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Ideally, a multitude of steps has to be taken before a commercial implementation of a pedestrian model is used in practice. Calibration, the main goal of which is to increase the accuracy of the predictions by determining the set of values for the model parameters that allows for the best replication of reality, has an important role in this process. Yet, up to recently, calibration has received relatively little attention within the field of pedestrian modelling. Most studies focus only on one specific movement base case and/or use a single metric. It is questionable how generally applicable a pedestrian simulation model is that has been calibrated using a limited set of movement base cases and one metric. The objective of this research is twofold, namely, to (1) determine the effect of the choice of movement base cases, metrics, and density levels on the calibration results and (2) to develop a multiple-objective calibration approach to determine the aforementioned effects. In this paper a multiple-objective calibration scheme is presented for pedestrian simulation models, in which multiple normalized metrics (i.e., flow, spatial distribution, effort, and travel time) are combined by means of weighted sum method that accounts for the stochastic nature of the model. Based on the analysis of the calibration results, it can be concluded that (1) it is necessary to use multiple movement base cases when calibrating a model to capture all relevant behaviours, (2) the level of density influences the calibration results, and (3) the choice of metric or combinations of metrics influence the results severely.

The creation and implementation of a commercial pedestrian simulation will, ideally, consist of multiple steps. One of those steps is calibrating the model whereby the goal is to increase the accuracy of the model predictions by obtaining the parameter set that results in the best replication of reality. As such, calibration is an important step.

Yet, up to recently, calibration has received relatively little attention within the field of pedestrian modelling [

It is questionable how generally applicable a pedestrian simulation model is that has been calibrated using a limited set of movement base cases. Campanella, Hoogendoorn, and Daamen [

To overcome the problem of obtaining different results when using different movement base cases and/or metrics, three multiple-objective calibration frameworks have been proposed in recent years which try to take a more inclusive approach. Wolinski et al. [

So, even though these works illustrate that the choice of the combinations of movement bases and metrics will influence the optimal parameter set obtained during calibration, all three studies have their limitations. For example, they do not explicitly examine the effect of the level of density which might be a relevant factor given that work by Campanella et al. [

Given these observations the objective of this research is twofold. Firstly, the objective is to determine the effect of the choice of movement base cases, metrics, and density levels on the calibration results. Secondly, the objective is to develop a multiple-objective calibration method for pedestrian simulation models to determine the aforementioned effects, taking into account the stochastic nature common to many microscopic pedestrian models.

This study aims to add value to the current body of literature by means of a more extensive study of the impact of calibration framework setup on the validity of a pedestrian simulation model. This extension provides, among other things, novel insights into the effect of the level of density of the movement base case and more detailed insights into the effect of using a range of metrics in the calibration process. Furthermore, this study features a different type of model (i.e., vision-based model [

The rest of the paper is organized as follows. Section

This section introduces pedestrian dynamics (PD), a microscopic pedestrian simulation model developed by INCONTROL Simulation Solutions. It offers a user the ability to model the movement behaviour of pedestrians at all three behavioural levels (strategic, tactical, and operational). Though, in this research pedestrians only have one activity, namely, to walk from their origin to their destination via a single route, and hence there is no need to model the activity choice, the activity scheduling or the route choice. The model featuring the operational walking dynamics is discussed in more detail underneath.

The operational behaviour of the INCONTROL model consists of two parts, i.e., route following and collision avoidance, which together determine the acceleration of a pedestrian at every time step. PD determines the acceleration of a pedestrian by the combination of ‘social forces’ and a desired velocity component. The pedestrian itself is represented by a circle with a radius

The desired velocity is determined according to the method proposed by Moussaïd et al. [

A pedestrian chooses the direction that results in the most direct path to its desired destination given the presence of both static and dynamic obstacles.

A pedestrian chooses the speed that, in case there is an obstacle in the preferred direction, results in the lowest time-to-collision whereby this time is always larger than

The pedestrian only takes into account obstacles that are within its field of vision (

There are two important notes regarding the implementation of this method in PD, namely:

The desired destination of each pedestrian is determined using the Indicative Route Method proposed by Karamouzas, Geraerts, and Overmars [

As is the case for many pedestrian models, PD is stochastic by nature (i.e., two simulations with exactly the same parameters and input but with different seeds result in different outcomes). In this study there are three main causes for this stochasticity, namely, the preferred speed, the initial destination point, and the exact point of origin. The first contributes to the stochasticity due to the fact that every pedestrian is randomly assigned a preferred speed from a given distribution. The latter two causes of stochasticity are points whose location influences the desired destination and whose exact position is a randomly determined location within a respective origin or destination area. The fact that the model is stochastic by nature has to be taken into account during the calibration and is discussed in more detail in the next section.

