negative numbers correspond to a jam cluster detected by FCD first. A positive median value indicates that a jam is detected earlier by the SDD/ASM than the FCD approach (height of bars). Nevertheless, there are more matchings where FCD recognize the jam situation significantly earlier than SDD (positive skew). The balanced statistical results show that both approaches are equally good in detecting matchable traffic jams, i.e., detected by both approaches. The larger the speed limit parameter is chosen, the smaller the deviation. However, FCD are able to find more relevant traffic jam clusters (394 and 472, for vcrit = 40 km/h and vcrit = 60 km/h, respectively) than SDD/ASM (372 and 407). This algorithm finds reliable matchings. Nevertheless, there are examples where the matching fails. In Fig. 5, a spatiotemporal area from April 21 is depicted. The horizontal lines denote the detector positions. The FCD jam section is marked in red, the SDD jam section is marked with bold black lines on the detector position lines. FCD detected a jam situation at 16:12 h, SDD at 16:42 h so the difference amounts to -30 min. Obviously, the detector positions are disadvantageous to detect this jam. 303
Fig. 5. Jam cluster from April 21 (NB), vcrit = 60 km/h 5. SUMMARY AND OUTLOOK In this work, a comparison between floating-car based speed data (FCD) and stationary detector speed data (SDD) is presented. In terms of spatial resolution, FCD outperform SDD since FCD are available over a whole stretch of the road in contrast to isolated detector positions. SDD, as direct speed measurements, outperform FCD in their temporal resolution. The results of a congestion cluster matching show that the speed datasets do not have any systematic bias or shift but are comparable. FCD allow for a spatial traffic monitoring close to real-time whereas detectors only offer observations at few locations. An analysis on which source detects a jam situation first demonstrates that no dataset clearly outperforms the other one. In general, FCD find more (smaller) congestion clusters compared to the smoothed detector data. In regions where detectors are placed densely, SDD benefit from the temporal advantage and differ from FCD by approx. 2 min. In regions between detector positions, FCD outperform SDD (Fig. 5). Generally, the results of the analysis show that the difference between the first occurrences of matched FCD and SDD jams takes larger minima than maxima (absolute values) (Fig. 6). Further research will include the combination of both datasets for recommendations to local authorities. ACKNOWLEDGEMENTS The authors would like to thank Autobahndirektion S¨ udbayern (ABDSB) and TomTom for providing the data. REFERENCES ABDSB (2017). http://www.abdsb.bayern.de/zahlen. Bogenberger, K. (2003). Qualit¨at von Verkehrsinformationen. Straßenverkehrstechnik, 47, 518–526. Bogenberger, K. and Hauschild, M. (2009). QFCD - A Microscopic Model for Measuring the Individual Quality of Traffic Information. ITSC World Congress, Stockholm, Sweden. Bogenberger, K. and Weikl, S. (2012). Quality Management Methods for Real-Time Traffic Information. Procedia - Social and Behavioral Sciences, 54, 936–945. Huber, G., Bogenberger, K., and Bertini, R.L. (2014). New Methods for Quality Assessment of Real Time Traffic Information. 93rd annual meeting of the transportation research board, 14(2918).
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(a) vcrit = 40 km/h, Pmin = 0.1: matchable jams: 152, deviations: mean = 0.2, median = 2, quartiles at −3 and 5, max = 21, min = −31
(b) vcrit = 60 km/h, Pmin = 0.1: matchable jams: 244, deviations: mean = −0.2, median = 1, quartiles at −3 and 4, max = 13, min = −31
(d) vcrit = 60 km/h, Pmin = 0.3: matchable jams: 211, deviations: mean = −0.2, median = 1, quartiles at −3 and 4, max = 11, min = −31
(c) vcrit = 40 km/h, Pmin = 0.3: matchable jams: 116, deviations: mean = 0.5, median = 2, quartiles at −2 and 5, max = 15, min = −31
(f) vcrit = 60 km/h, Pmin = 0.5: matchable jams: 168, deviations: mean = 0.4, median = 2, quartiles at −3 and 4, max = 11, min = −20
(e) vcrit = 40 km/h, Pmin = 0.5: matchable jams: 75, deviations: mean = 0.3, median = 2, quartiles at −2.75 and 4.75, max = 12, min = −20
Fig. 6. Deviation of primary jam detection (mean, median, quartiles, maximum and minimum each in min) Kessler, L., Huber, G., Kesting, A., and Bogenberger, K. (2018). Comparison of floating-car based speed data with stationary detector data. Presentation at 97th Annual Meeting of the Transportation Research Board. Kim, S. and Coifman, B. (2014). Comparing inrix speed data against concurrent loop detector stations over several months. Transportation Research Part C, 49, 59–72. Lux, C. (2011). QBench – Evaluation of Traffic Flow Quality. In C. Lotz and M. Luks (eds.), Qualit¨ at von on-trip Verkehrsinformationen im Straßenverkehr, volume 82 of Berichte der Bundesanstalt f¨ ur Straßenwesen : F, Fahrzeugtechnik, 56–63. Wirtschaftsverl. NW, Verl. f¨ ur Neue Wiss. Rainer, B. (2011). TMCplus - Improving the TMC information chain. In C. Lotz and M. Luks (eds.), Qualit¨ at von on-trip Verkehrsinformationen im Straßenverkehr, volume 82 of Berichte der Bundesanstalt f¨ ur Straßenwesen: F, Fahrzeugtechnik, 25–31. Wirtschaftsverl. NW,
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Verl. f¨ ur Neue Wiss. Rakha, H., Chen, H., Haghani, A., and Sadabadi, K.F. (2013). Assessment of data quality needs for use in transportation applications. Report MAUTC-2011-01. Rehborn, H., Kerner, B.S., and Palmer, J. (2011). How can we determine the quality of traffic information? In C. Lotz and M. Luks (eds.), Qualit¨ at von on-trip Verkehrsinformationen im Straßenverkehr, volume 82 of Berichte der Bundesanstalt f¨ ur Straßenwesen : F, Fahrzeugtechnik, 46–55. Wirtschaftsverl. NW, Verl. f¨ ur Neue Wiss. Treiber, M. and Helbing, D. (2002). Reconstructing the spatio-temporal traffic dynamics from stationary detector data. Cooper@tive Tr@nsport@tion Dyn@mics, 1, 3.1–3.24. Treiber, M., Kesting, A., and Wilson, R.E. (2011). Reconstructing the traffic state by fusion of heterogeneous data. Computer-Aided Civil and Infrastructure Engineering, 26, 408–419.
