The term shared space refers to a design concept which aims to improve road safety and quality of the sojourn in those urban areas where pedestrians demand using the space. A primary issue for traffic engineers in the planning and design phase is whether to choose this solution instead of a classical street layout. In this regard, it would be very useful to evaluate in advance the quality of traffic flow. This work provides a procedure to analyze the output of the microsimulation for shared spaces and to get an estimation of the quality of traffic movements. To include comfort and safety aspects a new holistic indicator  is developed. Three elements are considered, namely the traffic environment, the interaction apprehension and the physical movement. The procedure could also be applied to existing shared spaces, by analyzing the trajectory of road users captured on a video survey.

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1 Introduction

Considering the street design of urban city centers, traffic engineers may want to assign not only a movement function to the road environment, to allow the circulation of traffic, but also a place function, to make the street a public space for social and recreational activities. In those cases, traffic engineers may consider the possibility of a shared space design, rather than a classical one where road users are physically separated. The benefit is represented by a calmed motorized traffic environment, which is expected to improve pedestrian movement and comfort and to increase street vitality. A shared space aims to let traffic regulate itself, forcing road users to interact with each other spontaneously and negotiating the space via eye contact. These results are achieved by a minimized usage of traffic signs and marks, by removing kerbs, and by creating a continuous paved surface with minimum demarcation between the motorized and non-motorized area.
However, putting all road users together in a single shared surface without accurate rules, which is very fascinating from the social and urbanistic point of view, it involves many risks which must be properly evaluated.

Firstly, a safety problem must be considered. When road users are supposed to interact spontaneously, the overall number of traffic conflicts increases indeed. The main cause of concern lies in the weak users – pedestrians and cyclists – that are supposed to interact with road users with high operational speeds and physical features, i.e. motorized vehicles. To allow a safe interaction among them it is therefore important to reduce the intensity of traffic conflicts, first at all by reducing the operative speed of vehicles. Usually this is achieved by setting low speed limits on one hand, and by increasing the caution of motorists by a very basic and empty design on the other hand (thanks to the risk compensation effect).
Secondly, there is a problem of quality of traffic movements, namely the Level of Service of road users. Since the shared space designs are alternatives to classical ones – e.g. a bidirectional road with a pedestrian crossing – it would be interesting to compute the performances in terms of LOS for all road users, in order to compare them with classical alternatives. However, such an estimation is currently difficult to achieve for two main reasons. First at all, proper microsimulation tools, capable to simulate the behavior of road users, are not at disposal of traffic engineers; moreover, even if they were available, a methodological framework to evaluate the LOS of all traffic mode in shared spaces is currently missing.
The aim of this paper is to provide an approach to estimate the LOS of road users in a shared space in the design phase. Given that, in a near future, very likely reliable microsimulation tools for shared space will be available, this work provides a procedure to analyze the output of the microsimulation and to get an estimation of the quality of traffic flow. A real case study in the district of Bergedorf in Hamburg (introduced in Sec. 3) is used to test the plausibility of a delay-based approach to estimate the LOS (Sec. 4). A new holistic indicator to evaluate the quality of pedestrian flow is developed in Sec. 5, which includes not only quantitative aspects, like delay time, but also qualitative ones, like comfort.

2 Background

The concept of “shared space” originally refers to the idea of letting road users interact with each other in a road environment which is lacking lane markers, curbs, signs and traffic rules. The idea comes from the traffic engineer Hans Monderman, who firstly put this design approach into practice in the Dutch region of Fryslan during the 1970s, achieving interesting results in terms of road safety. According to this principle, the meagre and bare road design should lead road users in a state of alert and induce them to negotiate their own path with each other, respecting simple social and interaction rules rather than the classical ones.

This concept does not correspond entirely with the meaning that the term “shared space” has in the German context nowadays. The Bundesanstalt für Straßenwesen refers to them as a design concept which aims to improve road safety and the quality of the sojourn in those urban areas where pedestrians demand to use the space [1]. The way the increase in road safety and sojourn quality is achieved includes effectively an essential, minimal design (a continuous paved surface, for example), but the absence of traffic regulation, usually performed in the Dutch case, is not implied. Shared spaces in Germany are regulated as Verkehrsberuhigter Geschäftsbereich, i.e. by a 10 or 20 km/h speed limit, or as Verkehrsberuhigter Bereich, that is the equivalent of the Home Zone in the United Kingdom. In the first case car drivers have only to respect a low speed limit; in the second case pedestrians take priority over car traffic, which must drive at walking speed and neither endanger, nor obstruct pedestrians.