A sensitivity analysis is performed to determine to which particular parameters the model is sensitive. This section describes the methodology of the sensitivity analysis and presents the results of this analysis. The results of the sensitivity analysis are used to determine which parameters should be incorporated in the calibration process, as recalibrating all model parameters is not feasible within the time frame of this study. How the results are used to determine the calibration search space and why it is not feasible to include all parameters is explained in more detail in Section

The goal of the sensitivity analysis is to determine which of the 7 model parameters of the INCONTROL model (see Table

The seven parameters included in the sensitivity analysis.

Route following: | Preferred clearance |

Side pref. update factor | |

| |

Collision avoidance: | Relaxation time |

Viewing angle | |

Viewing distance | |

Min. desired speed | |

Personal distance |

The distribution of the instantaneous speeds of all pedestrians is used as the sole metric. This distribution contains all instantaneous speeds of all pedestrians and all replications. This metric is chosen because the distribution of the speeds is able to give insight into both the efficiency of the flow (a higher mean speed indicates a more efficient flow) and into the underlying behaviour (e.g., a high variance can indicate that interactions are not solved efficiently causing pedestrians to change their speed a lot).

The Anderson-Darling test [

To limit the amount of simulations only first-order effects are investigated. Note that the number of replications is already extensive due to the incorporation of seven scenarios and a vast number of replications to account for model stochasticity. Figure

Overview of the sensitivity analysis methodology. The process depicted in the figure is performed for all combinations of the 7 scenarios and 7 parameters.

For all these new distributions of speeds accordingly the following two checks are identified: (a) is the new distribution significantly different from the default distribution according to the Anderson-Darling test and (b) are the differences between the means and standard deviations of the distributions larger than one would expect based on the influence of the stochasticity (for more details see [

For a more detailed description of the methodology the reader is referred to [

Based on the methodology described above the following results are obtained. Firstly, the model is not sensitive to changes in the “Preferred clearance” parameter and changes in the “Viewing distance” parameter. Even in high density cases the model is not sensitive to changes in the viewing distance parameter. This is most likely the result of the fact that PD only takes into account the four closest pedestrians within the viewing field, which might all reside well within this radius.

In general, the model is not sensitive to changes in the “Personal distance”, the “Side pref. update factor”, and the “Min. desired speed”. In the case of the “Personal distance”, the model is slightly sensitive to changes in this parameter in the case of the bottleneck scenario. In the case of the “Side pref. update factor”, the model is slightly sensitive to the t-junction high density scenario. The model is also slightly sensitive to changes in the “Personal distance” for both scenarios. However, as the maximum differences between the means and the standard deviations are at most 2%, we conclude that within the

The only parameter to which the model is sensitive in all seven scenarios is the relaxation time. The model is, furthermore, sensitive to the viewing angle in all four high density scenarios. Figure

Results of the sensitivity analysis.

Relaxation time-mean

Viewing angle-mean

Relaxation time-std

Viewing angle-std

In conclusion, overall the INCONTROL model is not very sensitive to changes in many of the parameters given the

This section presents the reasoning behind the newly developed calibration methodology. Figure

Overview of the multiple-objective methodology where

All of these parts are discussed in more detail in this section. First the scenarios are identified. Accordingly, the metrics and the objective function are presented. This section furthermore elaborates on the optimization method and the manner that the stochasticities of the pedestrian simulation model are handled.

Contemporary, several datasets are available that feature the movement of pedestrians in multiple movement base cases and a similar population of pedestrians, among others [

Overview of the layout of the four movement base cases used during the calibration. (a) Bidirectional flow. (b) Unidirectional corner flow. (c) Merging t-junction flow. (d) Bottleneck. In the figure the hatched areas indicate the measurement areas; the dashed lines the location where the flow is measured and in the case of the bottleneck the grey area indicates the waiting area at the start of the simulation.

