Time geography is an elegant framework for analyzing human activity–travel behaviors across temporal and spatial dimensions. At the core of this framework are the concepts of space–time paths, which represent historical trajectories, and space–time prisms, which define potential future activity spaces. However, most studies examine space–time paths and prisms in isolation, overlooking the integrative nature of time geography as a theoretical framework that incorporates the past, present, and future within a continuous temporal dimension. This study addresses this gap by developing novel methods for measuring and querying the spatiotemporal proximity of these heterogeneous and heterochronous time-geographic entities. To operationalize these methods, a GIS tool was implemented to support the local density analysis of time-geographic entities. Comprehensive computational experiments were conducted to validate the developed methods using large-scale, network-constrained, and time-geographic datasets. The developed methods exhibited high computational efficiency (approximately 2 s) in computing the local density for each path within extensive prism collections. The experimental results demonstrate the effectiveness of the developed methods in analyzing and visualizing the local density of historical paths in the near future. The methods offer new insights into space–time interactions, advancing research in human mobility forecasting and spatial decision-making.

Data mining of network-constrained trajectories has broad applications in the GIScience field. The calculation of a complete trajectory similarity matrix is a key step in various data mining algorithms. However, computing this matrix is computationally intensive for large datasets, as it involves numerous point-to-point shortest-path (PPSP) queries. To tackle this issue, we propose a new spatiotemporal construct called the space-time tree, which directly delineates the network distance from a query trajectory to any network space-time point. By constructing the space-time tree, we can efficiently compute the trajectory similarity matrix without additional PPSP queries. The space-time tree supports several similarity metrics, including closest pair distance, furthest pair distance, longest common subsequence (LCSS), and distance-weighted LCSS. It can further integrate with advanced spatiotemporal query techniques for scalable partial trajectory similarity matrix calculations. A case study using real datasets was conducted to apply the space-time tree in the trajectory clustering application. The results show that the space-time tree completed the clustering task on 0.5 million trajectories within 49 minutes, achieving a nearly 147-fold speedup compared to state-of-the-art methods.

Clustering the trajectories of vehicles moving on road networks is a key data mining technique for understanding human mobility patterns, as well as their interactions with urban environments. The development of efficient and scalable trajectory clustering algorithms, however, still faces challenges because of the computational costs when measuring similarities among a large number of network-constrained trajectories. To address this problem, a novel trajectory clustering framework based on the well-developed Density-Based Spatial Clustering of Applications with Noise (DBSCAN) approach is proposed. This proposed framework accurately quantifies similarities using a trajectory representation of continuous polylines in the space and time dimensions, and does not require trajectory discretization. Further, the proposed framework utilizes the space-time buffering concept to formulate ε-neighborhood queries that directly retrieve the ε-neighbors of trajectories and thus avoids computing a trajectory similarity matrix. State-of-the-art trajectory databases and index structures are incorporated to further improve trajectory clustering performance. A comprehensive case study was carried out using an open dataset of 20,161 trajectories. Results show that the proposed framework efficiently executed trajectory clustering on the large test dataset within 3 min. This was approximately 2,700 times faster than existing DBSCAN algorithms.

The availability of Spatiotemporal Big Data has provided a golden opportunity for time geographical studies that have long been constrained by the lack of individual-level data. However, how to store, manage, and query a huge number of time geographic entities effectively and efficiently with complex spatiotemporal characteristics and relationships poses a significant challenge to contemporary GIS platforms. In this article, a hierarchical compressed linear reference (CLR) model is proposed to transform network-constrained time geographic entities from three-dimensional (3D) (x, y, t) space into two-dimensional (2D) space. Accordingly, time geographic entities can be represented as 2D spatial entities and stored in a classical spatial database. The proposed CLR model supports a hierarchical linear reference system (LRS) including not only underlying a link-based LRS but also multiple higher-level route-based LRSs. In addition, an LRS-based spatiotemporal index structure is developed to index both time geographic entities and the corresponding hierarchical network. The results of computational experiments on large datasets of space–time paths and prisms show that the proposed hierarchical CLR model is effective at storing and managing time geographic entities in road networks. The developed index structure achieves satisfactory query performance in milliseconds on large datasets of time geographic entities.