However, when the road is designed with the aim to decrease the dominance of car traffic and to promote pedestrian movement (usually called “pedestrian friendly design”), road users spontaneously tend to negotiate priority by social mechanisms and eye contact, and to pay less attention to traffic rules. Generally speaking, the original principle of spontaneous interaction is achieved in the German context under a clear regulation background, that does not limit the spontaneity of road users, but operates as a legal necessity only.

Traffic engineers may consider to design a road according to the shared space principle in those places where pedestrians claim to use the space, and motorized traffic is preferably not to be excluded at the same time. This design approach is an alternative to the classical one – generally intended as a road design where motorized and non-motorized vehicles are kept separated – when the aim is to increase pedestrian movement and comfort and to reduce the dominance of motor vehicles [2]. The real challenge of such an approach is to make pedestrians confident with the space despite the presence of motorized traffic. If motorized traffic is not calmed – e.g. by keeping an appropriate inflow and by moderating car speed - pedestrians would minimize interaction with car users because they would be perceived as threatening and dangerous. In these cases, it could be observed that they cross the street only perpendicularly, usually by walking at higher speeds as the desired ones or by waiting for cars to pass instead of trying to win the space. The undesirable result is that road users are behaving as in a classical design (i.e. considering the shared zone as a classical carriageway for car traffic) but safety and comfort would be compromised because the interaction is not controlled and contained, but imposed.

The success of a shared space design, in existing sites, could be evaluated by analyzing car and pedestrian behavior and movement. KARNDACHARUK et al. [3] evaluated pedestrian and car performances in shared space environments by analyzing the profiles of pedestrian demand, the activity of the pedestrians (movement or occupancy) and their trajectories, together with vehicular traffic volume and speed. The before-after comparison showed that, despite pedestrian usage of the space has not increased, the shared space design had encouraged pedestrians to move along and across the space (pedestrian movement has increased) while motorized vehicles showed consistent reductions in speed and volume (car dominance has decreased).

Moreover, conflict analysis could help in understanding the play of forces among motorized and non-motorized vehicles. KAPARIAS et al. [4] conceived a procedure to analyze conflicts between pedestrians and cars in shared space environments, based on indicators like Time To Collision (TTC), severity and complexity of the evasive action and distance to collision. The idea behind is that, in comparison to a classical design, the number of traffic conflicts reasonably raises but the intensity of them should decrease. Severe conflicts in fact discourage pedestrian to share the space with cars, which turns out in a decrease of safety perception.

In the design phase, the evaluation of the quality of a shared space solution is hard to achieve. Traffic engineers at the moment could only rely on specific guidelines, which could assist in the design process on the basis of technical recommendation and real examples [2], [5]. In Germany the reports of the Forschungsgesellschaft für Straßen- und Verkehrswesen [6] and of the Bundesanstalt für Straßenwesen [1] provide an application reference for traffic engineers. The first one contains practical design issues and recommendations, which are useful to test the feasibility of a shared space solution in a preliminary phase (examined in depth in Sec. 4). The second one offers a detailed analysis of a series of shared space already existing, with a collection of data about traffic volumes, traffic conflicts, accessibility and the quality of sojourns.

Detailed information about the behavior of traffic in shared spaces would be possible if a reliable microsimulation tool were available. Despite microsimulation models for shared spaces in the recent years made good progresses, there is actually no complete and exhaustive tool to realistically simulate them. GIBB [7] modelled pedestrian-motorist interaction in the VISSIM environment by substituting cars with groups of moving pedestrians (called dummy) and setting up priority rules for conflict areas to regulate the interaction. Research has already focused on shared space modeling, namely ANVARI et al. [8] in London, the project MixME (SCHÖNAUER et al. [9]) in Vienna and Graz, and the project MODIS - MultimODal Intersection Simulation (RINKE et al. [10]) in Hannover and Braunschweig. In view of the improvements in the field of shared space microsimulation, the current work shows which outputs of the software are useful to evaluate the quality of traffic.

3 Case study

The investigation for relevant indicators of traffic quality in a shared space is conducted by the help of a real case study, namely a shared space street in the district of Bergedorf in Hamburg, Germany. The site location is described in Sec. 3.1, while the process of data acquisition is in Sec. 3.2.

3.1 Site location

Data survey has been carried out in the area in front of the railway station of Bergedorf. In the period of 2008-2012 the area was redesigned according to the shared space principle and the new train and bus station was built. As showed in Fig. 1, the layout includes a gray toned paved surface, which is delimited by the train station on the north-west, a shopping mall on the south-west and retail stores on the east.