In this multiple-objective framework four different metrics are used to identify how different metrics impact the calibration results. In this research the choice is made to use two metrics at the macroscopic level, the flow and the spatial distribution, and two at the mesoscopic level, the travel time distribution and the effort distribution. These metrics are chosen because, on both levels, they describe different aspects of the walking behaviour. Microscopic metrics, i.e., trajectories, are not used for three reasons. Firstly, calibration based on trajectories requires a different approach than calibrating based on macroscopic and mesoscopic metrics. It would require many more simulations to use both microscopic and mesoscopic and/or macroscopic metrics and due to time limits this was not considered to be viable within this study. Secondly, the current approaches for calibrating based on trajectories do not deal with the stochastic nature of the model. Lastly, since pedestrian simulation models are mostly used to approximate the macroscopic properties of the infrastructure (e.g., capacity, density distribution) [

Only the travel times of those pedestrians who successfully traversed the whole measurement area during the measurement period are included in the distribution of the travel times.

In this research multiple objectives are combined into a single objective using the weighted sum method [

In order to make a fair comparison between objectives, normalization is necessary, as the metrics have different units and different orders of magnitude. Table

Normalization values.

| |
---|---|

Flow | 1.0 |

Spatial distribution | 0.18994 |

Travel time-mean | 0.99107 |

Travel time-std | 0.20728 |

Effort-mean | 0.04345 |

Effort-std | 0.00953 |

The objective function for a given metric and scenario is given by the normalized Squared Error (SE) which for the macroscopic metrics is determined by (

The objective functions for a given set of metrics and scenarios are combined into a single objective function as follows:

In this research a grid search is used to obtain the optimal parameter set, as it provides the researcher with more insight into the shape of the surface of objective space. The disadvantage of using a grid search is that other optimization methods, e.g., Greedy and Genetic algorithms, can potentially be faster. However, these methods do run the risk of getting stuck in a local minimum and do not necessarily give a good insight into the shape of surface of the objective space. As can be derived from (

Rudimentary calibration of PD has already been performed by the company. Thus, instead of calibrating all model parameters, the presented calibration method will be used in this research to identify the correctness of the variables with respect to which this model is most sensitive, namely the relaxation time and the viewing angle. Even though the model is less sensitive with respect to the radius, this parameter will also be included in the calibration as initial tests of the implementation of the scenarios illustrated that in the case of the bidirectional high density scenario the default radius of this model produced problematic results. The search space is defined as follows:

The upper and lower boundaries of the relaxation time and viewing angle are determined by a deviation of

For the radius the upper boundary is equal to the default value, the lower bound has a deviation of

As this research focuses on the effect of density levels, the metrics that are part of the objective function and movement base cases, the search space is not continuous and has been restricted in order to create reasonable computation times and a reasonably good insight into the shape of the objective function.

Similar to most pedestrian simulation models, PD is stochastic in nature. Therefore, it is essential to determine the minimum amount of replications one would need in order to assure that statistical differences are due to differences in model parameters instead of stochasticity in the model realization.

In this research the required number of replications is determined using a convergence method similar to [

Tests showed that regardless of the chosen values for

In this section the results of the individual objectives (a combination of a single scenario and a single metric) are discussed. Figures

Results of calibrating the model using a single objective. Graphs (a)-(d) show, per combination of metric and scenario, how the objective values (calculated according to (

Flow

Spatial distribution

Travel time

Effort

Flow

Spatial distribution

Travel time-mean

Effort-mean

Travel time-std

Effort-std

These plots provide insight into how the objective values are distributed but primarily show the order of magnitude of the minimal objective value if the model would be calibrated using only a single objective. The smaller the objective values the better the model results fit the reference data. By using a logarithmic scale the figure clearly illustrates how well the model fits to the data (when the optimal parameter set is used) and how this differs between the different scenarios and metrics.

Figures

Figures

Figures

Figures

In the case of the effort metric Figures

All figures show that both the size of the minimal objective value and the distribution of the errors depend on the particular combination of scenario and metric. Furthermore, the figure illustrates that the model can generally reproduce the metrics related to the performance of the infrastructure (the flow and travel time) better than those more related to the underlying microscopic and macroscopic pedestrian dynamics (spatial distribution and the effort). However, regarding the difference between the performances of the model on the different metrics, three things have to be noted.

