Pedestrian route-choice and activity scheduling theory and models

More documents

Recommendations

Info

172 S.P. Hoogendoorn, P.H.L. Bovy / Transportation Research Part B 38 (2004) 169–190 individuals. Nevertheless, the continuous theory is easily extended to include for instance taste variation. 4.1. Pedestrian behavioral levels In out approach we distinguish choices at the following three levels: 1. Departure time choice, and activity pattern choice (strategic level); 2. Activity scheduling, activity area choice, and route-choice to reach activity areas (tactical level); 3. Walking behavior (operational level). In this hierarchy, expected utilities at lower levels influence choices at higher levels. Choices at higher levels condition choice sets at lower levels. This article focuses on pedestrian behavior at the tactical level. The events and decisions causing the pedestrian to arrive at the walking facility are not considered; pedestrian arrival patterns, distinguishing groups of pedestrians having similar characteristics (activity sets, travel purpose, demographic characteristics, etc.) are assumed known a priori. With respect to the operational level, it is hypothesized that pedestrians adhere to their planned route (determined at the tactical level) as much as possible. In addition, walking is affected by interactions with other pedestrians or obstacles. For details, we refer to (Hoogendoorn, 2001). The tactical level behavior is influenced by both external factors (e.g. presence of obstacles, stimulation of the environment), and internal (or personal) factors (e.g. time–pressure, attitudes of the pedestrian). Together with the expected traffic conditions (congestion, average speeds), the decisions at the tactical level serve as input for pedestrianÕs walking behavior. In turn, the traffic conditions resulting from the pedestrian traffic demands and the collective walking behavior will affect the expected traffic conditions and thus the behavior at the tactical level. 4.2. Tactical level decision variables Before we present the problem formulation, let us introduce the key decision variables for the pedestrian behavior at the tactical level 1. The activity schedule S ¼fig, which is an ordered set describing which activities i 2 R are performed and in which order. 2. The velocity trajectory vðÞ yielding the route xðÞ through the facility. 3. The activity times T i at which activities i 2 S are performed, such that xðT i Þ2A ij for some j, where A ij denote the activity areas where activity i can be performed. A pedestrian arriving at the walking facility X R 2 aims to perform (a type of) activities from the subjective activity choice set R, which consists of possible activities to perform in the facility, e.g. ‘‘buy a newspaper’’, ‘‘buy a train ticket’’, ‘‘wait at the train platform’’, or ‘‘access the train’’. The activities are generic, and reflect the purposes of the pedestrians in the facility. The pedestrian chooses activities from the subjective activity choice set R, yielding the activity schedule S ¼fig. S describes which activities from R are performed and in which order. The
S.P. Hoogendoorn, P.H.L. Bovy / Transportation Research Part B 38 (2004) 169–190 173 pedestrian may have some freedom to choose where activity i from S is performed. This is modeled by considering different activity areas A ij X with j ¼ 1; ...; J i , where activity i can be performed. For example, a traveler can ‘‘buy a newspaper’’ at different ticket machines or ticket offices. Terminal time T i for activity i denotes the instant at which activity i is completed. That is, the difference T i T i 1 equals the expected walking time and the time needed to perform activity i. Together with the route xðÞ through the facility, the terminal time determines the activity area A ij chosen by the pedestrian, i.e. xðT i Þ2A ij (assuming that the pedestrian will not move while performing the activity). The route xðÞ is a continuous function, uniquely determined by the velocity path vðÞ xðÞ :¼ fxðsÞ 2Xjt 0 6 s 6 t 1 s:t: _xðsÞ ¼vðsÞ and xðt 0 Þ¼x 0 g ð1Þ 4.3. Subjective utility optimization at the tactical level We hypothesize that at the tactical level, a pedestrian makes a simultaneous decision at time t 0 minimizing the expected disutility or cost C. This decision will cover all decision variables described in the previous section (activity patterns S, terminal times T i , and the velocity path vðÞ). The expected disutility C ¼ CðS; fT i g i2S ; vðÞjt 0 ; x 0 Þ of the combined choice of a pedestrian entering the walking facility at instant t 0 at location x 0 stems from performing specific activities at certain activity areas, the order in which the activities are performed, and the expected cost of walking between the activity areas. We assume that the total disutility can be written as follows CðS; fT i g i2S ; vðÞjt 0 ; x 0 Þ :¼ X i2S C i ðT i ; vðÞjT i 1 ; xðT i 1 ÞÞ þ wðSÞ ð2Þ where C i denotes the combined cost of walking from the location xðT i 1 Þ2A i 1j to xðT i Þ2A ij where activity i is performed, and the cost (or utility U ij ) of performing activity i at activity area A ij ; w denotes the cost of the activity scheduling (e.g. due to the specific order of activities). In the remainder, the components C i are specified. Subjective utility optimization then yields that the pedestrian makes the following combined choice at the tactical level ðS ; fT i g i2S ; v ðÞÞ ¼ arg minCðS; fT i g i2S ; vðÞjt 0 ; x 0 Þ ð3Þ Activity i may be performed at multiple activity areas A ij , yielding different utilities U ij . These differences reflect personal preferences for using a certain area (e.g. describing that pedestrians expect different waiting times at different ticket offices). Some activities are discretionary, others are mandatory, which is described by high penalties / i experienced when activity i is not performed. The order in which activities are performed generally depends on the directness (Helbing, 1997) and results from the simultaneous choices made at the tactical level. Directness is reflected by the cost stemming from the trajectory xðÞ; wðSÞ is generally only used describe that the activity order is restricted, implying that some activities can be performed only once others are completed. Although pedestrian route choice is mostly subconscious, assuming that route choice strategies are applicable to predict pedestrian choice behavior is fruitful from a modeling viewpoint (Hill, 1982). We therefore assume that the pedestrian route choice is based on utility optimization. The disutility C i of a route will depend among other things on (Chiolek, 1978; Gipps, 1986):
Page 1 and 2: Transportation Research Part B 38 (
Page 3: S.P. Hoogendoorn, P.H.L. Bovy / Tra
Page 7 and 8: S.P. Hoogendoorn, P.H.L. Bovy / Tra
Page 9 and 10: Substitution of running cost (9) yi
Page 19 and 20: 6.2. Activity order choice S.P. Hoo

Pedestrian route-choice and activity scheduling theory and models

Create successful ePaper yourself

Delete template?

Save as template?