Bild 1: location. Aerial view (a) and picture from the bus station in point P (b)

The surface is crossed diagonally by a road segment (here called circulation zone) where vehicular traffic is allowed to pass through – and it represents an intensive pedestrian cross between the square and the train station. The circulation zone is overall 63 meters long, it is ruled as Verkehrsberuhigter Geschäftsbereich and has a speed limit of 20 km/h. It must be accounted that according to this regulation priority is assigned to vehicular traffic, while crossing pedestrians and cyclists must wait to cross the road until a sufficient gap between cars is found. Despite that, the data survey has shown that cars and pedestrians negotiate the space spontaneously, giving priority to each other as a courtesy rather than follow road regulation.

3.2 Data acquisition

Video recordings were conducted on Saturday, April 2nd 2016 from 2 to 5 p.m. with two video cameras, mounted at an elevation of about 7 meters. Cameras were placed at opponent borders of the circulation zone, across from each other, so that all road users in the area could be properly captured (Fig. 1a, points C1 and C2). The result of the video survey can be seen in Fig. 2, where the pictures of the two cameras represent the same moment (as a reference, please notice the white car).

Bild 2: Video output. Camera C1 (a) and Camera C2 (b)

The aim of video observation was to obtain useful information about the road users’ movement and behavior. More in deep, the aim was to estimate the spatio-temporal evolution of the trajectory of all road users, namely motorists, pedestrians, cyclists and motorcyclists.

The trajectories of road users were manually recorded by the software tool Tracker for a period of 30 minutes. The interval was chosen among the overall video recordings because of the high presence of vehicular traffic (rush period for motorists). Position of road users was extracted at a time step of 0.5 seconds and the final trajectories were than superimposed onto the real map. The data thus obtained are the basis for the analysis that is performed in the next section.

4 Evaluation using German guidelines

The “Hinweise zur Straßenräumen mit besonderem Querungsbedarf” [6] are useful in the planning phase to check if a shared space solution could generally be considered, i.e. to test if the basic conditions for a share space exist. The guidelines identify six control indicators, easy to measure in the field, which can be compared to defined thresholds (see Tab. 1). Beyond basic recommendations about operating speed and longitudinal length, the key point of the matter is to keep under control the volumes of the two traffic movements, namely longitudinal traffic, composed by motorized vehicles, and crossing traffic, made of pedestrians and cyclists. While the first one is supposed to be not close to the road capacity for a bidirectional two-lane road, the second one must exceed a minimum value, computed as an hourly crossing density. Moreover, the ratio between these traffic volumes has to be above 0.5 (at least one pedestrian crossing every two cars travelling longitudinally). The idea behind is that motorized traffic must not predominate over the non-motorized one, otherwise pedestrianswould feel uncomfortable and they would prefer to tolerate car dominance instead of trying to interact.

Tabelle 1:Benchmarks for the application of the Shared Space concept according to FGSV, compared with the present case study

The indicators for the case study of Bergedorf have been computed among the 30-min rush period, then multiplied per 2 to obtain hourly rates. As can be seen in the fourth column of Tab. 1, both motorized and non-motorized traffic volumes match well with the recommended values - in particular, crossing traffic volume is significantly above the minimum value. As a consequence, the ratio between crossing and longitudinal traffic is also greatly respected (one car correspond to more than 6 pedestrians). However, it must be noticed that the data related to crossing traffic should be computed in the overall day and not in the rush period. Nonetheless, the recorded remaining 2.5 hours do not show a notable decrease in crossing traffic, which would suggest that the value may not be drastically reduced. Finally, operating speed and longitudinal length of the shared space are compliant with the thresholds.

Summarizing, the comparison of the observed values with the benchmarks shows that the test area represents a shared space according to the German guidelines. However, to gain more detailed information about the operation of the shared space, i.e. the LOS, the simulation of traffic movements in a software environment is necessary.

4.1 Level of Service according to HBS

For the estimation of the LOS of an intersection, the Handbuch für die Bemessung von Straßenverkehrsanlagen (HBS), as well as the Highway Capacity Manual (HCM), provide an approach based on the computation of the delay time for every traffic relations. Whether the delay time is computed in an existing case or in a microsimulation environment, it is compared with thresholds values in order to assess the LOS category (from A to F).

With the goal to evaluate the LOS in a shared space following the delay approach, the T-junction case of HBS is used as an analogy (S5.2.2, Intersection without traffic light). The sketch from the manual is shown in Fig. 3a, while the proposed approach for a shared space is presented on the right in Fig. 3b. The delay for T-junction matters for 6 car traffic relations and 3 pedestrian and cyclist ones; for the shared space case, only two car traffic streams must be considered (longitudinal traffic), while all the pedestrian and cyclists movements from one side to the other of the circulation zone are considered altogether.

Bild 3: Sketch of traffic streams in a T-junctionfrom HBS (a) and a Shared Space, proposed here (b)

Firstly, it must be noticed that pedestrian traffic is not crossing the intersection on a fixed point of the road but on the overall length. For this reason, one unique O/D relation is identified for all pedestrians (F12).

