Spatio-temporal prediction of freeway congestion patterns using discrete choice methods

Metzger, Barbara; Loder, Allister; Kessler, Lisa; Bogenberger, Klaus Article Spatio-temporal prediction of freeway congestion patterns using discrete choice methods EURO Journal on Transportation and Logistics (EJTL) Provided in Cooperation with: Association of European Operational Research Societies (EURO), Fribourg Suggested Citation: Metzger, Barbara; Loder, Allister; Kessler, Lisa; Bogenberger, Klaus (2024) : Spatio-temporal prediction of freeway congestion patterns using discrete choice methods, EURO Journal on Transportation and Logistics (EJTL), ISSN 2192-4384, Elsevier, Amsterdam, Vol. 13, Iss. 1, pp. 1-19, https://doi.org/10.1016/j.ejtl.2024.100144 This Version is available at: https://hdl.handle.net/10419/325214 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/4.0/ Contents lists available at ScienceDirect EURO Journal on Transportation and Logistics journal homepage: www.elsevier.com/locate/ejtl Spatio-temporal prediction of freeway congestion patterns using discrete choice methods Barbara Metzger a,∗, Allister Loder b, Lisa Kessler a, Klaus Bogenberger a aChair of Traffic Engineering and Control, Technical University of Munich (TUM), Arcisstrasse 21, 80333 Munich, Germany bProfessorship of Mobility Policy, TUM School of Social Sciences and Technology, Technical University of Munich (TUM), Arcisstrasse 21, 80333 Munich, Germany ARTICLE INFO Keywords: Traffic state prediction Mixed logit Congestion patterns Freeway traffic ABSTRACT Predicting freeway traffic states is, so far, based on predicting speeds or traffic volumes with various methodological approaches ranging from statistical modeling to deep learning. Traffic on freeways, however, follows specific patterns in space–time, such as stop-and-go waves or mega jams. These patterns are informative because they propagate in space–time in different ways, e.g., stop and go waves exhibit a typical propagation that can range far ahead in time. If these patterns and their propagation become predictable, this information can improve and enrich traffic state prediction. In this paper, we use a rich data set of congestion patterns on the A9 freeway in Germany near Munich to develop a mixed logit model to predict the probability and then spatio-temporally map the congestion patterns by analyzing the results. As explanatory variables, we use variables characterizing the layout of the freeway and variables describing the presence of previous congestion patterns. We find that a mixed logit model significantly improves the prediction of congestion patterns compared to the prediction of congestion with the average presence of the patterns at a given location or time. 1. Motivation Crawling, stop and go, or total stoppage — traffic jams are a phenomenon that occurs in road traffic all over the world. Speed in congestion ranges from slow rolling or stop and go to a complete stoppage in traffic. Congestion lengths vary from short stretches of roads to miles-long lines of vehicles. They can also widely vary in time: some congestion events dissipate in minutes, while others can paralyze traffic for hours. A crucial element in the study of congestion is the analysis of historical data. In the data sets, a considerable amount of information on each congestion’s spatial and temporal position can be found. This information is of great importance as it provides insights and can help to make data-based decisions on how to avoid, resolve, or predict congestion. Using historical data, statements can be made about the probabilities of ‘congestion’ or ‘no congestion’. These statements and predictions about the traffic state help to increase traffic safety on the roads in general and the freeways in particular. Predicting traffic conditions is especially important for freeways because they have a high traffic density and are considered major arterials. On freeways, congestion and traffic delays can have a significant impact, not only because of delays, but they also increase the risk of accidents due ∗Corresponding author. E-mail address: [email protected] (B. Metzger). to abrupt braking and the resulting rear-end collisions. We want to provide information on the probability of congestion, especially for freeway operators because it affects many vehicles or people in this context. The speed can be very high, especially without a general speed limit, and adequate prediction methods are not yet integrated. With the information from our model, the freeway operators can adjust and prepare the traffic information systems and traffic management systems for the traffic for the following day or the following hours/minutes. According to Li et al. (2022), accurate and dependable short-term traffic forecasting holds a crucial significance in numerous key applications within the field of traffic and transportation. By providing trustworthy predictions of traffic quantities, short-term traffic forecasting enables traffic managers to promptly respond and make informed decisions to prevent congestion. Predicting congestion patterns and, thus, the duration, size, and impact of a congestion event contributes to improving traffic safety. We focus on four congestion patterns mentioned by Karl et al. (2019). These are Jam Wave,Stop and Go,Wide Jam, and Mega Jam, whereas they range from a short speed