Firstly, as Liao, Zhang, Zheng, and Zhao [

Secondly, as pointed out by Benner, Kretz, Lohmiller, and Sukennik [

Lastly, some metrics might be more sensitive to changes in parameters of the pedestrian simulation model that are not taken into account in this study than the parameters included in the search space of the calibration. The sensitivity to these ‘other’ parameters is due to two things. First, the sensitivity analysis was performed before the choice of metrics for this calibration. Second, the speed distribution was used in the sensitivity analysis to determine significant differences in model result. Thus, this suggests that it is not only important to include multiple scenarios in the sensitivity analysis but also multiple metrics. This would ensure enhanced insight into the model’s sensitivity and hence also better insight into which are the most important parameters to include in the search space during calibration.

This research aims to determine how different choices regarding scenarios and metrics influence the calibration and not calibration of the InControl model. Therefore, differences between the simulation model results and the data are not investigated in more detail in this paper.

In this section the results of different calibration strategies are discussed. First, a general analysis of the results is performed based on the obtained optimal parameter sets for all of the 16 combinations. Afterwards, the results of different strategies are compared to determine the influence of movement base cases, density levels and metrics. Table

Tested combination of scenarios and metrics, where the acronyms identify the metrics (i.e., Q = flow, SD = spatial distribution, Eff = effort, and TT = travel time) and the scenarios (i.e., B-H = bidirectional high, B-L = bidirectional low, B = bottleneck, C-H = corner high, C-L = corner low, T-H = T-junction high, and T-L = T-junction low).

Combination | Metrics | Scenarios | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Q | SD | TT | Eff | B-H | B-L | C-H | C-L | T-H | T-L | B | |

1. Bidirectional high (B-H) | x | x | x | x | x | ||||||

2. Bidirectional low (B-L) | x | x | x | x | x | ||||||

3. Corner high (C-H) | x | x | x | x | x | ||||||

4. Corner low (C-L) | x | x | x | x | x | ||||||

5. T-junction high (T-H) | x | x | x | x | x | ||||||

6. T-junction low (T-L) | x | x | x | x | x | ||||||

7. Bottleneck (B) | x | x | x | x | x | ||||||

8. Flow (Q) | x | x | x | x | x | x | x | x | |||

9. Spatial distribution (SD) | x | x | x | x | x | x | x | x | |||

10. Travel time (TT) | x | x | x | x | x | x | x | x | |||

11. Effort (Eff) | x | x | x | x | x | x | x | x | |||

12. High density scenarios (HD) | x | x | x | x | x | x | x | x | |||

13. Low density scenarios (LD) | x | x | x | x | x | x | x | ||||

14. All scenarios - Macro (Macro) | x | x | x | x | x | x | x | x | x | ||

15. All scenarios - Meso (Meso) | x | x | x | x | x | x | x | x | x | ||

16. All combined (All) | x | x | x | x | x | x | x | x | x | x | x |

Table

Calibration results, where

Combination | | Relaxation | Viewing angle | Radius |
---|---|---|---|---|

1. Bidirectional high | 0.1329 | | | 0.15296 |

2. Bidirectional low | 0.0588 | | | 0.19120 |

3. Corner high | 0.0561 | 0.395 | | 0.23900 |

4. Corner low | 0.0742 | | 61.50 | 0.23900 |

5. T-junction high | 0.1190 | 0.590 | | 0.21998 |

6. T-junction low | 0.0468 | | 68.25 | 0.23900 |

7. Bottleneck | 0.1093 | 0.395 | 68.25 | 0.20076 |

8. Flow | 0.0146 | | 59.25 | 0.20076 |

9. Spatial distribution | 0.2015 | 0.575 | 59.25 | 0.21988 |

10. Travel time | 0.1814 | | 59.25 | 0.15296 |

11. Effort | 0.1798 | 0.500 | | 0.23900 |

12. High density scenarios | 0.2647 | 0.575 | | 0.21032 |

13. Low density scenarios | 0.0722 | 0.500 | | 0.23900 |

14. All scenarios - Macro | 0.1444 | 0.545 | 59.25 | 0.21988 |

15. All scenarios - Meso | 0.2012 | | 59.25 | 0.15296 |

16. All combined | 0.1814 | 0.575 | | 0.21032 |

The search space is limited both by its boundaries and by its precision. To obtain insight into the likelihood that the results would change significantly (i.e., the location of the optimal parameter set changes significantly) an analysis is performed. The analysis is based on visual inspection of two types of graphs.