ScienceDirect
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Comparing Speed Data from Stationary Comparing Speed Data from Stationary Comparing Speed Data from Stationary Detectors Against Floating-Car Data Comparing Speed Data from Stationary Detectors Against Floating-Car Data Detectors Against Floating-Car Data Detectors Against Floating-Car Data Lisa Kessler ∗∗ Gerhard Huber ∗∗ Arne Kesting ∗∗ ∗∗
Lisa Kessler ∗∗ Gerhard Huber ∗∗ Arne Kesting ∗∗ ∗ Bogenberger Lisa Kessler ∗ Klaus Gerhard Huber ∗ Arne Kesting ∗∗ ∗ ∗ Klaus Bogenberger ∗ Lisa Kessler Klaus Gerhard Huber Arne Kesting ∗∗ Bogenberger ∗ Klaus Bogenberger ∗ ∗ ∗ Munich University of the Federal Armed Forces, Germany of the Federal Armed Forces, Germany ∗ Munich University (e-mail: Munich University of [email protected]) the Federal Armed Forces, Germany ∗ ∗∗ (e-mail: Munich University of [email protected]) the Federal Armed Forces, Germany TomTom Development Germany [email protected]) ∗∗ ∗∗ (e-mail: [email protected]) Development Germany ∗∗ (e-mail: TomTom Development Germany ∗∗ TomTom Development Germany Abstract: This paper compares speed data measured by induction loops of stationary detectors Abstract: This paper compares speed data measured by induction loops of stationary detectors with reported speeds floating-car data,measured which arebybased on most recent GPS observations Abstract: This paperfrom compares speed data induction loops of stationary detectors with reported speeds from floating-car data,measured which arebybased on most recent GPS observations Abstract: This paper compares speed data induction loops of stationary detectors of probe vehicles. Detector data are aggregated over aa one minute time interval and that means with reported speeds from floating-car data, which are based on most recent GPS observations of probe vehicles. Detector data are aggregated over one minute time interval and that means with speeds floating-car data, which based on most recent GPS observations a 30 sreported delay occurs on from average. delay issues respect to floating-car data aremeans quite of probe vehicles. Detector dataThe are time aggregated overare awith one minute time interval and that a 30 s delay occurs on average. The time delay issues with respect to floating-car data are quite of probe vehicles. Detector dataThe are aggregated over awith one respect minute time interval and that means with many influences: (i) the update frequencies from vehicles to the backend server, aconvoluted 30 s delay occurs on average. time delay issues to floating-car data are quite (i)time the update frequencies from vehicles to the backend convoluted with many influences: a 30the s delay occurs average. The delay issues withflow, respect to floating-car datatreatment. areserver, quite (ii) fleetwith sizemany ofon floating cars, (iii)the theupdate current traffic and (iv) the convoluted influences: (i) frequencies from vehicles to provider the backend server, (ii) the fleet size of floating cars, (iii) the current traffic flow, and (iv) the provider treatment. convoluted with many influences: (i) the update frequencies from vehicles to provider the length backend server, The floating-car dataset has a high spatial resolution with an average segment of 100 (ii) the fleet size of floating cars, (iii) the current traffic flow, and (iv) the treatment. Thethe floating-car dataset has a high spatial resolution with an and average segment length of 100 m m (ii) fleet size dataset of floating (iii) theand current traffic flow, (iv) segment the provider treatment. suited for large-scale traffic observation management. The spatial dimension of detector The floating-car has cars, a high spatial resolution with an average length of 100 m suited for large-scale traffic observation and management. The spatial dimension of detector The has observation a high spatial resolution with an average segment length 100 m data floating-car can be dataset reconstructed ex-post from spotty positions (mean detector positions distance suited foronly large-scale traffic and management. The spatial dimension of of detector data can only be reconstructed ex-post from spotty positionsThe (mean detector positions distance suited for large-scale traffic observation and management. spatial dimension of detector approx. 1.3 km). data can1.3 only be reconstructed ex-post from spotty positions (mean detector positions distance approx. km). data can1.3 only be reconstructed ex-post from spotty positions (mean detecting detector positions distance The paper analyzes which approx. km). The paper analyzes which source source is is more more advantageous advantageous in in terms terms of of detecting traffic traffic jams, jams, high high approx. 1.3 km). temporal of detector data or advantageous detailed spatial resolution of floating-car data.high An The paperavailability analyzes which source is more in terms of detecting traffic jams, temporal availability of detector data or detailed spatial resolution of floating-car data. An The paperavailability which source is more advantageous in terms of detecting traffic jams, high algorithm isanalyzes presented compute the orjam detection duration, which means we are able to temporal oftodetector data detailed spatial resolution of floating-car data. An detection duration, which we aredata. ableAn to algorithm is presentedoftodetector compute the orjam temporal availability data detailed spatial resolution of means floating-car recognize which data source detects the earliest. The results demonstrate that there exist algorithm is presented to compute the jam detection duration, which means we are able to recognize which data source detects the jam earliest. The results demonstrate that there exist algorithm is presented to compute the jam detection duration, which means we are able to regions along certain road stretches where floating-car data clearly outperform stationary data. recognize which data source detects the jam earliest. The results demonstrate that there exist regions along certain road stretches where floating-car dataresults clearlydemonstrate outperform stationary data. recognize which data source detects the jam earliest. The that there exist However, in regions detectorswhere are densely placed,data stationary sensor data stationary recognize adata. jam regions along certainwhere road stretches floating-car clearly outperform However, in regions where detectorswhere are densely placed,data stationary sensor data stationary recognize a jam regions certain road stretches floating-car clearly situationalong approx. 