arXiv subjects
Publications and source records attributed to Tobias Kretz.
A function for the dependence of flow on pedestrian density is derived analytically from the Social Force Model (SFM) for the case of a homogeneous population walking in the same direction and being in steady state. Assuming that only nearest Voronoi neighbors effectuate forces the resulting function matches a variety of very different fundamental diagrams that were found empirically.
Pedestrian's crossing from unsignalized locations at intersections or midblock locations is a risky decision that could lead to fatal accidents. Despite making a decision to accept a safe gap to cross the street is a personal choice, studying this phenomena and its affecting variables are crucial for accident analysis and traffic safety investigations. In this paper we used video taped data to study pedestrian gap acceptance behavior at an unsignalized intersection and a midblock facility in Tehran, Iran. Multi way ANOVA test indicates simultaneous effect of gender and child accompaniment have the highest effect on size of accepted gap and waiting time. In addition, number of rejected gap is mostly affected by the child accompaniment status. Investigation about critical gap shows in general, critical gap was bigger at unsignalized intersection and for women. We defined a latent variable named caution behavior based on some observable indicators and using structural equation modeling it was estimated and used as an input in a binary mixed logit model. This variable identified important in gap acceptance decision. Despite both structural equation and logit models are used in previous gap acceptance studies, but according to our best knowledge this is the first use of the hybrid mixed logit modeling approach in this field and we developed a new methodology to combine psychological and behavioral aspects of pedestrians' gap acceptance studies. Modeling approach shows pedestrian decision regarding acceptance or rejection of a gap to be highly influenced by the size of current gap, caution behavior and waiting time.
The Social Force Model of pedestrian dynamics is formulated in a way that a) most of its parameters do not have an immediate interpretation, b) often one single parameter has an impact on many aspects of walking behavior and c) a certain aspect of walking behavior results from the values of more than one parameter. This makes calibration difficult. The aim of this paper is to give practitioners an indication of how to proceed in the calibration process. For this by analytical transformations the parameters of the Social Force Model are related to real properties that have a clear and immediate meaning and which are also highly relevant result properties of a simulation: extent and clearance time of a queue, respectively maximum density and capacity flow. The theory for this is presented as well. As a side effect it can give a deeper understanding of the model for everyone interested in theoretical aspects.
It was recently found that the Social Force Model of pedestrian dynamics in a macroscopic limit for 1d movement does not reproduce the empirically found inflection point of the speed-density relation. It could be shown that, however, a simple and intuitively comprehensible extension of the Social Force Model shows the inflection point. Motivated by this observation in this contribution the relation of the Social Force Model with the Kladek formula for the speed-density relation of urban motorized traffic is discussed. Furthermore the models are compared to results data from experiments on vehicular, cycling, and pedestrian dynamics.
It has been argued that the speed-density digram of pedestrian movement has an inflection point. This inflection point was found empirically in investigations of closed-loop single-file pedestrian movement. The reduced complexity of single-file movement does not only allow a higher precision for the evaluation of empirical data, but it occasionally also allows analytical considerations for micosimulation models. In this way it will be shown that certain (common) variants of the Social Force Model (SFM) do not produce an inflection point in the speed-density diagram if infinitely many pedestrians contribute to the force computed for one pedestrian. We propose a modified Social Force Model that produces the inflection point.
The Social Force Model is one of the most prominent models of pedestrian dynamics. As such naturally much discussion and criticism has spawned around it, some of which concerns the existence of oscillations in the movement of pedestrians. This contribution is investigating under which circumstances, parameter choices, and model variants oscillations do occur and how this can be prevented. It is shown that oscillations can be excluded if the model parameters fulfill certain relations. The fact that with some parameter choices oscillations occur and with some not is exploited to verify a specific computer implementation of the model.
It is tested in this contribution if and to which extend a method of a pedestrian simulation tool that attempts to make pedestrians walk into the direction of estimated earliest arrival can help to automatically distribute pedestrians - who are initially distributed arbitrarily in the scenario - equally on the various exits of the scenario.
Applying assignment methods to compute user-equilibrium route choice is very common in traffic planning. It is common sense that vehicular traffic arranges in a user-equilibrium based on generalized costs in which travel time is a major factor. Surprisingly travel time has not received much attention for the route choice of pedestrians. In microscopic simulations of pedestrians the vastly dominating paradigm for the computation of the preferred walking direction is set into the direction of the (spatially) shortest path. For situations where pedestrians have travel time as primary determinant for their walking behavior it would be desirable to also have an assignment method in pedestrian simulations. To apply existing (road traffic) assignment methods with simulations of pedestrians one has to reduce the nondenumerably many possible pedestrian trajectories to a small subset of routes which represent the main, relevant, and significantly distinguished routing alternatives. All except one of these routes will mark detours, i.e. not the shortest connection between origin and destination. The proposed assignment method is intended to work with common operational models of pedestrian dynamics. These - as mentioned before - usually send pedestrians into the direction of the spatially shortest path. Thus, all detouring routes have to be equipped with intermediate destinations, such that pedestrians can do a detour as a piecewise connection of segments on which they walk into the direction of the shortest path. One has then to take care that the transgression from one segment to the following one no artifacts are introduced into the pedestrian trajectory.
It has become widely known that when two flows of pedestrians cross stripes emerge spontaneously by which the pedestrians of the two walking directions manage to pass each other in an orderly manner. In this work, we report about the results of an experiment on crossing flows which has been carried out at a German school. These results include that previously reported high flow volumes on the crossing area can be confirmed. The empirical results are furthermore compared to the results of a simulation model which succesfully could be calibrated to catch the specific properties of the population of participants.
