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In this paper we consider the estimation of an origin-destination (OD) matrix, given a target OD-matrix and traffic counts on a subset of the links in the network. We use a general nonlinear bilevel minimization formulation of the problem, where the lower level problem is to assign a given OD-matrix onto the network according to the user equilibrium principle. After reformulating the problem to a single level problem, the objective function includes implicitly given link flow variables, corresponding to the given OD-matrix. We propose a descent heuristic to solve the problem, which is an adaptation of the wellknown projected gradient method. In order to compute a search direction we have to approximate the Jacobian matrix representing the derivatives of the link flows with respect to a change in the OD-flows, and we propose to do this by solving a set of quadratic programs with linear constraints only. If the objective function is differentiable at the current point, the Jacobian is exact and we obtain a gradient. Numerical experiments are presented which indicate that the solution approach can be applied in practice to medium to large size networks.

Several European railway traffic networks experience high capacity consumption during large parts of the day resulting in delay-sensitive traffic system with insufficient robustness. One fundamental challenge is therefore to assess the robustness and find strategies to decrease the sensitivity to disruptions. Accurate robustness measures are needed to determine if a timetable is sufficiently robust and suggest where improvements should be made.Existing robustness measures are useful when comparing different timetables with respect to robustness. They are, however, not as useful for suggesting precisely where and how robustness should be increased. In this paper, we propose a new robustness measure that incorporates the concept of critical points. This concept can be used in the practical timetabling process to find weaknesses in a timetable and to provide suggestions for improvements. In order to quantitatively assess how crucial a critical point may be, we have defined the measure Robustness in Critical Points (RCP). In this paper, we present results from an experimental study where a benchmark of several measures as well as RCP has been done. The results demonstrate the relevance of the concept of critical points and RCP, and how it contributes to the set of already defined robustness measures.

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Microscopic simulation of pedestrian traffic is an important and increasingly popular method to evaluate the performance of existing or proposed infrastructure. The social force model is a common model in simulations, describing the dynamics of pedestrian crowds given the goals of the simulated pedestrians encoded as their preferred velocities.The main focus of the literature has so far been how to choose the preferred velocities to produce realistic dynamic route choices for pedestrians moving through congested infrastructure. However, limited attention has been given the problem of choosing the preferred velocity to produce other behaviors, such as waiting, commonly occurring at, e.g., public transport interchange stations.We hypothesize that: 1) the inclusion of waiting pedestrians in a simulated scenario will significantly affect the level of service for passing pedestrians, and 2) the details of the waiting model affect the predicted level of service, that is, it is important to choose an appropriate model of waiting.We show that the treatment of waiting pedestrians have a significant impact on simulations of pedestrian traffic. We do this by introducing a series of extensions to the social force model to produce waiting behavior, and provide predictions of the model extensions that highlight their differences. We also present a sensitivity analysis and provide sufficient criteria for stability.

Origin-destination (OD) matrices are essential for various analyses in the field of traffic planning, and they are often estimated from link flow observations. We compare strategies for allocating link flow detectors to a traffic network with respect to the quality of the estimated OD-matrix.First, an overview of allocation strategies proposed in the literature is presented. Second, we give an experimental environment where any allocation strategy can be evaluated, and compared to others, in terms of the quality of the estimated ODmatrix. Third, this environment is used to evaluate and compare three known allocation strategies. Studies are made on the Sioux Falls network and on a network modelling the city of Linköping. Our conclusion is, that the most commonly studied approach for detector allocation, the OD-pair coverage strategy, seems to be unfavourable for the quality of the estimated OD-matrix.

We identify the on-time performance as a key to evaluate a railway timetable's robustness to disturbances and evaluate the on-time performance for two single services on the Swedish Southern Mainline for the autumn period 2011. We analyse the punctuality by studying how the performance develops en route. Typically the time spent in the stations is underestimated, which partly is compensated for by time margins along the line, giving rise to a sawtooth formed delay muster with an increasing trend. The standard deviation in the delay reports seems to be a good indicator for the precision in the traffic. In this material it is almost linearly increasing with a good minute per hour scheduled running time. Two attempts are made to change the timetable for a better performance. By using socio-economic values a customer-oriented description of the current timetable is calculated as a trade-off between high punctuality and short travel time. This timetable does not affect any other traffic. Minor effects to other traffic would be the result if the existing margins are re-distributed to better match the demand en route in some sense. As long as no more time supplement is added, we will, however, not improve on the punctuality to the final destination. For future research is left, how the decrease in precision can be accounted for already in the timetable construction.

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