2 min earlier than floating-car based data. outperform However, in regions where detectors are densely placed,speed stationary sensor data recognize adata. jam situation approx. 2 min earlier than floating-car based speed data. sensor data recognize a jam However, in regions where detectors are densely placed, stationary The cover a of 80 days for driving situation approx. 2 min earlier based speed data. directions The datasets datasets cover a period period ofthan 80 floating-car days in in 2015 2015 for both both driving directions on on the the German German situation approx. 2 min earlier than floating-car based speed data. directions autobahn A9 in the north of Munich. The datasets cover a period of 80 days in 2015 for both driving on the German autobahn A9 in the north of Munich. The datasets cover a period of 80 days in 2015 for both driving directions on the German autobahn A9 in the north of Munich. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. autobahn A9 in the north of Munich. Keywords: Information displays/system, Automotive sensors and actuators, Navigation, Keywords: Information displays/system, Automotive sensors and actuators, Navigation, System integration and displays/system, supervision, Floating-car data, Inductive detector data, Speed Keywords: Information Automotive sensors and loop actuators, Navigation, System integration and displays/system, supervision, Floating-car data, Inductive detector data, Speed Keywords: Information Automotive sensors and loop actuators, Navigation, measurements System integration and supervision, Floating-car data, Inductive loop detector data, Speed measurements System integration and supervision, Floating-car data, Inductive loop detector data, Speed measurements measurements 1. These 1. INTRODUCTION INTRODUCTION These two two approaches, approaches, stationary stationary and and floating-car floating-car based based traffic measurements, be compared towards different 1. INTRODUCTION These two approaches,can stationary and floating-car based traffic measurements, can be compared towards different 1. INTRODUCTION These two stationary and floating-car based data,approaches, e.g. speedcan values. Stationary counted traftraffic measurements, be compared towards different Traffic data measurements from stationary devices have data, e.g. speedcan values. Stationary counted trafTraffic data measurements from stationary devices have traffic traffic measurements, be compared towards different fic data have the advantage of registering every passing traffic data, e.g. speed values. Stationary counted trafplayed adata dominant role in traffic over the last Traffic measurements fromobservations stationary devices have fic datadata, havee.g. the speed advantage of Stationary registering every passing over the last played a dominant role in traffic observations traffic values. counted trafTraffic measurements from stationary devices have vehicle frequency) but with aa low spatial data (number have theand advantage of registering every passing decades. In recent years, measurements derived played adata dominant role inspeed traffic observations over thefrom last fic vehicle (number and frequency) but with low spatial decades. In recent years, speed measurements derived from fic data have the advantage of registering every passing played dominant role inspeed traffic observations over thefrom last vehicle availability. The amount of floating-car data a(FCD) obser(number and frequency) but with low spatial frequenta In uploads GPS datameasurements from probe vehicles have decades. recent of years, derived The amount of floating-car data a(FCD) obserfrequent In uploads of GPSspeed datameasurements from probe vehicles have availability. vehicle andthe frequency) with low spatial decades. recent of years, derived from vations (number depends on number ofbut passing This availability. The amount of floating-car data vehicles. (FCD) obserbecome a serious alternative to the infrastructural-based frequent uploads GPS data from probe vehicles have vations depends on the number of passing vehicles. This become a serious alternative to the infrastructural-based availability. The amount of floating-car data vehicles. (FCD) obserfrequent of GPS data probe vehicles have becomes and more with sample vations depends on more the number of irrelevant passing This approachauploads for traffic monitoring. Traffic observation with limitation become serious alternative to from the infrastructural-based limitation becomes more and more irrelevant with sample approach for traffic monitoring. Traffic observation with vations depends on the number of passing vehicles. This become a for serious alternative to whole the infrastructural-based rates of some percent of the volume. addibecomes more andtotal moretraffic irrelevant withIn sample floating cars istraffic possible over the road network while approach monitoring. Traffic observation with limitation rates of some percent of the total traffic volume. In addifloating cars is possible over the whole road network while limitation becomes more and more irrelevant with sample approach forage monitoring. Trafficroad observation with rates tion, the main advantage is of of some of the totalscalability traffic volume. In addithe average of the speedthe observations used in traffic floating cars istraffic possible over whole network while tion, the mainpercent advantage is the the scalability of floating-car floating-car the average age of the over speedthe observations used in traffic rates of some percent ofcan the total