breakdown to more distinctive congestion in time and space. The differentiation is conducted https://doi.org/10.1016/j.ejtl.2024.100144 Received 14 March 2023; Received in revised form 10 September 2024; Accepted 13 September 2024 EURO Journal on Transportation and Logistics 13 (2024) 100144 Available online 18 September 2024 2192-4376/© 2024 The Authors. Published by Elsevier B.V. on behalf of Association of European Operational Research Societies (EURO). This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ ). B. Metzger et al. via virtual trajectories to simulate driving vehicles through a congested space–time domain. We refer to the original paper for a more detailed description. Customized actions can be developed against individual congestion patterns to reduce the effects of congestion or keep congestion small. No method still predicts the traffic state, which is simultaneously simple, fast, and comprehensible for traffic managers. The prediction of speeds and, thus, the prediction of travel times or travel time losses for entire routes are necessary for routing and route selection. For the rudimentary estimation of the danger of ‘‘traffic jam’’, the prediction of the exact speed is not necessary. Defining and predicting traffic conditions using specific thresholds rather than forecasting directly observed traffic variables has the advantage that the resulting condition classifications – such as Jam Wave,Stop and Go, Wide Jam, and Mega Jam – provide more meaningful information about traffic problems. As a result, more targeted measures can be initiated. These categorizations may be easier for discrete models or machine learning systems to predict because, unlike traffic variables such as speed and density, which are often volatile, they represent clearly defined and measurable criteria that can be captured more reliably in real-time. In the best case, the traffic flow can be optimized in advance by the model developed here, and a traffic jam does not occur at all or does not evolve to the same extent without prior knowledge and optimized traffic management. This paper uses a discrete choice model: the multinomial logit model, to address the predictability of congestion patterns on freeways. This approach already existed in a comparable version in a 1998 paper. Still, it was not pursued further, and now we want to contribute and apply the latest computing technology to this methodology (Cottrell, 1998). By forecasting congestion events, freeway operators can control and interpret traffic optimally. When developing helpful tools for freeway operators, they must be easy to understand and logically interpretable. Also, the results are comprehensible and provide reliable and fast guidance. The proposed model is a statistical model that evaluates the historical traffic data of the freeway segment. Fig. 1 sketches the methodology applied in the paper: (1) Data preparation and processing; (2) Division of the study area into cells; (3) Spatio-temporal superimposition of historical data; (4) Prediction of the probability of a congestion pattern in a space–time cell. In Kessler et al. (2020), an approach is described to identify congestion hot spots for these individual congestion patterns on a freeway stretch. The proposed algorithm first isolates coherent congested clusters from a spatio-temporally discretized speed matrix and then assigns one of the four congestion patterns to each cluster. Considering the spatial and temporal start and end points of each cluster, along with its assigned congestion pattern, accumulated occurrences of congestion can be determined. Regarding this analysis, the question arises about how the individual congestion events relate to each other spatially and temporally. The hot spot analysis of Kessler et al. (2020) showed that clusters of individual congestion patterns over time and road segments exist but lacks the question of whether individual congestion events are also predictable by historical data. Many authors have tried to predict various variables in traffic using many machine learning and artificial intelligence methods. However, we want to develop an easy-to-interpret model suitable for public authorities. This paper is structured as follows. First, we describe the state of the art of traffic prediction models and the usage of statistical regression models in this field of research. Section 3presents the data used for this study and explains four congestion patterns proposed in Karl et al. (2019). Thereafter, the prediction model is described in detail. Section 5contains the model implementation results and the application of the methodology proposed in Molloy et al. (2021) to the data derived from the German autobahn A9. The last section gives a discussion, a summary, and an outlook on future research. 2. State of the art This section contains the current state of research on different prediction capabilities of congestion, congestion patterns, and currently used statistical prediction models in this field of study. 