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Nowadays traffic flow and congestion is one of the main societal and economical problems related to transportation in industrialized countries. In this respect, managing traffic in congested networks requires a clear understanding of traffic flow operations; i.e. insights into what causes congestion, what determines the time and location of traffic breakdown, how does the congestion propagate through the network, etc., are essential. For this purpose, during the past fifty years, a wide range of traffic flow theories and models have been developed to answer these research questions. This paper presents a overview of some fifty years of modelling vehicular traffic flow. A rich variety of modelling approaches developed so far and in use today will be discussed and compared. The considered models are classified based on the level-of-detail with which the vehicular flow is described. For each of the categories, issues like modelling accuracy, applicability, generalizability, and model calibration and validation are discussed.

SUMMARYGaining insights into pedestrian flow operations and assessment tools for pedestrian walking speeds and comfort is important in, for instance, planning and geometric design of infrastructural facilities, as well as for management of pedestrian flows under regular and safety-critical circumstances. Pedestrian flow operations are complex, and vehicular flow simulation modelling approaches are generally not applicable to pedestrian flow modelling. This article focusses on pedestrian walking behaviour theory and modelling. It is assumed that pedestrians are autonomous predictive controllers that minimize the subjective predicted cost of walking. Pedestrians predict the behaviour of other pedestrians based on their observations of the current state as well as predictions of the future state, given the assumed walking strategy of other pedestrians in their direct neighbourhood. As such, walking can be represented by a (non-co-operative or co-operative) differential game, where pedestrians may or may not be aware of the walking strategy of the other pedestrians. Copyright # 2003 John Wiley & Sons, Ltd.KEY WORDS: walker model; differential games; feedback control; micro-simulation BACKGROUNDResearch of pedestrian behaviour started in the 1960s, when pedestrian flows in urban areas were studied. The main purpose of these early investigations was to provide guidelines for optimal design of walkway infrastructure. Weidmann [1] presents a concise overview of empirical facts about pedestrian walking behaviour, concerning among other things the relation between walking speed and energy consumption, the factors influencing walking speeds, and the use of space by pedestrians. In his review, Weidmann shows that pedestrian walking speeds are dependent on personal characteristics of pedestrians (age, gender, size, health, etc.), characteristics of the trip (walking purpose, route familiarity, luggage, trip length), properties of the infrastructure (type, grade, attractiveness of environment, shelter), and finally

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