trafficwherever volume. In addifloating cars is possible whole road used network while based technology: data be collected traffic tion, the main advantage is the scalability of floating-car services depends on both the probe sample and the total the average age of the speed observations in traffic technology: data canisbe collected wherever traffic is is services depends onthe both the probe sampleused and in thetraffic total based tion, the mainallows advantage the scalability ofnetwork-wide floating-car the average age of speed observations flowing. This for new applications in based technology: data can be collected wherever traffic is traffic flow. services depends on both the probe sample and the total flowing. This allows for new applications in network-wide traffic flow. based technology: data can be collected wherever traffic is services depends on both the probe sample and the total traffic monitoring and management applications. flowing. This allows for new applications in network-wide traffic flow. traffic monitoring and management applications. flowing. This allows for new applications in network-wide Nowadays, all traffic providers like TomTom, Google, Intraffic flow. all traffic providers like TomTom, Google, In- traffic monitoring and management applications. Nowadays, aspect the time both trafficmain monitoring and applications. rix, and Here floating-car technology on a big Nowadays, all use traffic providers based like TomTom, Google, In- One One main aspect is is themanagement time delay delay of of both measurement measurement rix, and Here use floating-car based technology on a big Nowadays, all traffic providers like TomTom, Google, Inapproaches to capture the current real-world traffic One main aspect is the time delay of both measurement scaleand to offer ‘live’ or ‘real-time’ traffic services re- approaches to capture the current real-world rix, Hereso-called use floating-car based technology on a big traffic sitsitscaleand to offer so-called ‘live’ or ‘real-time’ traffic services re- One main aspect is the timestate delayestimation of both measurement rix, Hereso-called use floating-car based technology onspeeds. a big uation. FCD-based traffic depends on approaches to capture the current real-world traffic sitporting delays for detected traffic incidents or link scale to offer ‘live’ or ‘real-time’ traffic services reuation. FCD-based traffic state estimation depends on porting delays for detected traffic incidents or link speeds. to capture the current real-world traffic sitscale to offer so-called ‘live’ or ‘real-time’ traffic services re- approaches the rate of observations, which, in turn, depends on the uation. FCD-based traffic state estimation depends on This data-driven technology is established itself as stateporting delays for detected traffic incidents or link speeds. the rate of observations, which, in turn, depends on the This data-driven technology is established itself as stateuation. trafficwhich, state inestimation depends on porting delays for technology detected traffic incidents or linkasspeeds. penetration rate of probe vehicles and on the traffic rate FCD-based of observations, turn, depends onflow. the of-the-art for routing applications. With increasing per- the This data-driven is established itself statepenetration rate of probe vehicles and on the traffic flow. of-the-art for routing applications. With increasing per- the rate of detector observations, which, in turn, depends onflow. the This data-driven technology is established itself as stateStationary data (SDD) can be used for spatial penetration rate of probe vehicles and on the traffic centage of for probe vehicles, this technology becomes more of-the-art routing applications. With increasing per- Stationary detector data (SDD) can be used for spatial centage of for probe vehicles, this technology becomes more rate ofwhen probe vehicles andbe ondetectors the traffic flow. of-the-art routing applications. With increasing per- penetration speed estimations double-loop not Stationary detector datathe (SDD) can used for are spatial and more also for traffic management applicacentage of attractive probe vehicles, this technology becomes more speed estimations when the double-loop detectors are not and more attractive also for traffic management applicaStationary detector data (SDD) can be used for spatial centage of probe vehicles, this technology becomes more too far apart. On the considered autobahn A9 the mean estimations when the double-loop detectors are not tions.more attractive also for traffic management applica- speed and too far apart. On the considered autobahn A9 the mean tions. speed the double-loop detectors not and distance of detector is just 1.3 Therefarestimations apart. On when thecross-sections considered autobahn A9km. theare mean tions.more attractive also for traffic management applica- too distance of detector cross-sections is just 1.3 km. Theretoo apart. On thecan considered autobahn A9km. theTheremean tions. fore,far detector speeds be considered as benchmark. On distance of detector cross-sections is just 1.3 This work was supported by the German Federal Ministry for the This work was supported by the German Federal Ministry for the fore, detector speeds can be considered as benchmark. On distance of detector cross-sections is just 1.3be km.theTherea road with less detectors the contrary could case. fore, detector speeds can be considered as benchmark. On Environment, Nature Conservation, Building and Nuclear Safety. This work was supported by the German Federal Ministry for the a road with less detectors the contrary could be the case. Environment, Nature Conservation, Building and Nuclear Safety. fore, detector speeds can bethe considered benchmark. On a road with less detectors contrary as could be the case. This work was supported by the German Ministry for the Environment, Nature Conservation, BuildingFederal and Nuclear Safety. a road with less detectors the contrary could be the case. Environment, Nature Conservation, Building and Nuclear Safety.