2.1. Congestion prediction In the literature, traffic prediction can be done using different techniques. These techniques can be grouped into several categories: statistical models such as Yildirimoglu and Geroliminis (2013), tree modeling such as Zhao et al. (2009), intelligence techniques such as Mahmuda et al. (2021) and Dia (2001), and mixed modeling. The critical challenges in predicting traffic, particularly the importance of observability and uncertainty, have been identified in recent research (Li et al.,2022). It was noted that perfect observability, where all state variables can be fully reconstructed from available measurements, is a theoretical but not practical condition for perfect predictability of traffic systems. While strict determinism and perfect observability theoretically guarantee predictability, both conditions are difficult to meet in transportation networks due to unobservable variables such as demand, route choice patterns, and individual behavior. As a result, predicting traffic in large networks remains challenging, as highlighted by Li et al. (2022), and requires the development of interpretable models with traceable parameters. Kerner’s traffic flow theory (Kerner and Rehborn,1996;Kerner, 2001,2004;Kerner et al.,2004;Kerner,2009;Palmer et al.,2011) describes the phenomenon of traffic congestion in detail. This theory distinguishes three phases of traffic: free-flow, synchronized flow, and wide moving jam. However, it should be emphasized that our study does not only divide congested traffic into two phases but we analyze four spatio-temporal patterns. Many existing approaches deal with the prediction of travel times for specific routes. van Lint et al. (2002) presents a recurrent neural network approach for freeway travel time prediction. The proposed recurrent neural network addresses these limitations by implicitly capturing spatio-temporal relationships derived from a state-space formulation of the travel time prediction problem. van Lint (2006) showed that by using an ensemble of State-Space-Neural-Network (SSNN) models, a measure of the reliability of each prediction can also be generated. A method combining stationary detector data and probe vehicle data to predict freeway congestion fronts was presented, as highlighted by Rempe et al. (2017). In Rempe and Bogenberger (2019), a forecast algorithm was applied to urban road networks with farther links taken into account. A clustering algorithm was used to analyze the level of congestion within clusters, which was integrated into a K-nearest neighbors travel time prediction algorithm. Rempe et al. (2021) proposed a physically informed deep learning method to estimate traffic conditions at locations without detection. The authors found that this method improved the estimation and understanding of traffic density in real freeway traffic data through data fusion. Two methods for predicting the breakup point of traffic congestion were presented by Lee et al. (2014). The first method uses a model that records spatial and temporal changes in congestion on road networks with multiple junctions. In contrast, the second method uses an algorithm that finds similar historical congestion patterns and calculates drainage timing from these templates. Weather data were analyzed and used for congestion prediction in Lee et al. (2015), where big data processing technology and multiple linear regression analysis explored the relationship between weather and traffic congestion. CPM-ConvLSTM, a novel deep learning-based model for traffic congestion prediction, was presented by Di et al. (2019). The model leverages the observed congestion patterns to predict the congestion level of road segments by using a spatial matrix to incorporate both the congestion patterns and the spatial relationships between road segments. EURO Journal on Transportation and Logistics 13 (2024) 100144 2 B. Metzger et al. Fig. 1. Methodology described in the paper. The Congestion-based Traffic Prediction Model (CTPM), which improves predictions using congestion propagation patterns, was introduced, as demonstrated by Nagy and Simon (2021). Performance studies show a significant improvement in forecasts. The new model PCNN described in Chen et al. (2018) uses a deep convolutional neural network to analyze periodic traffic data and make short-term congestion predictions, incorporating techniques such as time series convolution and multi-grained learning to capture local time dependencies and multi-scale traffic patterns. Experiments with real traffic data show that PCNN performs significantly better than comparable methods. The estimation and prediction of origin–destination (OD) flow is also a crucial issue and a possible solution in the fields of dynamic traffic management and traffic estimation and prediction systems, according to Antoniou et al. (2006). Advances in traffic data collection technologies have provided an abundance of untapped data that can be utilized in OD estimation and prediction. This study introduces a flexible and general methodology to estimate and predict OD flow, incorporating information from various conventional and innovative traffic data sources, such as automatic vehicle identification systems and probe vehicles. Many of the methods mentioned specialize in forecasting travel times but not traffic conditions. The expected travel time is a statement for the individual driver and should be available before the start of a trip. Likewise, a constant update of the travel time prediction for the selected or possible alternative routes is handy. The prediction of the traffic condition and, if applicable, the size of congestion is mainly important for the freeway operators. The individual road user benefits from the generally safer and smoother traffic flow. In the literature, this has not yet been applied to freeways with a comprehensible modeling approach to the best of our knowledge. 