|The relationship between speed and density plays an important role in modeling of pedestrian traffic. It is useful for planning and design of pedestrian facilities, and it is also a required input or calibration criterion for models of pedestrian dynamics. The relationship is specified under the assumption that the traffic system is at equilibrium (stationary and homogeneous). The analysis we have performed, based on the data collected in the Lausanne train station, rules out the use of a unique equilibrium relationship due to a high scatter in the data. This scatter may be explained by the violation of the equilibrium assumptions, as documented in the literature.
To characterize the observed scatter we have developed a multi-class model of the speeddensity relationship based on the latent class modeling approach. The model is derived by relaxing the homogeneity assumption of equilibrium relationships. It is assumed that pedestrian population is heterogeneous (e.g. different trip purpose, different time to departure, etc.) and that this heterogeneity leads to the existence of multiple pedestrian classes that are characterized by different behavior. There are two specification issues related to the panel data set (data collected over multiple time periods for the same sample of individuals) that we use in our analysis. The first is serial correlation across the observations of the same individual due to unobserved individual factors that persist over time. The second is related to dynamics, meaning that the speed in one period may depend on the speed values in the past. We have addressed the first issue by introducing an agent effect in the model formulation, which captures individual related unobserved factors. The aim of this project will be to deal with the second issue, or dynamics. We will start with the simplified assumption that the speed at time t is influenced by the speed at time t - 1 only. This would lead to a dynamic Markov model. Conditional maximum likelihood estimation using a correction as proposed by Wooldridge (2010) would be a starting methodological point to extent the model. The performance of the approach will be tested using real data.|