Secondly, in the shared space case not all traffic streams cross the circulation zone undisturbed, like traffic streams 2,3, and 8 in the T-junction (major-street through vehicles are assumed to experience zero delay). In fact, despite the regulation of a shared space allows priority to the longitudinal or the crossing traffic, in the reality there is always a negotiation of priority from both sides. This means that all traffic streams are potentially delayed and must be considered for LOS evaluation.

Thirdly, cyclists are not crossing on specific facilities but use all the area and drive in different directions. Many of them are driving according to longitudinal traffic, others may cross as pedestrians over F12. This implies difficulties when computing the delay time, which are explained later.

Following the example of the T-junction, LOS could be appositely evaluated by computing the delay time for all traffic streams, then finally compared with the benchmarks of HBS for the case of “regulation with priority sign” (S5.2.2), reported in Tab. 2. The way the delay time is computed in the specific case of share spaces will be covered in the next subsection.

Tabelle 2: Benchmarks: mean delay time for the Level of Service estimation according to HBS 2015 (S5 Urban streets, intersection without traffic light)

4.2 Delay time in a Shared Space

Delay time at an intersection is defined as the time difference between the real time spent to cross it and the time that would be needed if no priority has to be given (free-flow condition).
In the practical application, the value is computed for every road user and successively averaged for every traffic relation for a fixed time period, e.g. 1 hour.
For car traffic the time in free-flow is computed by assuming a desired speed and considering the length of the circulation zone, where the interaction takes place (Eq. 1). Desired speed can be assumed as the planned v85, since we expect cars to drive approximately at the same speed.

Formel (1) siehe PDF.

For the delay calculation of pedestrian traffic, the computation of the crossing time in free-flow conditions is needed. In absence of car traffic, a pedestrian would probably cross the shared zone according to desire lines (represented by the F12i relations in Fig. 1b) and with a desired speed. This is assumed to be the free-flow condition, which would lead the pedestrian to the destination by the most direct path, according to the preferred walking pace. Indeed, delay is triggered by deviations from the preferred trajectory or decelerations.

A real example is shown in Fig. 4: A group of two pedestrians walks slowly in order to understand the intention of the approaching car; as the car decelerates, the group deviates to cross the road perpendicularly and increases the walking pace. It must be observed that the presence of the car has led the group to evacuate the circulation zone as soon as possible, i.e. by accelerating and deviating to the left at the same time. Both deviation and acceleration are typical reactions to conflicts with motorized vehicles, and must be both accounted in the delay definition.

Bild 4: Pedestrian crossing the shared zone: video frame (a), eye ́s bird view (b) and speed profile (c)

The delay time for a single pedestrian is computed according to Eq. 2.

Formel (2) siehe PDF.

The desired path ld is assumed as the direct connection between origin and destination, which are located close to the longitudinal borders of the circulation zone (represented in Fig. 4a and 4b respectively by a black circle and an asterisk); the desired speed vd is known as it is given by the modeler as an input for the simulation.

Delay time for cyclists can be computed following the approach of pedestrians. It must, however, be remembered that in free-flow conditions cyclists do not ride over direct lines, because mechanical constraints of the cycle forces them to use smooth trajectories with limited curvatures. An approach for computing free-flow trajectories for cyclists has been developed by RINKE et al. [10] but is not used in this paper.

4.3 Application

Delay time is computed for car and pedestrian traffic in the case study of Bergedorf. The aim is to test the capability of delay time to represent the quality of the traffic movement, in conjunction with its usability. Bicycle traffic is not considered here since the amount of the cyclist observed is too low to draw conclusions.

4.3.1 Car delay

With reference to Eq. 1, v85 is assumed as the speed limit of the circulation zone, l is its total length, and ti is the overall time spent by the car i to pass through the zone. The delay time is computed for every car observed in the video in the 30-min investigation period.

The value of mean delay, used for the determination of the LOS category, results from the aggregation of single delay times over a fixed time period, usually the 60-min interval with the highest demand. Since here the investigation period covers only a limited time, the analysis is performed by one-minute intervals and dividing by lane (Fig. 5). The delay is compared with the benchmarks listed in Tab. 2, which are indicated with different horizontal lines

Bild 5: Delay time of cars for both lanes, gathered in 1-minute intervals

It can be noticed that the mean delay varies highly from minute to minute depending on the temporary traffic conditions. Car delay is caused not only by the interaction with pedestrians, but also by the necessity to adapt the driving behavior to the speed of the vehicle ahead (car- following).