2.2. Multinomial logit estimation Logit models are frequently used for predictions in the transport sector, mostly for predicting accidents and their severities or the mode choice of road users. Mixed logit models were developed to analyze driver injury severities and the differences between single-vehicle and multi-vehicle crashes on rural two-lane highways in New Mexico over two years, as demonstrated by Wu et al. (2014) and Dong et al. (2018). A series of significant contributing factors are considered, including driver behavior, weather conditions, environmental characteristics, roadway geometric features, and traffic compositions. The research findings indicate significant differences in the causal attributes determining driver injury severities between these two types of crashes. The tendency of drivers to engage in crash avoidance maneuvers based on certain circumstances and characteristics of the accident is the focus of research by Kaplan and Prato (2012). The analysis is conducted utilizing a mixed logit model that represents the selection among five emergency lateral and speed control maneuvers. A methodology that addresses a driver’s decision of a damaged car following a traffic accident is presented in Hamed and Al-Eideh (2020). The choice set includes three alternatives. A random parameter (mixed) logit model with heterogeneity in the means is specified and estimated to gain more insight into the driver’s decision-making process following a traffic accident. In Li et al. (2010), the discrete choice model is also used to predict the duration of an incident. There, a multinomial logit model is constructed to predict the duration of an incident. 62,941 recorded incidents of the Beijing Transportation Management Bureau were used for the development, and another 10,000 records for the validation. The average relative error of the model is 27.3%. Route choice models were used for estimation approaches to obtain mode-specific values of travel time savings, based on data from Zurich, as demonstrated by Schmid et al. (2021). They use the estimates of the value of leisure and the values of benefits derived from the conditions experienced while traveling. Combining these two values at their individual level allows for a detailed analysis of the value of time assigned to travel distributions. The same code is used from Schatzmann and Axhausen (2021) for the study for the examination of the substitution effects of long-distance buses in Switzerland (50 km+) and how they EURO Journal on Transportation and Logistics 13 (2024) 100144 3 B. Metzger et al. Fig. 2. Sketch of considered road stretch: stationary detectors (dashed green), interchanges (cyan), ramps (magenta). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) will affect the mode choice of trains and cars. They estimate standard Multinomial Logit and Mixed Multinomial Logit models to account for unobserved heterogeneity in cost and travel time sensitivities and also incorporate typical social-demographic variables. 2.3. Congestion prediction using mixed logit models A discrete choice model that predicts recurrent congestion on freeways was developed, as described by Cottrell (1998). This paper from the year 1998 presents a model that estimates the probability of recurrent congestion at existing and potential freeway bottlenecks. The objectives of the model were to accept data that are commonly collected, evaluate existing conditions, predict future conditions, and evaluate the effects of mitigation measures. A logistic regression equation was developed from 163 observations. The model correctly classifies 83% of the data locations used in its development but should be tested on additional data. To the best of our knowledge, there is no other paper in this field of research, and the named model was not further pursued. We consider the potential of modeling with discrete choice methods to reach a very high level today, as there is now a higher and denser data availability and also the computational capacities have grown enormously. 3. Data This section introduces the road stretch, presents all data used in the study and describes the data processing. 3.1. Freeway data The proposed methodology is applied to data collected on the freeway A9 in Bavaria, Germany. As a test site, the freeway stretch from Holledau to Munich is chosen with a stretch length of 50 km. Holledau is located at km 480, Munich at km 530 (Fig. 2). Speed data from inductive loops are available from 44 sensors with an average spacing of 1.2 km, which gathers speed data minute-byminute. Data were recorded in eight months in 2019. Table 1 ASM parameter values used for smoothing local speed data. Parameter Value Spatial grid distance 500 m Temporal grid distance 1min Speed in congestion −18 km/h Free-flow speed 80km/h Crossover from free to congested traffic 80km/h Width of the transition region 10 km/h 3.2. Data interpolation All speed data are interpolated using the Adaptive Smoothing Method (ASM), introduced by Treiber and Helbing (2002,2003), Treiber et al. (2011) and Schreiter et al. (2010). Briefly summarized, raw data of a sparse input source are smoothed in two traffic-characteristic directions: 𝑣𝑐𝑜𝑛𝑔 denominating the wave speed in congested traffic conditions, and 𝑣𝑓𝑟𝑒𝑒 denominating the wave speed in free-flow conditions. In a discrete time–space domain, the resulting complete speed matrices 𝑉𝑐𝑜𝑛𝑔(𝑡, 𝑥)and 𝑉𝑓𝑟𝑒𝑒(𝑡, 𝑥)are combined cell-wise: 𝑉𝐴𝑆𝑀 (𝑡, 𝑥) = 𝑤(𝑡, 𝑥)𝑉𝑐𝑜𝑛𝑔(𝑡, 𝑥) + (1 − 𝑤(𝑡, 𝑥))𝑉𝑓𝑟𝑒𝑒(𝑡, 𝑥).