Figure

The deviation from optimal GoF versus the distance to the optimal parameter set.

Bidirectional low

Bottleneck

Bidirectional high

Travel time

Figure

Figure

The main conclusion of the visual inspection of these graphs for all 16 combinations is that for most of the low density cases, the exception is the T-junction low case, and the flow case it is likely that the location of the optimal parameter set could change significantly if the precision of the search space in increased. For all other cases this is not the case.

Figure

Examples of surface plots showing how the objective value changes over the search space. The green dot identifies the location of the optimal parameter set.

For example, Figures

Figures

Performing this analysis for all 16 combinations yields the conclusion that, for all cases where the previous analysis did conclude that an increase in the precision is unlikely to change the results, an extension of the search space is likely to increase the differences between the cases instead of decreasing it.

Overall, the analysis shows that for some cases the location of the optimal parameter set could change significantly if the search space if changed. However, it also shows that the large differences between the optimal parameter sets, currently found, are also likely to be found if the search space is adapted. Hence, the authors expect that an extension of the search space results in even larger differences in the optimal parameter sets than the differences identified in this paper.

In order to illustrate the differences between the optimal parameter sets a cross-comparison of the goodness-of-fit is performed. These comparisons are based on the difference between the optimal GoF of combination A and the GoF of combination A when the optimal parameter set of combination B is used (see (

Figure

The distribution of the objective values per movement base case combination is displayed by the boxplots. The markers indicate, per used parameter set, how much the objective value would deviate from its optimum if the optimal parameter set, obtained using another (combination of) movement base case(s), would be used. The combinations are identified by their acronyms as found in Table

The figure shows the distribution of the objective values for the different movement base cases. The markers depict the objective value if the optimal parameter set obtained using another movement base case is used. The difference between the location of the marker and the minimal objective value, as indicated by the boxplot, indicates the difference in GoF.

The boxplots show that, generally, the low density cases have a higher GoF and that they are less sensitive to changes in the parameter set regarding their fit to the data. Furthermore, for both the low and high density cases the corner scenarios seem least sensitive to changes in the parameter set. The data, moreover, illustrates that in all cases the GoF of the individual movement base cases decreases when the parameter set based on another movement base case or a set of movement base cases is used. However, the size of the decrease clearly depends on the scenario as well as which scenario’s optimal parameter set is used. A few notable observations can be made regarding the decreases in GoF.

Firstly, in the case of the high density bidirectional scenario (B-H) all other optimal parameter sets from the other high density combinations lead to a similar decrease in GoF. This is also the case for the low density bidirectional scenario (B-L). However, in this case the optimal parameter set obtained when combining all three low density scenarios results in a far smaller decrease in GoF indicating that the bidirectional scenario has a strong influence on the objective function of this combination. Overall, both observations indicate that the bidirectional movement base case contains behaviours which are not well captured by other movement base cases.

Secondly, the high density t-junction scenario (T-H) also seems to contain behaviours which are not captured well by other high density movement base cases. Furthermore, as the decrease of GoF is clearly smallest for the optimal parameter set obtained using a combination of all four high density scenarios, it is clear that the objective function of this combination is strongly influenced by the t-junction scenario.

Thirdly, in the cases of the low density corner (C-L) and t-junction scenarios (T-H, T-L) the decrease in GoF is very small when the optimal parameter set of the other scenario is used. Table

Overall, based on this analysis we conclude that different movement base cases contain different behaviours which are not necessarily captured when the model is calibrated using other movement base cases. The exceptions are the corner and t-junction base cases at low densities (C-L, T-L). Using an optimal parameter set obtained by combining multiple movement base cases mitigates this problem somewhat. However, this still results in clear decreases in the GoF for all movement base cases.

In Figure

The distribution of the objective values per density level combination is displayed by the boxplots. The markers indicate, per used parameter set, how much the objective value would deviate from its optimum if the optimal parameter set, obtained using the same (combination of) movement base case(s) but a different density level, would be used. The combinations are identified by their acronyms as found in Table

The data also illustrates that the decrease in GoF of the combination of high density scenarios is larger when the optimal parameter set of the combination of low density is used than vice versa. This remains the case even if the bottleneck scenario is omitted from the high density set, such that the high density set contains exactly the same movement base case as the low density set. In this case the decrease in GoF for the high density set becomes even larger.