Delay time seems to be a good measure of traffic quality for motorized vehicle in shared spaces. Firstly, the computation is simple and straightforward. Secondly, delay time can be computed also in design alternatives (e.g. traffic light, zebra crossings) and compared with the shared space scheme. The threshold for the LOS classification could be eventually set up as a function of the length of the shared space l, which affects the value of delay time.

4.3.2 Pedestrian delay

The desired path for pedestrians is assumed to be the direct connection between the first and the last tracked point detected in the video, which are always close to the boundaries of the circulation zone. The desired speed is more difficult to compute: Even while walking in free flow conditions, walking pace is not steady but it oscillates due to the alternation of steps, whose length can vary during the trip.
In order to find an acceptable value of desired walking speed, the speed profile for each pedestrian is analyzed. The aim is to extract the part of the curve where speed oscillates around the same value for a reasonable number of time steps. As an example, a real pedestrian crossing the intersection is taken and its profile is plotted in Fig. 6a. The curve can be divided into three parts: The first one (A) where speed decreases in reaction to a conflict situation; the second one (B) where the pedestrian accelerates after the conflict is solved; the third one (C) where he proceeds undisturbed with an approximately constant walking pace. The goal is to identify the part C and to extract the mean value of this segment. This is carried out by a three-step methodology.

1. Clustering. K-means algorithm is performed on a two-dimensional dataset with walking speed and acceleration. An example is shown in Fig. 6b, where 4 clusters have been detected. For every cluster j, the centroid is identified by the mean walking speed and the mean acceleration

2. Cluster evaluation. For every cluster j, the statistic Kj is computed:

Formel (3) siehe PDF.

where is the size of the cluster j.

3. Minimization of the statistic K. The minimum value of is assumed to be representative of the free-flow condition (in Fig. 6b, the cluster 3 has the minimum Kj).

In order to get a better approximation, the overall process is repeated 3 times by setting the number of clusters (in step 1) to 2,3 and 4. The value of which belongs to the cluster with the minimum is assumed as the desired speed.

Bild 6: Crossing pedestrian. Speed profile (a) and speed-accelerationclustering(b)

The desired speed has been computed for all crossing pedestrians according to the methodology described above and showed a mean value of 1.28 m/s with a standard deviation of 0.29. Given the observed time needed by each pedestrian to cross the circulation zone, the delay time can be easily computed by Eq. 2.

4.4 Limits of delay time for pedestrians

The comparison of the video sequence where a pedestrian crosses the road, with the associated value of delay time computed as in 4.3, allows to analyze whether only delay - as the sole criterion - is representative for the determination of the LOS. In other words, the question is if the pure delay could represent the quality of the trip in a road environment which owns a place function, more than a merely traffic one. The shared environment, in this sense, has to encourage people to interact with cars and must assure a good level of comfort and safety, more than taking them to the other side of the road as soon as possible. To answer this question, different situations with similar delay time are juxtaposed and the quality of the movement is visually compared.

The first example regards situation 1 (Fig. 7a and 7b) and situation 2 (Fig. 7c and 7d), which both have a delay time of approximately 1 second. In situation 1, a couple of pedestrians smoothly deviate to the right in order to allow the black car to clear the space, without decreasing the walking pace. However the black car suddenly decelerates (to let another pedestrian pass, not shown in the picture), forcing them to deviate intensively to the right to avoid the collision. Despite the safety of the pedestrians has not ever been compromised, the strong deviation was uncomfortable and unpleasant however – also because of the presence of a second car. In situation 2 a pedestrian walks slowly, prudently, in order to find out if the upcoming car will let him pass, or will drive by. Successively, as the car decelerates, the pedestrian increases the walking pace and reaches the other side of the road. The action is comfortable, the car decelerates well in advance and the scene is free from other motorized vehicle. Compared with situation 1, the quality of the movement is absolutely better.

Bild 7: Situation 1 (a)(b) and situation 2 (c)(d)

Another example is given in the case of delay time close to 0 seconds, i.e. pedestrians neither deviate, nor decelerate. In situation 3 (Fig. 8a) a pedestrian uses the time gap between cars to get to the other side of the road, tenaciously. The risk of a collision is high, since cars are present in both lanes, driving at around 20 km/h. Moreover a motorcycle passes by, and a parked car disturbs the crossing. In situation 4 (Fig. 8b) the space is clear and no car is on the horizon; moreover the presence of other pedestrians nearby instills serenity to the crossing pedestrian, just as he were in a pedestrian zone.

The conclusion is that situation 3 and 4 highly differ for the quality of the crossing movement.
Summarizing, considering the improvement of pedestrian movement and comfort as a major aim for shared spaces, the quality of movement could not only be a matter of delay time but it should include all the aspects that makes a trip comfortable, pleasant and safe. Therefore, in the next section it is investigated which factors, and to what extent, play a role in determining the overall quality of the movement.