(1) The weight 𝑤(𝑡, 𝑥)is adaptive and favors low speeds: 𝑤(𝑡, 𝑥) = 1 2(1 + tanh(𝑉𝑡ℎ𝑟 − min(𝑉𝑐𝑜𝑛𝑔(𝑡, 𝑥), 𝑉𝑓 𝑟𝑒𝑒(𝑡, 𝑥)) 𝛥𝑉 ))(2) with 𝑉𝑡ℎ𝑟 a threshold where weight 𝑤(𝑡, 𝑥)equals to 0.5 and 𝛥𝑉 a parameter to control the steepness of the weight function. As an example, the resulting interpolated speed distribution from Jul 13, 2019, is illustrated in Fig. 4. The 𝑥-axis shows the time running from early morning to late evening. The 𝑦-axis shows the locations in the direction of travel (from bottom to top). Each cell of the space– time domain is colored depending on the speed, which is indicated in the color bar on the right. To derive such a figure, the ASM parameter values given in Table 1 are applied. They refer only to the preparation – especially the interpolation – of the speed data out of the stationary detectors for the congestion pattern detection. 3.3. Congestion classification The congestion classification introduced by Kessler et al. (2020) is then applied to the data set. The algorithm detects individual congestion elements based on the algorithm (Kessler et al.,2018) and assigns them to one of the congestion patterns defined by Karl et al. (2019). The schematic workflow of the methodology is sketched in Fig. 3. The parameter values of the congestion pattern definition can be found in Table 2. Starting from a discretized speed distribution, congested cells (speed below a threshold 𝑣𝑐𝑟𝑖𝑡) are identified. A cluster is a set of neighbored congested cells. Using virtual trajectories, clusters that are located close to each other are merged. Close to each other means that the travel time in uncongested conditions between two clusters is not larger than a threshold 𝑡𝑚𝑒𝑟𝑔𝑒. This way, the final congestion clusters are determined. In order to assign a congestion pattern to each cluster, the convex hull (to make the cluster unique) is embedded in free-flow conditions, again crossed by virtual trajectories, and the speed profile of each single trajectory traversing the congestion cluster is analyzed. Depending on the frequency and the duration of each trajectory in congested conditions, one of the four congestion patterns is assigned to the cluster. The sensitivity of the methodology has been assessed in Karl et al. (2019). It is a robust algorithm that can identify and classify occurring congestion even beyond different data sources (Kessler and Bogenberger,2023). It is also conceivable that the detection and classification work very well on the fused data. This is relevant for sections of freeways where more than one data source is available. A possible approach for the fusion would be Kessler et al. (2021). We refer EURO Journal on Transportation and Logistics 13 (2024) 100144 4 B. Metzger et al. Fig. 3. Computation of congestion clusters and classification of congestion type (Kessler et al.,2020,2018;Karl et al.,2019). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Table 2 Parameter values to identify and classify congestion clusters according to Karl et al. (2019). Parameter Value Velocity threshold 𝑣crit 40 km/h Free-flow speed 𝑣freeflow 120 km/h Minimum free-flow time between congested areas 𝑡merge 4 min Minimum size of congested areas 𝐴𝑚𝑖𝑛 12 km min Maximum duration of Jam Wave 𝑡𝐽𝑎𝑚𝑊 𝑎𝑣𝑒 3 min Minimum duration of Mega Jam 𝑡𝑀𝑒𝑔𝑎𝐽𝑎𝑚 30 min Minimum number of speed drops 𝑛𝑆𝑡𝑜𝑝𝑎𝑛𝑑𝐺𝑜 2 Temporal offset of starting trajectories 𝑡𝑟5 min Minimum share of congestion patterns (2 patterns) 𝑛2patterns 0.51 Minimum share of congestion patterns (3 patterns) 𝑛3patterns 0.41 to the original papers (Kessler et al.,2018;Karl et al.,2019;Kessler et al.,2020;Kessler,2021) for further details. Applying this congestion classification to the speed distribution in Fig. 4, the result is depicted in Fig. 5. In the literature mentioned above, the origin and justification of the four congestion patterns are explained in great detail. For the prediction with statistical models, mainly recurrent congestion is relevant. However, the data analysis shows that each of the four defined congestion patterns occurs more frequently in location and time. A list containing all identified congestion patterns and these interpolated speed distributions of the considered eight months in 2019 over the 50 km stretch forms the basis for further investigations. 