2405-8963 © © 2018 2018, IFAC IFAC (International Federation of Automatic Control) Copyright 299 Hosting by Elsevier Ltd. All rights reserved. Copyright © under 2018 IFAC 299 Control. Peer review responsibility of International Federation of Automatic Copyright © 2018 IFAC 299 10.1016/j.ifacol.2018.07.049 Copyright © 2018 IFAC 299
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The main disadvantage of SDD are the high installation and maintenance costs, therefore the infrastructural-based measurement technology remains limited to just a few corridors. It is obvious that floating-car based technology does not require any measurement infrastructure except the telecommunication network. This paper is structured as follows. After the state of the art the datasets of SDD and of FCD are described in sec. 3. Section 4 treats the question which of both data sources detects a jam event earlier. An algorithm to find reliable congestion cluster matchings and the results of the analysis are presented. Finally, a conclusion and an outlook on further research are given. 2. STATE OF THE ART
(lat, long) = (48.1787, 11.5955)) and triangle Holledau (at (48.5841, 11.5801)). Data are available for both driving directions, in northbound direction (NB) comprising 47.7 km, in southbound direction (SB) 31.4 km. Data are collected within April to June 2015 (80 days). The A9 is one of Germany’s most used freeways. In 2013, more than 150, 000 vehicles per day have been counted on average at interchange Munich-Nord for both directions (ABDSB (2017)). This freeway is equipped with variable message signs and the shoulder is in part-time use. The number of lanes is typically 3 − 4 in each direction. Together with the part-time use of hard shoulder the number of available lanes goes up to 5. 3.2 Stationary Detector Data
In literature many studies investigate up to which degree broadcasted traffic information is able to mirror real traffic situations accurately. Some of these studies focus on specific aspects of traffic information services such as the latency with which traffic related incidents are reported. In Rainer (2011), it is stated that for traffic messages broadcasted in Austria, via the traffic message channel, the average time of delay was about 10 min. In Kim and Coifman (2014) traffic information provided by Inrix is assessed. The results of this analysis indicate that the reported Inrix speeds tended to lag those stationary detector data by almost 6 min on average. The authors of Rakha et al. (2013) also assess Inrix data and compare them to stationary sensor data but rather focus on travel time and travel time reliability. Other studies such as Bogenberger (2003), Bogenberger and Hauschild (2009), Lux (2011), Rehborn et al. (2011), Huber et al. (2014) discuss quality of traffic information via indices (see Bogenberger and Weikl (2012) for an overview of these studies). The fundamental idea of all these approaches is to interpret ‘quality’ as the level of similarity between the broadcasted traffic information and a ground truth representing the real traffic situation adequately. It is either generated by tracking test vehicles (Bogenberger and Hauschild (2009), Lux (2011)) or by applying traffic state reconstruction methods on the basis of stationary detector data (Bogenberger (2003), Rehborn et al. (2011), Huber et al. (2014)). Those approaches significantly differ from the idea presented here and in our preceding work (Kessler et al. (2018)) where neither the detector data nor the floating-car data are considered as a reference. Furthermore, jam event messages are compared directly and without regarding one of the sources as ground truth. Both types of data show strengths and weaknesses when being compared to each other. One of the central objectives of the described research is to identify these strengths and weaknesses in order to obtain a comprehensive understanding which of the data types are suited for which purposes. 3. DESCRIPTION OF THE DATA 3.1 Test Site: Autobahn A9, Germany The following analysis considers autobahn A9 in the north of Munich between intersection Munich-Schwabing (at 300
Stationary detector data (SDD) are available from 33 (NB) respectively 27 (SB) cross-sections. The inductive double-loop detectors allow for direct speed measurements. Aggregated data have a resolution of one minute. The flowweighted mean speed over all car and truck lanes is given as one combined speed data value per minute. The average distance of 1.3 km between cross-sections allows for interpolating the time-series data. For this purpose, the Adaptive Smoothing Method (ASM) (Treiber and Helbing (2002), Treiber et al. (2011)) has been applied to derive (smoothed) speed values also for the space between detector positions. The ASM algorithm uses two smoothing kernels, one for free-flow conditions with a downstream propagation and another one for congested flow in upstream direction. Both kernels are weighted combined depending on the speed. The spatiotemporal smoothing kernels interpolate spatially between detector positions but also in time at one detector position. Therefore, ASM compensates for gaps in the original time series (Fig. 1), for example due to a system break down.
Fig. 1. SDD time series at location 494.84 km (NB) for April 1. In the night hours speed = 0 is provided at some minutes due to no vehicles passing in those minutes (flow = 0 ⇒ speed = 0). Note that smoothing preserves the jam fronts during the morning peak. Since the ASM interpolation uses forward and backward times at different locations this method can only be applied in a post-processing analysis (ex-post), in contrast to FCD. See table 1 for used ASM parameters.