5 A new indicator for pedestrian traffic quality

Two main aspects are assumed to affect the quality of pedestrian movement. The first one is the delay time, which is objective and directly measurable. The second one is the comfort of the trip, which is subjective and includes factors which are more difficult to estimate.

Comfort evaluation in road environments is provided both in HBS and HCM in relation to footways. The approach is to determine the LOS of a footway section by determining the pedestrian density in [ped/m2] and then by comparing it with reference values. Despite the indicator is known under the name of “traffic quality for pedestrians”, it is in practice a measure of comfort that depends only on the level of crowding.

The DEPARTMENT OF TRANSPORT of the United Kingdom [2] has developed a Comfort Guidance for the City of London for traffic planner and local authorities to perform a comfort assessment on footways and crossings. In this guidance, The Pedestrian Comfort Level (PCL) is defined as a function of pedestrian inflow, geometrical measures of the footway and other parameters.
SARKAN [11] also studied the comfort needs of pedestrians in urban walkways. In his work, he created a method to assess pedestrian comfort by indicators like level of noise and pollution, provision of seating or stopping places and protections from adverse weather conditions.

In regard to shared spaces, KAPARIAS et al. [12] investigated what influences the perception of comfort in a shared space, including person-, context- and design-specific factors. From the survey, it emerged that low vehicular traffic and high pedestrian traffic positively contribute to the perception of comfort.

In this work, the aim is to provide an indicator of comfort based on directly measurable parameters which could be collected in a real scenario - or as the output of a microsimulation software. The focus is on the spatial and temporal evolution of the trajectory of road users, which can be tracked in real life - or obtained from the software - on a fixed time step. Factors like temperature, pollution or lighting, which may also influence the perception of comfort, are neglected from the analysis. Three main aspect are considered, namely the traffic environment, the interaction apprehension and the physical movement. Parameters are firstly introduced and mathematically described in section 5.1. The new indicator of traffic quality, which includes both delay and comfort aspects, is finally calibrated in section 5.2.

5.1 Aspects considered

An overview of all the factors which may influence pedestrian comfort in shared space environments is given in Tab. 3.

Tabelle 3: Factors considered in the development of a new indicator of pedestrian traffic quality

5.1.1 Traffic environment

The first aspect concerns the traffic environment in the time interval when the pedestrian is moving across the road. The hypothesis is that the presence of motorized traffic negatively affects pedestrian comfort. Moreover, a pedestrian could more likely feel comfortable if it was surrounded by many other pedestrians, which would give it the perception of a calmed and pedestrian-friendly environment - note that this hypothesis has been confirmed by KAPARIAS et al. [12].

This information is expressed mathematically by the parameter, which is the mean value of the number of road users of mode k present on the road, in the time interval when the pedestrian moves across the circulation zone. The value is corrected by considering only the road users within a certain distance dl to the pedestrian, which is assumed to be 25 meters for motorized vehicles and 15 meters for non-motorized ones. For a pedestrian i crossing the road from time steps tsA to tsB, the parameter is computed as follows:

Formel (4) siehe PDF.

where is the number of road user at the time step ts. The value is computed for the transport modes motorists, motorcycles, cyclists and pedestrians. Parked cars are also considered in the analysis assuming a distance dl equal to 15 meters.

5.1.2 Interaction apprehension

While crossing the circulation zone, the necessity to avoid collisions with other users, and even to keep a safety distance from them, leads pedestrians to modify walking direction and/or speed. This mechanism is quite automatic when the conflicting user is also a pedestrian. The Social Force Model [13] is based indeed on the assumption that interaction among pedestrians is automatic and does not imply any complex evaluation or decisional process. Otherwise, if the interacting user is a motorized vehicle – or a cyclist also - the reaction has to be considered carefully because it may lead to severe injuries. This evaluation process implies a psychological stress due to the necessity to think on a proper strategy, which could involve a physical reaction (e.g. to decelerate, to deviate) or not. In other words, if a motorized vehicle is approaching a pedestrian, the pure necessity to think on how to behave is assumed as a discomfort.

To quantify the stress due to conflict situations, a procedure to detect conflict among users is developed. The procedure is repeated at every time step ts and consist on three steps.

1. Given the position of all pedestrians and car in the last 4 time steps, the expected behavior of the users is computed by fitting a cubic smoothing spline to the points, then by predicting the x-y position within the next 8 seconds.

2. The expected behavior of all road users is projected and the algorithm compares the relative distance between all the pairs in all the future time steps.

