Space–time prism bounds of activity programs: a goal-directed search in multi-state supernetworks

Abstract

Space-time prism (STP), which envelops the spatial and temporal opportunities for travel and activity participation within a time frame, is a fundamental concept in time geography. Despite many variants, STPs have been mostly modeled for one flexible activity between two anchor points. This study proposes a systemic approach to construct the STP bounds of activity programs that usually include various possible realizations of activity chains. To that effect, multi-state supernetworks are applied to represent the relevant path sets of multi-activity travel patterns. A goal-directed search method in multi-state supernetworks is developed to delineate the potential space-time path areas satisfying the space-time constraints. Particularly, the approximate lower and upper STP bounds are obtained by manipulating the goal-directed search procedure utilizing landmark-based triangular inequalities and spatial characteristics. The suggested approach can in an efficient fashion find the activity state dependent bounds of STP and potential path area. The formalism of goal-directed search through multi-state supernetworks addresses the fundamental shift from constructing STPs for single flexible activities to activity programs of flexible activity chains.

Exact space–time prism of an activity program: bidirectional searches in multi-state supernetwork

“…As Figure 3. Schematic representation at the search frontier nj s using the method of Liao (2019). The partial ATP from nj s to H 1 has activity sequence red→blue→green.…”

“…To keep consistency, this study adopts the same setup as Liao (2019). Links in static transport network G are travel links representing physical movement, activity locations are distributed at nodes of G, and all possible ATPs for conducting an AP are represented in SNK.…”

“…Focusing on a general activity program (AP) of multiple activities, Kang and Chen (2016) generated the feasible space-time region by first uniting all location-specific space-time regions belonging to an activity and then intersecting all activity-specific space-time regions belonging to the AP. As summarized in Liao (2019), these three approaches have shortcomings (illustrated in Part 1 of the supplementary document). First, the way of building STP blocks tends to underestimate the overall STP since fixed activity sequencing unfavorably eliminates STP fractions associated with other activity sequences.…”

“…First, the existing two-stage bidirectional search (TBS) methods Othman 2009, Chen et al 2016) are applied in multi-state supernetworks. Second, the unidirectional search method using ALT (Liao 2019) is extended to TBS (referred to as TBS with ALT). Third, two simultaneous bidirectional search (SBS) methods for point-to-point (P2P) routing, i.e.…”

“…The remainder of this paper is organized as follows. Section 2 provides the preliminary knowledge of the existing TBS methods for constructing trip-based STPs and the unidirectional goal-directed search method in Liao (2019). Section 3 formally analyzes the correctness and search spaces of the TBS methods and presents a naïve and goaldirected SBS method.…”