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Table 1. ASM parameters used for smoothing the detector data Parameter Spatial grid distance Temporal grid distance Speed in congestion Free-flow speed Crossover from free to congested traffic Width of the transition region
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single probe measurement is known (determined by the upload frequency (typically 1-3 min) and the time needed for the map-matching process (in general a few seconds)). Since the reported speed is based on several latest probe observations, the average age may vary. Here, the focus is on delays in capturing speeds due to the underlying data collection methodology. For a better comparison, SDD have also been capped above the TomTom free-flow speed values.
value 100 m 30 s -18 km/h 80 km/h 70 km/h 10 km/h
3.3 TomTom Speed Data TomTom offers a product called TomTom Flow, which is a live data feed reporting current speeds for links in the road network with a time update of 1 min. The level of spatial resolution can be customized. The dataset used in this academic study uses a link aggregation defined by segments with an average link length of about 100 m (maximum of 198 m). The reported speed is calculated in a ‘fusion engine’, which determines a consistent speed for each link in each update cycle from various input sources. The speed estimation is basically driven by a weighted average over the last observations from individual probes plus some blackbox refinements, which are in the scope of data interpretation and control of the provider. The probe speed measurements are derived from mapmatched GPS positions. These floating-car data are a permanent input stream in TomTom’s live processing chain depicted in Fig. 2. Probes Providing GPS Data
Asynchronous Upload (typical frequencies of 1-3 min)
Other Sources than GPS
Fusion Engine: Periodic Updates of 30 sec
Map Matching
Data Delivery: Conversion, Filtering Client Sessions
Data Formats and Feeds
Fig. 2. Processing chain of TomTom’s live traffic service In the dataset, a free-flow speed is provided for each link. This speed is defined by the minimum of the map speed limit and the free-flow speed measured from historic floating-car data. This free-flow speed is used to define an upper bound for the reported speeds. Thus, there is no higher speed in the FCD than the free-flow speed (although individual probe speeds may be higher). 3.4 Combination of Datasets The spatial resolution of FCD is high (100 m on average; traffic information per segment) compared to SDD with typical spacings of 1-3 km between detector positions (traffic information per location point). Therefore, FCD can be plotted directly to illustrate the spatiotemporal traffic dynamics while SDD need to be interpolated for reconstructing the spatiotemporal dynamics in a postprocessing step (ASM data), cf. Fig. 3. The temporal resolution of both datasets is 1 min, which is sufficient for most traffic-management related applications. All times mentioned here are local times (UTC+02:00). The SDD timestamps refer to the end of each 1-minute measurement interval. Subsequently, the aggregated data are 30 s old on average. For a floatingcar based speed measurement method only the age of a 301
Fig. 3. Spatiotemporal speed contour plots from April 30 in NB direction (decreasing kilometrage). Speeds are visualized in different colors. The light green horizontal bars indicate general speed limits of 80 km/h. A qualitative comparison of speed colors in Fig. 3 indicates that both sources report very similar speeds in both freeflow and congested regimes. The FCD contour plot shows the spatiotemporal dynamics at a higher level of detail compared to the situation derived from SDD. For example, the reduced speeds during the night hours at KM 515 (probably a speed limit effective at night) as well as the traffic jam fronts are spatially more precisely pictured in the FCD. The traffic jam at KM 490 (downstream front) is a separate structure in FCD while it becomes conjoined with the congestion pattern at KM 494 due to the interpolation of SDD. 4. PRIMARY CONGESTION DETECTION ANALYSIS In the following, an approach is described to systematically compare which of the data sources allows for detecting
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congestion earlier. The ability to detect emerging traffic congestion promptly is essential for the provision of advance congestion warnings to drivers. FCD profit from not being bound to discrete positions along the considered road corridors. Contrarily, SDD may profit from temporal latencies of FCD due to the data processing. Which of the effects is dominating will be analyzed in the following. The algorithm works in three steps. First single congestion events (‘congestion clusters’) are identified based on SDD as well as on FCD. In a second step, SDD and FCD congestion clusters are associated with each other. The third step comprises the comparison between the temporal starts of the resulting pairs of congestion clusters. Hence, it can be decided on the basis of which data source a congestion warning could have been provided earlier in the respective situation. 4.1 Associating SDD Jams and FCD Jams Let FCD be available for a road corridor X and a time period T . A spatiotemporal speed function vF CD returns the speed value where the FCD are reported for any location x ∈ X and any time t ∈ T . Furthermore, let X be separated into a set of links {Li }i=1,...,I , the spatial resolution of FCD. Similarly, let T be separated into a set of time intervals {Tj }j=1,...,J . Sets {Li } and {Tj } separate the spatiotemporal area X × T into a grid, and function vF CD is constant within each cell Li × Tj of this grid (see part 1 of Fig. 4). Space
1. Speed function 𝒗𝒗𝑭𝑭𝑭𝑭𝑭𝑭 :
2. Identification of congested areas: Space