3. If the distance gets below a certain threshold, the moment of the pair where the distance is minimum is identified and two elements are noted:

- The minimum relative distance among users, in meters

- The temporal proximity of the situation of minimum relative distance

Formel (5) siehe PDF.

where T is the temporal length of a time step. This condition is here defined as interaction, meaning that the pedestrian and the car would find themselves at a non-negligible distance, if their movements remain unchanged. Note that this condition is a generalization of the concept of conflict, which is an interaction that would imply the collision between the users. In this paper is assumed to be 5 meters.

During the motion to the destination, a pedestrian could experience many interaction situations against cars, even at the same time step ts. As a measure of the interaction against cars, three elements are saved:

- IA1: the number of seconds, where the pedestrian experienced a critical interaction situation with d * ij <2 and t * ij <5.

- IA2: the minimum among all interactions.

- IA3: the related of the situation detected in IA2.

IA1 is a measure of discomfort given by the continuous apprehension generated by cars. On the other hand, IA2 and IA3 describe the worst situation in the trip.

5.1.3 Physical movement

Interaction among users is performed by deviations and change in walking speed, whose intensity is determined by the transport mode of the interacting user and the severity of the situation. The discomfort is due to the physical effort needed to modify the current behavior.

Deviations from the current direction are particularly unpleasant if they are rapid and immediate; moreover, the discomfort increases as the walking pace rises. To obtain an indicator of directional change, which could resume the entire operation of crossing, the change of direction d’ts is computed at every time step ts as:

Formel (6) siehe PDF.

where is the normalized vector of the direction at time step ts and T is the time length of a time step. The squared root of, weighted for the walking pace, is summed up for the overall period between and and finally divided by T.

Formel (7) siehe PDF.

Variations of speed are considered as unpleasant only when negative, i.e. when there is a deceleration. The term ME2, which represents the discomfort due to the modification of speed, is computed in analogy with ME1.

Formel (8) siehe PDF.

where is the acceleration at time step ts.

5.2 Model formulation

The aim of this section is firstly to detect which parameters are relevant in determining the quality of the crossing action performed by pedestrians, which is assumed to be subjective and dependent from the personal perception; Secondly, to give a formulation of the quality of pedestrian movement which could be easily applied.

First at all, a total of 120 video sequences has been selected, each one consisting on a single pedestrian while crossing the circulation zone. The sequence start as the pedestrian appears on the screen, and ends as he disappears at the opponent side of the road. The total length of the video sequence depends on the time needed by the pedestrian to cross, and varies between 0 and 22.81 seconds.

The set of 120 crossing pedestrians was selected - among the total of about 1200 - so that they could represent different combinations of the parameters considered in section 5.1. For doing that, delay time and all parameters of Tab. 3 were computed for every pedestrian (the boxplot is shown in Fig. 9). If a pedestrian experienced no conflict situation, the variables IC2 and IC3 where respectively assumed as 5 meters and 7.61 seconds (which was the highest detected in conflict situations). Successively a K-means clustering has been performed (number of clusters set to 120), and the element close to the centroid of the cluster was chosen. The associated pedestrian was then identified and the video sequence was cut.

Bild 9: Boxplot of the predictors for the multilinear regression model

5.2.1 Questionnaire

A set of 60 respondents was selected to evaluate the quality of the crossing operation. Respondents were chosen by mixed attributes of gender (male 53%, female 47%), age (between 13 and 70 years old), and personal knowledge on shared spaces (from high knowledge to “ever heard”).

Respondents were firstly asked to view a brief Power Point presentation, which included an explanation of the subject of the survey and technical information to perform the evaluation. To get familiar with the evaluation, two video sequences were shown. In the first one, a pedestrian crosses the road in a moment where no motorized vehicle is present. The second video displays a group of pedestrians who try to cross the road in a congested situation: Someone of them takes advantages of the short temporal gap among vehicles to pass through, while others remain safely on the margin of the circulation zone, waiting for the cars to pass. The situations were described by help of subtitles, which made the respondents notice indisputable attributes (“no car is present”, “high amount of traffic”,” crossing is easy/difficult”) and without directly referring to the hypothesized elements of discomfort. At the end of the presentation an example video sequence with a crossing pedestrian was shown, and the respondents was asked how the crossing movement was personally perceived on a 5-set spectrum, including very pleasant (++), pleasant (+), neutral (0), unpleasant (-), very unpleasant (--).

Successively, each respondent received a list of 12 videos to watch and to evaluate. The videos were randomly selected with the only issue that at the end of the survey each video had to be evaluated 6 times in the overall. Before watching the video, a screenshot of the first video frame was shown, where the pedestrian under analysis was circled. To facilitate the evaluation, the respondents were allowed to view the video sequence as many times as they desired.