Overall, it can be concluded that the level of density of the scenario does influence the calibration results. Therefore, it is concluded that it is more important to include the high density scenarios than the low density scenarios. Furthermore, depending on the movement base case, it can even be the case that the low density variant can be omitted as it will not add any value.

In Figure

The distribution of the objective values per metric combination is displayed by the boxplots. The markers indicate, per used parameter set, how much the objective value would deviate from its optimum if the optimal parameter set, obtained using another (combination of) metrics(s), would be used. The combinations are identified by their acronyms as found in Table

These results show that the choice of metrics does influence the results of the calibration. Depending on the choice of metric or combination of metrics, different optimal parameter sets are found which in turn lead to different results regarding the GoF.

The findings of this research regarding the influence of the movement base cases are found to be consistent with both [

Hence, this research confirms that one needs to use multiple movement base cases when calibrating a model intended for general usage. However, when the intended use of the model is more limited (i.e., it does not need to accurately replicate all movement base cases and or metrics), it might be preferred to use a limited set of movement base cases during the calibration, in particular, given the fact that the GoF of the individual movement base case decreases when multiple movement base cases are used during the calibration.

The level of density also influences the calibration results. Thus, depending on the intended use of the model different density levels should be taken into account during the calibration. Furthermore, this study concludes that it is more important to incorporate high density scenarios. As a result, one can omit some of low density scenarios, in particular the bidirectional and corner low density scenarios.

This study also finds that the calibration results depend on the choice of metric or combinations of metrics. Depending on the combination of metrics, also the choice of objective function and normalization method influences the results. Consequently, depending on the usage of the model, one should decide which metric or metrics are most important and how to reflect the difference in importance of these metrics when combining multiple objectives into one.

The results also show that the relaxation time is the only parameter to which the model is sensitive to in all scenarios. Its exact value thus has a large impact on how well the simulations fit the data. Reference [

A number of things have to be noted when reflecting on the method of handling the multiple objectives. In light of the goal of this study, the method presented in this study was chosen to assure as little as possible bias towards any of the metrics or scenarios. However, if one calibrates a model given a certain type of model usage, one might use different weights or even different optimization method. For example, one can search for the Pareto optimal solution [

Though this study is more extensive than previous studies, it still has a number of limitations. Firstly, due to limitations of the available dataset, this study did not include a crossing movement base case. So, it is unclear whether and to what extent the crossing movement base case contains behaviours which are not captured by other movement base cases. More research, in which also effects of the intersecting movement base cases are included, is needed to create a comprehensive overview of the effect the choice of movement base cases has on the calibration. Secondly, only one microscopic model was used in this study. Therefore, as such, it is unclear to what extent the current findings can be generalized and whether the conclusions of this study also hold for other microscopic models. The fact that the results are consistent with [

All in all, the results show two important things. Firstly, the optimal parameter set obtained using a single or limited amount of objectives does not always provide an accurate fit of the model to the data for other combinations of scenarios and metrics. Besides that, using multiple objectives (e.g., using multiple high density scenarios) to calibrate the model decreases the GoF of the model to the data for all the individual objectives. These two conclusions imply that the intended use of the model should be taken into account when deciding which scenarios, metrics, objective functions and method for combining multiple objectives one should use. These results also raise an important question. Is the implicit assumption that the behaviour of the pedestrians is independent of the flow situation, which is at the foundation of most pedestrian simulation models, valid? This research cannot answer this question because of, among other, its limitations on the number of parameters included in the search space. Hence it is an interesting topic for future research.

Lastly, these results show that a model only provides accurate results for scenarios and metrics that the model has been calibrated and validated on. Using the model for predictions of other scenarios and metrics is likely to result in large inaccuracies. Hence, it is essential that calibration or validation attempts include multiple scenarios and multiple metrics.

The empirical data used in this study can be found at

The authors declare that there are no conflicts of interest regarding the publication of this paper.

The research presented in this paper is part of the research program “Allegro: Unravelling slow mode traveling and traffic: with innovative data to a new transportation and traffic theory for pedestrians and bicycles” (ERC Grant Agreement no. 669792), a Horizon 2020 project which is funded by the European Research Council. Additionally, the research presented in this paper has been presented at the Transportation Research Board 97th Annual Meeting (2018, Washington DC, United States).