Pedestrian route-choice and activity scheduling theory and models

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182 S.P. Hoogendoorn, P.H.L. Bovy / Transportation Research Part B 38 (2004) 169–190 Fig. 1. Snapshot from Schiphol Plaza simulation using the NOMAD model (Hoogendoorn, 2001). Fig. 2. Expected minimum perceived disutility functions W and example routes describing combined route-choice and activity area choice for (a) leaving Schiphol Plaza via either of the escalators E6 and E7 to the train platforms and (b) leaving Schiphol Plaza via either of the exits E1–E5. The numbers indicate the generalized walking time (in seconds).
S.P. Hoogendoorn, P.H.L. Bovy / Transportation Research Part B 38 (2004) 169–190 183 routes that all lead to the escalator E6. In this case, combined route-choice/activity area choice yield different routes but the same activity area. Fig. 2b shows three exemplar routes leading to the exits. Not all routes lead to the same exit in this case. 5.6. Pedestrian route choice and activity area choice for congested operations Section 5.5 showed how we can determine the optimal walking paths for pedestrians under the assumption that pedestrian flow conditions are time-independent (and no time restrictions apply). However, in practice pedestrian traffic conditions will deteriorate due to other pedestrians walking in the same area. This deterioration will restrict the maximum speed v 0 ðt; xÞ at which pedestrians can walk, and increase the discomfort experienced in crowded areas. Pedestrians will reconsider the former route choice by including the additional delays due to the prevailing congestion into their path choice. To include prevailing and future conditions in the pedestrian pathfinding behavior, two options are considered in the ensuing: 1. Pedestrians consider instantaneous information regarding prevailing conditions. 2. Pedestrians anticipate on future conditions, by incorporating the anticipated behavior of other pedestrians and the resulting expected future traffic conditions. In the remainder of this article, the case where pedestrians react on current flow conditions is considered. Anticipation on future conditions involves using predictions of the pedestrian traffic conditions in the walking infrastructure, which can be achieved by simultaneously solving the HJB equation (24) and a dynamic model describing pedestrian traffic conditions (Hoogendoorn, 2001). To include the reaction to current traffic conditions, average walking speeds vðt; xÞ are determined based on the average speeds of the pedestrians in the microscopic simulation model (Hoogendoorn, 2001), or any other model describing pedestrian flow operations. These speeds are subsequently used to restrict the speeds according to v 0 ðt; xÞ ¼vðt; xÞ ð35Þ Secondly, the L 4 ðt; x; vÞ ¼cðt; xÞ is updated to include the current traffic conditions in the running cost function L. Generally, it will suffice to determine the average traffic concentration kðt; xÞ, and use rðt; xÞ ¼cðkðt; xÞÞ. Having updated both the maximum speed and the interaction cost, we can again solve the HJB equation numerically. We hypothesize that pedestrians will not continuously reconsider their route-choice, but only at discrete time intervals, say at each 10s. Example 2 (Route choice for congested conditions). Fig. 3 shows the case where pedestrians enter at x 1 ¼ 0 and walk towards the destination at x 1 ¼ 40 m and 17:5 m6 x 2 6 22:5 m. We assume that the speed is constant (1.5 m/s). According to the optimal control law, pedestrians walk in the direction perpendicular to the iso-cost curves. Fig. 3a shows the minimal route costs W ðt; xÞ and the resulting route choice for free-flow conditions. Fig. 3b shows the optimal cost function W ðt; xÞ, when the reduction in speed caused by congestion is taken into account. Clearly, pedestrians are inclined to change their route to avoid the congestion.
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