5.2.2 Multilinear regression model

For every crossing situation, a single score is computed as the mean of the scores given by the respondents, in a range between -2 (--) and +2 (++). A multilinear regression is then performed, where the predictors consist on the parameters of Section 5.1 and the delay time. In order to have a meaningful interpretation of the intercept estimates in the multilinear model, predictors are centered on their mean. The aim of the regression is to detect which variables influence the quality of the crossing movement, and then to formulate a multilinear model to predict the response.

Before starting with the regression, predictors are checked for multicollinearity by computing the correlation matrix with the Kendall method. The highest value among the off-diagonal coefficients regards predictors PM1 and PM2 (0.68) and could be explained by the fact that deviations and deceleration (which are both possible reactions to conflict situations) are usually performed together. Medium correlation (-0.61) was also detected for the pair IA1-IA2: the reason could be that the duration of a conflict is related with its severity (for low values of the minimum distance, more time is needed to solve the conflict). Non-negligible correlation was also found for the pairs IA2-PM1 (-0.55) and IA2-PM2 (-0.53).

Despite any variable appears to be highly correlated with any other, the off-diagonal coefficients suggest that the significance of single predictors in the regression model could be partially hidden by another one. For this reason, the regression is not performed just once (with all predictors together) but at different stages, where at every stage only the most significant predictor is added. This is needed to include in the model formulation as less variable as possible, and the most significant.

In the first stage, a set of linear regressions is performed considering one predictor at a time. The regression is carried out in R-statistics by the function lm, which uses the Least Squared Method to estimate the intercept and the coefficient of the predictor p. Two outputs of the regression are analyzed: the R-squared statistic, which is a measure of goodness of fit of the linear model, and the t-statistic, which indicates the significance of the predictor. The result is shown in Tab. 4.

Tabelle 4: Regression analysis for linear models K0 + Kp1*p1

All variables except TE2, TE3 and TE4 are significant (p-value < 0.05), but the linear model with the highest R-squared regards D. For this reason it is included as variable in the model (p1=D).

The process is repeated in the next stages i always by adding only one predictors at a time to the model formulation. The variable that is selected must fulfill two conditions: first, it must be significant; second, it must provide the highest contribution to the model by the R-squared statistic. In Tab. 5 it is shown which variable has been introduced to the model at every stage.

Tabelle 5: Regression analysis for multilinear models, and significant variable chosen

At the stage 5, no significant variable has been found. Moreover, the increase in R-squared was negligible in comparison to the stage 4. For this reason the variables D, IC2, TE1 and IC3 are chosen for the final formulation, which is:

Formel (9) siehe PDF.

It is noticed how the increase of delay time and the number of cars make the pedestrian comfort decrease. Moreover, as the intensity of the conflict increases (lower IC2 and IC3), pedestrian comfort decreases. The final R-squared could be compared to the model at stage one, where delay was the only variable in the model: The improvement correspond to the 47% (from 0.45 to 0.66).
As a way of example, the new indicator has been computed for the pedestrians shown in Fig. 6 and 7. The results (see Tab. 6) confirm the expectations described in Sec. 4.4. Moreover the procedure has given a higher score to situation 2 (1.29 seconds delay) in comparison to situation 3 (almost no delay), confirming that lower delay times are not synonymous with better quality of the movement.

Tabelle 6: Pedestrian score computed for Situation described in Sec. 4.4

6 Conclusions and future research

In this paper the evaluation of traffic quality in a shared space has regarded motorists and pedestrians. Both transport modes pay the prize of the sharing with a decrease in traffic quality. Motorists, compared to being on a classical roadway, take a longer time to travel the road section because of the presence of crossing pedestrians. Pedestrians, compared to being in a pedestrian zone, lose in comfort and safety perception – as well as in time spent – as a result of the interaction with cars. Based on these considerations, delay time can be considered a good measure of traffic quality for motorists, but insufficient for pedestrians. For this reason, in Sec. 5 a new indicator has been developed for pedestrian motions. The indicator can be computed once the position of pedestrians at discrete steps is known, as a result from a video survey in a real case, or as an output of a microsimulation.

Thanks to these indicators, different street layouts – also including classic ones – could be compared in the field of the quality of the traffic flow. The next step of this research, indeed, is to use the developed indicators to compare a shared space design with reasonable alternatives like a traffic light, a pedestrian refugee and zebra crossing.

Moreover, the results of this paper will be included in the research project MODIS (MultimODal Intersection Simulation), which deals with the development of a microsimulation software for shared spaces. The final aim is to realistically simulate the movement of road users in a shared space and to evaluate the quality of the traffic flow with the indicators developed in this paper.

Acknowledgements

The authors sincerely thank Lisa Höper for the intense work of data acquisition and preparation. Many thanks also to Sebastian Vogt for revising the abstract of this paper in German language.

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