3.4. Data processing We divide the investigated stretch into equidistant space–time cells and store the known information per cell. The spatial cell size amounts to 500 m, the temporal to one minute. For each of the cells, spatial and temporal information is stored in addition to the congestion pattern and speed. Spatial information is whether the segment comprises a ramp (exit or parking lot), an interchange, and how far from Munich the cell is located. Temporal information is about the weekday and a binary value on the rush hour. This information is assigned to the individual cells of every investigated day. Thus, it is impossible that Table 3 Sample characteristics. Characteristics Value Percentage Days 238 Jams 836 Location-sections (X) 100 Time-sections (T) 840 Total cells 20 088 269 1.0000 Free-flow cells 19 199 348 0.9558 Jam Wave cells 28 850 0.0014 Stop and Go cells 548 318 0.0273 Wide Jam cells 224 528 0.0112 Mega Jam cells 87 225 0.0043 Weekday cells 14 397 222 0.7167 Weekend cells 5 691 047 0.2833 Rush hour cells 7 165 836 0.3567 No rush hour cells 12 922 433 0.6433 Cells with a ramp 2574 952 0.1282 Cells without a ramp 17 513 317 0.8718 Cells with an interchange 1 187 113 0.0591 Cells without an interchange 18 901 156 0.9409 several congestion patterns are assigned to one cell since only one congestion pattern can be present at any given date, time, and location. In addition, each cell is assigned the current speed at that point in time. Table 3 gives an overview of the cell properties. The entire data set (50 km and from 6 am to 8 pm) consists of 20,088,269 cells. From these, 95.58% are without congestion. 0.14% of the cells are assigned to Jam Wave, 2.73% to Stop and Go, 1.12% to Wide Jam, and 0.43% to Mega Jam.Fig. 6 shows the distribution of both the frequency and the location of the clusters of the congestion patterns, respectively. White means very rare or not at all, and black means frequent occurrences. Regarding temporal characteristics, 72% of all cells are flagged as weekday and 36% as rush hour (defined from 6 to 9 am and from 4 to 7 pm). The proportion of the individual congestion patterns in the total number of cells can be seen in the graphs (a) to (e) in Fig. 6. The percentages of the respective congestion patterns are shown in black. In the graphs, the time is limited from 6 am til 8 pm (the time axis represents the minutes of a day) because congestion is hardly present EURO Journal on Transportation and Logistics 13 (2024) 100144 5 B. Metzger et al. Fig. 4. Interpolated speed distribution. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Fig. 5. Classified congestion clusters. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) during night hours. In these graphs, it can also be seen that free flow is predominantly detected. The spatial criteria conditions can be seen in Fig. 2. There are three interchanges in the interior of the entire stretch, excluding the intersection with B2R at the very end of the freeway. In addition, there are eight ramps and two parking lots along the stretch. The stretch contains several areas with a different number of lanes. It varies from two to four lanes. 13% of the cells have the information that there is a ramp for an exit or a parking lot, and 6% of the cells are flagged with the information that there is an interchange in the area. Initial probabilities can already be drawn from the cells. For example, Fig. 7 shows the probability of Stop and Go congestion on weekdays. This diagram shows a hot spot on weekdays of Stop and Go traffic in the morning hours around km 520–530. In the following, a mixed logit model is developed that can predict if there is a specific congestion pattern or free-flowing traffic for the EURO Journal on Transportation and Logistics 13 (2024) 100144 6 B. Metzger et al. Fig. 6. Spatio-temporal distribution of the jam patterns. next minutes. The model predicts the congestion pattern while considering both the speed and the congestion patterns in the temporally and spatially preceding cells and the infrastructural parameters. To compare the added value of labeling the prevailing cells with congestion patterns, we set a model that only includes the speed and the infrastructural parameters. The logit model predicts the probability of the presence of one of five traffic patterns: free-flow, Jam Wave, Stop and Go, Wide Jam, or Mega Jam. We select a mixed logit model to model the discrete outcomes or choices and a mixed model to correct for the panel data structure of our model (Train,2009). In contrast to deep learning methods, explainable parameter values are retrieved that can be used for modeling and decision-making. This also enhances its applicability in traffic operations centers as the model’s behavior is more transparent. EURO Journal on Transportation and Logistics 13 (2024) 100144 7 B. Metzger et al. Fig. 7. Most likely weekday congestion pattern. For a better prediction of the current congestion pattern, the cells that are spatially upstream and temporally ahead of the current cell are considered. The triangular area of the cells, which are zero to five steps in space and in time before the current cell builds a funnel, are considered; see Fig. 8. The properties of these cells in the funnel and the cells on the diagonal at the funnel (marked in bold in Fig. 8) are added to the already given information of each individual cell. 4. Modeling the congestion prediction This section describes the setup of the prediction model and its estimation. In Section 4.1, two very simple naive forecasting methods from data analysis are used. The results are in Table 7. Section 4.2 shows the structure of two variants of a mixed logit model. The estimation model formulas are presented in the last section of this chapter. We used the package mixl in R (Molloy et al.,2021). Predicting congestion patterns using a mixed logit model is not based on random utility theory, and no human utility function is associated with each congestion pattern. Here, we use the model structure of the mixed logit model to predict congestion patterns as they are in the data in an explanatory way. Our result is the latent propensity score of congestion patterns. 