In vehicular traffic planning it is a long standing problem how to assign demand such on the available model of a road network that an equilibrium with regard to travel time or generalized costs is realized. For pedestrian traffic this question can be asked as well. However, as the infrastructure of pedestrian dynamics is not a network (a graph), but two-dimensional, there is in principle an infinitely large set of routes. As a consequence none of the iterating assignment methods developed for road traffic can be applied for pedestrians. In this contribution a method to overcome this problem is briefly summarized and applied with an example geometry which as a result is enhanced with routes with intermediate destination areas of certain shape. The enhanced geometry is used in some exemplary assignment calculations.
A generic method for dynamic assignment used with microsimulation of pedestrian dynamics is introduced. As pedestrians - unlike vehicles - do not move on a network, but on areas they in principle can choose among an infinite number of routes. To apply assignment algorithms one has to select for each OD pair a finite (realistically a small) number of relevant representatives from these routes. This geometric task is the main focus of this contribution. The main task is to find for an OD pair the relevant routes to be used with common assignment methods. The method is demonstrated for one single OD pair and exemplified with an example.
For the simulation of pedestrians a method is introduced to find routing alternatives from any origin position to a given destination area in a given geometry composed of walking areas and obstacles. The method includes a parameter which sets a threshold for the approximate minimum size of obstacles to generate routing alternatives. The resulting data structure for navigation is constructed such that it does not introduce artifacts to the movement of simulated pedestrians and that locally pedestrians prefer to walk on the shortest path. The generated set of routes can be used with iterating static or dynamic assignment methods.
For simulation models of pedestrian dynamics there are always the issues of calibration and validation. These are usually done by comparing measured properties of the dynamics found in observation, experiments and simulation in certain scenarios. For this the scenarios first need to be sensitive to parameter changes of a particular model or - if models are compared - differences between models. Second it is helpful if the exhibited differences can be expressed in quantities which are as simple as possible ideally a single number. Such a scenario is proposed in this contribution together with evaluation measures. In an example evaluation of a particular model it is shown that the proposed evaluation measures are very sensitive to parameter changes and therefore summarize differences effects of parameter changes and differences between models efficiently, sometimes in a single number. It is shown how the symmetry which exists in the achiral geometry of the proposed example scenario is broken in particular simulation runs exhibiting chiral dynamics, while in the statistics of 1,000 simulation runs there is a symmetry between left- and right-chiral dynamics. In the course of the symmetry breaking differences between models and parameter settings are amplified which is the origin of the high sensitivity of the scenario against parameter changes.
This contribution demonstrates the potential gain for the quality of results in a simulation of pedestrians when estimated remaining travel time is considered as a determining factor for the movement of simulated pedestrians. This is done twice: once for a force-based model and once for a cellular automata-based model. The results show that for the (degree of realism of) simulation results it is more relevant if estimated remaining travel time is considered or not than which modeling technique is chosen -- here force-based vs. cellular automata -- which normally is considered to be the most basic choice of modeling approach.
A combination of a telepresence system and a microscopic traffic simulator is introduced. It is evaluated using a hotel evacuation scenario. Four different kinds of supporting information are compared, standard exit signs, floor plans with indicated exit routes, guiding lines on the floor and simulated agents leading the way. The results indicate that guiding lines are the most efficient way to support an evacuation but the natural behavior of following others comes very close. On another level the results are consistent with previously performed real and virtual experiments and validate the use of a telepresence system in evacuation studies. It is shown that using a microscopic traffic simulator extends the possibilities for evaluation, e.g. by adding simulated humans to the environment.
It is shown in this work that the average individual egress time and other performance indicators for egress of people from a building can be improved under certain circumstances if counterflow occurs. The circumstances include widely varying walking speeds and two differently far located exits with different capacity. The result is achieved both with a paper and pencil calculation as well as with a micro simulation of an example scenario. As the difficulty of exit signage with counterflow remains one cannot conclude from the result that an emergency evacuation procedure with counterflow would really be the better variant.
This contribution proposes a method to make agents in a microscopic simulation of pedestrian traffic walk approximately along a path of estimated minimal remaining travel time to their destination. Usually models of pedestrian dynamics are (implicitly) built on the assumption that pedestrians walk along the shortest path. Model elements formulated to make pedestrians locally avoid collisions and intrusion into personal space do not produce motion on quickest paths. Therefore a special model element is needed, if one wants to model and simulate pedestrians for whom travel time matters most (e.g. travelers in a station hall who are late for a train). Here such a model element is proposed, discussed and used within the Social Force Model.
In this paper the results of a simulation of a prisoner's dilemma robin-round tournament are presented. In the tournament each participating strategy plays an iterated prisoner's dilemma against each other strategy (round-robin) and as a variant also against itself. The participants of a tournament are all strategies that are deterministic and have the same size of memory with regard to their own and their opponent's past actions: up to three most recent actions of their opponent and up to two most recent actions of their own. A focus is set on the investigation of the influence of the number of iterations, details of the payoff matrix, and the influence of memory size. The main result is that for the tournament as carried out here, different strategies emerge as winners for different payoff matrices, even for different payoff matrices being similar judged on if they fulfill relations T + S = P + R or 2R > T + S. As a consequence of this result it is suggested that whenever the iterated prisoner's dilemma is used to model a real system that does not explicitly fix the payoff matrix, one should check if conclusions remain valid, when a different payoff matrix is used.