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Fig. 4. Computation of congestion clusters for FCD Also let SDD be available for the aforementioned road corridor X and time period T . The detector position locations along X are denoted with x1 , . . . , xD , D ∈ N. A spatiotemporal speed function vSDD returns for any location x ∈ {x1 , . . . , xD } and any time t ∈ T the latest speed value measured by the corresponding detector. Cells of interest for this analysis are only those which contain a speed value below vcrit since they are congested. Two cells Li1 ×Tj1 and Li2 ×Tj2 are denoted as ‘connected’ if the following two conditions hold: 302
i1 ∈ {i2 − 1, i2 , i2 + 1} (1) (2) j1 ∈ {j2 − 1, j2 , j2 + 1} This definition of congestion clusters leads to many very small clusters. Furthermore, it can be observed that these clusters frequently are located closely to each other. In order to achieve a smoothing effect clusters which are located closely to each other are merged into one single cluster. ‘Closely’ means that a driver needs not more than tmerge ∈ R≥0 to get from one cluster to the other. For the merging it is iterated over all clusters located in X × T . For each of these clusters a set of virtual driving trajectories is computed. This set consists of one driving trajectory starting from each corner of a cell belonging to the considered cluster (see part 3 of Fig. 4, illustrated with tmerge = 2 for cluster A). This can be done for some starting point (xS , tS ) ∈ X × T by solving the ordinary differential equation dx = vF CD (x(t), t) (3) dt with initial condition x(tS ) = xS (x as function returning a location in dependency of time). For each virtual trajectory the computation is terminated as soon as time tS + tmerge is reached. All clusters touched by one of the generated trajectories are assigned to the original cluster. This means that all congested cells belonging to one of these clusters to be part of the same cluster (part 4). Congestion clusters are also computed for SDD. Analogously to FCD, jam clusters are identified for detector data. In order to identify one coherent cluster for discrete detector positions, the ASM is again used as the smoothing method. Clusters are found iterating the ASM data applying the methodology described in Fig. 4. For the resulting ASM congestion clusters the jammed times from the original detector data positions x1 , . . . , xD are taken to compare the first congested timestamps instead of the smoothed speed values, again with the threshold vcrit . For all detector positions in the spatial range of one found ASM congestion cluster, the first temporal occurrences are computed and the detector position with the least time value is taken as reference to compare the SDD speeds to the FCD congestion cluster. In order to associate FCD and SDD congestion clusters, it iterates over the set of all congestion clusters. All FCD congestion clusters, which show any intersection with an SDD congestion cluster, are assigned to the SDD cluster with the earliest beginning. However, to reduce the risk of incorrectly matched clusters, the identified pairs of clusters need to fulfill additional conditions: Let CF CD ⊆ X × T denote the spatiotemporal area of an FCD cluster, CSDD ⊆ X × T of an SDD cluster. Furthermore, let | A | denote the size of an area A ⊆ X × T . CF CD can only be assigned to CSDD if they fulfill (4)–(6): | CSDD ∩ CF CD | ≥ Pmin (4) | CSDD | | CSDD ∩ CF CD | ≥ Pmin (5) | CF CD | (6) | CSDD ∩ CF CD | ≥ Amin Pmin ∈ [0, 1] denotes the minimum percentage of the area of the FCD and the SDD cluster that has to be covered by both clusters. Amin ∈ R≥0 denotes the minimum area that
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needs to be covered by the intersection of both clusters. Conditions (4) and (5) ensure that significant parts of clusters are congested according to both data types, (6) ensures that small clusters are ignored. Finally, the earliest time at which a congestion warning could have been made on the basis of FCD is denoted by tmin (CF CD ) with (7) tmin (CF CD ) := min{t ∈ T : t ∈ CF CD }. Time tmin (CSDD ) is defined analogously. Both data sources yield to jam areas with a different level of detail: ASM data result in more coherent clusters due to the smoothing (fewer clusters in total), FCD in more separate small clusters due to the direct measurements (more clusters in total). Therefore, it can happen that one congestion of one source is matched to an area with several congestions of the other source. The algorithm preserves the different number of jam clusters in an 1:n matching, otherwise (4)–(6) would not hold, especially (4) and (5) would yield to wrong first timestamps. The described approach presents one reliable possibility to compare FCD and SDD with regard to their ability to provide advance congestion warnings. One main drawback of the proposed procedure is the high parameter number. However, the findings of the computational analysis indicate that different parameter sets only have little influence. 4.2 Results of Primary Jam Detection Analysis The algorithm described in the previous section has been tested with several parameterizations (vcrit ∈ {40 km/h, 60 km/h}, Pmin ∈ {0.1, 0.3, 0.5}) while tmerge = 4 min and Amin = 2 km·min have been kept constant. The jam clusters have been determined for both FCD and SDD and these clusters have been matched. For a match, the deviation between the start times can be calculated. Figure 6 shows the probability distributions for the time differences tdiff = tmin (CF CD ) − tmin (CSDD ) for all matchable jam events. Median and quartile values are given in the corresponding captions. Negative numbers correspond to a jam cluster detected by FCD first. A positive median value indicates that a jam is detected earlier by the SDD/ASM than the FCD approach (height of bars). Nevertheless, there are more matchings where FCD recognize the jam situation significantly