4.1. Base model specification When analyzing the basic strategies for predicting traffic patterns, it becomes clear that simplicity, especially at the beginning of an analysis, often takes precedence over complexity when selecting methods. Initial forecasts benefit from naive methods due to their simplicity, their economy of calculation, and their usually easy possibility of interpretation. There is a variety of naive methods: two of these methods are characterized by their practicality and applicability to our problem: the persistence model, which assumes that the future value reflects the immediate past, and the mean value method, which makes forecasts based on the average of past data. The persistence model Base model P is remarkable as it assumes short-term continuity of traffic flows and is therefore suitable for stable conditions. However, it is not sufficient during the beginning and termination of congestion. This has safety implications and emphasizes the need for accurate predictions at critical moments. In contrast, the averaging approach uses historical frequency to anticipate future conditions and provides a statistical prediction: Base model A. The very simple basis variation that analyzes the data used to determine the probability of a traffic condition in a cell. An example of a result of the basic variant for weekdays is shown in Fig. 7. These naive forecasting models serve as a valuable benchmark. If sophisticated algorithms fail to outperform the baseline established by these methods, their application can be reconsidered. However, the results must also be treated with caution and scrutinized carefully. A simple method can perform well, but it does not necessarily reflect complexity. This illustrates the importance of such elementary prediction techniques in the early stages of traffic pattern analysis. 4.2. Mixed logit model specification The data set with approx. 20 million cells is used as a basis for the logit model (see Table 3). The data set is divided into a training set of 80% of random days and a test set consisting of the remaining 20% of the days. This way, we get more than six months of training data and almost two months of test data. Then, two variants (models I and II) and a basic investigation of the model are created. The simple basis variation that analyzes the data visualized in Fig. 1 determines the probability of a traffic condition in a cell. An example of a result of the basic variant for weekdays is shown in Fig. 7. Model I calculates the probability of a traffic condition from historical data and spatial and temporal information. The input data are the historical data of the traffic jams and the parameters of the individual cells: the information on ramps, parking lots, or interchanges, and weekday or rush hour. To estimate the probability of the current traffic pattern, the speed is analyzed and included in the determination of the likelihood of the current cell. The development of model II has the same parameters as model I but with the labeling of the congestion patterns. More precisely, the model I only has the infrastructural information and speed information of the current and the previous funnel cells. In contrast, model II additionally uses the information on the congestion patterns in the funnel cells. This aims to demonstrate the benefit of historical knowledge of the congestion pattern in the previous cells and allows the analysis of the impact of congestion patterns for the prediction. Model II also considers the speed in cell −3(see Fig. 8). The speed of this cell allows us to infer the congestion pattern by the different frequencies and values of the speed. Cell −3has a value frequently lower than 50 km/h for Stop and Go, whereas the speed for Wide Jam is significantly more often above 75 km/h (see Fig. 9). Additionally to the speed in cell −3, the difference of the speed of cell −5to cell −1is considered in model II. Fig. 10 shows that the speed difference is often zero for Stop and Go as the general speed value is low. For Wide Jam, the speed drop is often more recognizable. It should be noted that the number of observations per congestion pattern is different. The plots in Figs. 9 and 10 are normalized. To include the characteristic spatiotemporal propagation of congestion, we use a co-moving coordinate system in the modeling through the funnel. The explanatory variables are summarized in the following list, and their hypothesis on the effects of prediction is explained: •Average speed in funnel 𝑠𝑝𝑒𝑒𝑑𝑓𝑢𝑛𝑛𝑒𝑙: This parameter is used for the first sequence of models I and II. We expect that if the average speed in the funnel is lower, the probability of congestion is higher. •Location to Munich 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑀𝑢𝑛𝑖𝑐ℎ: The nearer the city and thus the metropolitan area, the higher the probability of congestion. •Speed cell −3𝑣𝑐𝑒𝑙𝑙−3: The speed in cell −3of the funnel is shown in detail in Fig. 9. The higher the speed in this cell, the more likely are the congestion patterns Wide Jam or Mega Jam. •Rush hour 𝑟ℎ: The cells have the binary information on rush hour. The assumption is that at rush hour times, smaller congestion patterns such as Jam Wave and Stop and Go will occur more likely. EURO Journal on Transportation and Logistics 13 (2024) 100144 8 B. Metzger et al. Fig. 11. Spatio-temporal distribution of the application example. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Table 9 Hit rate of application example for prediction horizon of one, five and 30 min. Prediction at time Hit rate of 1 min prediction Hit rate of 5 min prediction Hit rate of 30 min prediction 690 1 1 0.965 698 0.980 0.976 0.949 700 0.980 0.974 0.947 870 0.980 0.976 0.989 875 0.970 0.974 0.994 880 0.980 0.988 0.998 6. Discussion, conclusion, and outlook In this paper, we applied a mixed logit model, a discrete choice model, to predict congestion patterns using empirical data from a freeway in Germany. We make use of the congestion patterns introduced by Karl et al. (2019). The data set comprises the daytime hours from 6 am to 8 pm and a stretch length of 50 km. Four different models were built for prediction: (i) a base model (A) that predicts congestion patterns by the average occurrence of a congestion pattern at a given location; (ii) a second base model (P) which uses the actual observed pattern from the last period as a forecast for the next period; (iii) a mixed logit model only with infrastructure effects and speed (Model I); (iv) a mixed logit model with infrastructure effects, speed and information on the existence of previous congestion patterns (Model II). However, while Base Model P shows slightly better results in terms of certain metrics, it is a reactive model that simply extends the current traffic state without considering broader contextual factors. In contrast, Model II, despite showing lower scores, offers a more advanced and proactive approach by incorporating infrastructure, speed, and previous congestion patterns. This makes Model II better suited for real-world traffic management, where anticipating and preventing congestion is crucial for improving safety and traffic flow. The model is a complex statistical tool that provides detailed insights into decision-making processes. The model can choose between the five traffic patterns (Free Flow, Jam Wave, Stop&Go, Wide Jam, and Mega Jam). The biggest influencing parameters are the presence and distribution of the congestion patterns in the funnel. Here, the funnel mainly takes into account the congestion front movement. It is conceivable that the vehicle movement, i.e., almost perpendicular to the congestion front, also influences the forecast — similar to the anisotropic smoothing kernel. We conclude that the approach to predicting congestion pattern probabilities with discrete choice methods and then analyzing the result for the most likely pattern is applicable and a promising avenue to improve the prediction of traffic patterns. However, the free-flow pattern is a dominant outcome in the data, which can result in overfitting issues. We will further extend the parameter set by adding some dynamic information about the start or end of each congestion pattern. In addition, more attention will be paid to how artificial intelligence, e.g., neural networks, can support the prediction of congestion patterns – like van Cranenburgh et al. (2022) presented in their work – but without losing the comprehensibility as in the logit model presented here. In conclusion, the practical implications of this novel and innovative approach are at least twofold: First, the prediction of congestion times comprises the spatio-temporal extent of the congestion patterns in the space–time diagram. This can exceed the prediction of traffic patterns in a single segment. Therefore, additional information is available for traffic management centers and map operators to improve their predictions. This prediction can be conceptualized in two steps, firstly for a long-term forecast using only a simple static accumulation analysis of the congestion patterns and including the information about the location and time or date. The second step is to use the results of the newly developed multinomial logit model to produce a short-term forecast of up to 30 min. There are advantages here regarding traffic safety, optimization of traffic flow, and knowledge of possible diversions in the event of major and atypical traffic jams. This is particularly important for freeways, as these are (still) the main traffic arteries — EURO Journal on Transportation and Logistics 13 (2024) 100144 15 B. Metzger et al. Fig. 12. Predicting congestion patterns; Start of congestion. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) EURO Journal on Transportation and Logistics 13 (2024) 100144 16 B. Metzger et al. Fig. 13. Predicting congestion patterns; End of congestion. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) EURO Journal on Transportation and Logistics 13 (2024) 100144 17 B. Metzger et al. especially in Germany. Second, the applicability of a prediction based on a mixed logit or related model in traffic management centers is feasible. In particular, as the model parameters can be re-estimated on a rolling horizon basis and these parameters are explainable, it is a feature that is difficult to achieve in novel deep learning approaches. This is evidently an advantage to getting the support of traffic managers and decision-makers to implement such a prediction model. CRediT authorship contribution statement Barbara Metzger: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing – original draft, Writing – review & editing. 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