earlier than SDD (positive skew). The balanced statistical results show that both approaches are equally good in detecting matchable traffic jams, i.e., detected by both approaches. The larger the speed limit parameter is chosen, the smaller the deviation. However, FCD are able to find more relevant traffic jam clusters (394 and 472, for vcrit = 40 km/h and vcrit = 60 km/h, respectively) than SDD/ASM (372 and 407). This algorithm finds reliable matchings. Nevertheless, there are examples where the matching fails. In Fig. 5, a spatiotemporal area from April 21 is depicted. The horizontal lines denote the detector positions. The FCD jam section is marked in red, the SDD jam section is marked with bold black lines on the detector position lines. FCD detected a jam situation at 16:12 h, SDD at 16:42 h so the difference amounts to -30 min. Obviously, the detector positions are disadvantageous to detect this jam. 303
Fig. 5. Jam cluster from April 21 (NB), vcrit = 60 km/h 5. SUMMARY AND OUTLOOK In this work, a comparison between floating-car based speed data (FCD) and stationary detector speed data (SDD) is presented. In terms of spatial resolution, FCD outperform SDD since FCD are available over a whole stretch of the road in contrast to isolated detector positions. SDD, as direct speed measurements, outperform FCD in their temporal resolution. The results of a congestion cluster matching show that the speed datasets do not have any systematic bias or shift but are comparable. FCD allow for a spatial traffic monitoring close to real-time whereas detectors only offer observations at few locations. An analysis on which source detects a jam situation first demonstrates that no dataset clearly outperforms the other one. In general, FCD find more (smaller) congestion clusters compared to the smoothed detector data. In regions where detectors are placed densely, SDD benefit from the temporal advantage and differ from FCD by approx. 2 min. In regions between detector positions, FCD outperform SDD (Fig. 5). Generally, the results of the analysis show that the difference between the first occurrences of matched FCD and SDD jams takes larger minima than maxima (absolute values) (Fig. 6). Further research will include the combination of both datasets for recommendations to local authorities. ACKNOWLEDGEMENTS The authors would like to thank Autobahndirektion S¨ udbayern (ABDSB) and TomTom for providing the data. REFERENCES ABDSB (2017). http://www.abdsb.bayern.de/zahlen. Bogenberger, K. (2003). Qualit¨at von Verkehrsinformationen. Straßenverkehrstechnik, 47, 518–526. Bogenberger, K. and Hauschild, M. (2009). QFCD - A Microscopic Model for Measuring the Individual Quality of Traffic Information. ITSC World Congress, Stockholm, Sweden. Bogenberger, K. and Weikl, S. (2012). Quality Management Methods for Real-Time Traffic Information. Procedia - Social and Behavioral Sciences, 54, 936–945. Huber, G., Bogenberger, K., and Bertini, R.L. (2014). New Methods for Quality Assessment of Real Time Traffic Information. 93rd annual meeting of the transportation research board, 14(2918).
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(a) vcrit = 40 km/h, Pmin = 0.1: matchable jams: 152, deviations: mean = 0.2, median = 2, quartiles at −3 and 5, max = 21, min = −31
(b) vcrit = 60 km/h, Pmin = 0.1: matchable jams: 244, deviations: mean = −0.2, median = 1, quartiles at −3 and 4, max = 13, min = −31
(d) vcrit = 60 km/h, Pmin = 0.3: matchable jams: 211, deviations: mean = −0.2, median = 1, quartiles at −3 and 4, max = 11, min = −31
(c) vcrit = 40 km/h, Pmin = 0.3: matchable jams: 116, deviations: mean = 0.5, median = 2, quartiles at −2 and 5, max = 15, min = −31
(f) vcrit = 60 km/h, Pmin = 0.5: matchable jams: 168, deviations: mean = 0.4, median = 2, quartiles at −3 and 4, max = 11, min = −20
(e) vcrit = 40 km/h, Pmin = 0.5: matchable jams: 75, deviations: mean = 0.3, median = 2, quartiles at −2.75 and 4.75, max = 12, min = −20
Fig. 6. Deviation of primary jam detection (mean, median, quartiles, maximum and minimum each in min) Kessler, L., Huber, G., Kesting, A., and Bogenberger, K. (2018). Comparison of floating-car based speed data with stationary detector data. Presentation at 97th Annual Meeting of the Transportation Research Board. Kim, S. and Coifman, B. (2014). Comparing inrix speed data against concurrent loop detector stations over several months. Transportation Research Part C, 49, 59–72. Lux, C. (2011). QBench – Evaluation of Traffic Flow Quality. In C. Lotz and M. Luks (eds.), Qualit¨ at von on-trip Verkehrsinformationen im Straßenverkehr, volume 82 of Berichte der Bundesanstalt f¨ ur Straßenwesen : F, Fahrzeugtechnik, 56–63. Wirtschaftsverl. NW, Verl. f¨ ur Neue Wiss. Rainer, B. (2011). TMCplus - Improving the TMC information chain. In C. Lotz and M. Luks (eds.), Qualit¨ at von on-trip Verkehrsinformationen im Straßenverkehr, volume 82 of Berichte der Bundesanstalt f¨ ur Straßenwesen: F, Fahrzeugtechnik, 25–31. Wirtschaftsverl. NW,
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Verl. f¨ ur Neue Wiss. Rakha, H., Chen, H., Haghani, A., and Sadabadi, K.F. (2013). Assessment of data quality needs for use in transportation applications. Report MAUTC-2011-01. Rehborn, H., Kerner, B.S., and Palmer, J. (2011). How can we determine the quality of traffic information? In C. Lotz and M. Luks (eds.), Qualit¨ at von on-trip Verkehrsinformationen im Straßenverkehr, volume 82 of Berichte der Bundesanstalt f¨ ur Straßenwesen : F, Fahrzeugtechnik, 46–55. Wirtschaftsverl. NW, Verl. f¨ ur Neue Wiss. Treiber, M. and Helbing, D. (2002). Reconstructing the spatio-temporal traffic dynamics from stationary detector data. Cooper@tive Tr@nsport@tion Dyn@mics, 1, 3.1–3.24. Treiber, M., Kesting, A., and Wilson, R.E. (2011). Reconstructing the traffic state by fusion of heterogeneous data. Computer-Aided Civil and Infrastructure Engineering, 26, 408–419.