Spatiotemporal proximity analysis to determine spatiotemporal proximal paths is a critical step for many movement analysis methods. However, few effective methods have been developed in the literature for spatiotemporal proximity analysis of movement data. Therefore, this study proposes a space-time-integrated approach for spatiotemporal proximal analysis considering space and time dimensions simultaneously. The proposed approach is based on space-time buffering, which is a natural extension of conventional spatial buffering operation to space and time dimensions. Given a space-time path and spatial tolerance, space-time buffering constructs a space-time region by continuously generating spatial buffers for any location along the space-time path. The constructed space-time region can delimit all space-time locations whose spatial distances to the target trajectory are less than a given tolerance. Five space-time overlapping operations based on this space-time buffering are proposed to retrieve all spatiotemporal proximal trajectories to the target space-time path, in terms of different spatiotemporal proximity metrics of space-time paths, such as Fréchet distance and longest common subsequence. The proposed approach is extended to analyze space-time paths constrained in road networks. The compressed linear reference technique is adopted to implement the proposed approach for spatiotemporal proximity analysis in large movement datasets. A case study using real-world movement data verifies that the proposed approach can efficiently retrieve spatiotemporal proximal paths constrained in road networks from a large movement database, and has significant computational advantage over conventional space-time separated approaches.

Travel time uncertainty has significant impacts on individual activity-travel scheduling, but at present these impacts have not been considered in most accessibility studies. In this paper, an accessibility evaluation framework is proposed for urban areas with uncertain travel times. A reliable space-time service region (RSTR) model is introduced to represent the space-time service region of a facility under travel time uncertainty. Based on the RSTR model, four reliable place-based accessibility measures are proposed to evaluate accessibility to urban services by incorporating the effects of travel time reliability. To demonstrate the applicability of the proposed framework, a case study using large-scale taxi tracking data is carried out. The results of the case study indicate that the proposed accessibility measures can evaluate large-scale place-based accessibility well in urban areas with uncertain travel times. Conventional place-based accessibility indicators ignoring travel time reliability can significantly overestimate the accessibility to urban services.

There has been a resurgence of interest in time geography studies due to emerging spatiotemporal big data in urban environments. However, the rapid increase in the volume, diversity, and intensity of spatiotemporal data poses a significant challenge with respect to the representation and computation of time geographic entities and relations in road networks. To address this challenge, a spatiotemporal data model is proposed in this article. The proposed spatiotemporal data model is based on a compressed linear reference (CLR) technique to transform network time geographic entities in three-dimensional (3D) (x, y, t) space to two-dimensional (2D) CLR space. Using the proposed spatiotemporal data model, network time geographic entities can be stored and managed in classical spatial databases. Efficient spatial operations and index structures can be directly utilized to implement spatiotemporal operations and queries for network time geographic entities in CLR space. To validate the proposed spatiotemporal data model, a prototype system is developed using existing 2D GIS techniques. A case study is performed using large-scale datasets of space-time paths and prisms. The case study indicates that the proposed spatiotemporal data model is effective and efficient for storing, managing, and querying large-scale datasets of network time geographic entities.

Large-scale global positioning system (GPS) positioning information of floating cars has been recognised as a major data source for many transportation applications. Mapping large-scale low-frequency floating car data (FCD) onto the road network is very challenging for traditional map-matching (MM) algorithms developed for in-vehicle navigation. In this paper, a multi-criteria dynamic programming map-matching (MDP-MM) algorithm is proposed for online matching FCD. In the proposed MDP-MM algorithm, the MDP technique is used to minimise the number of candidate routes maintained at each GPS point, while guaranteeing to determine the best matching route. In addition, several useful techniques are developed to improve running time of the shortest path calculation in the MM process. Case studies based on real FCD demonstrate the accuracy and computational performance of the MDP-MM algorithm. Results indicated that the MDP-MM algorithm is competitive with existing algorithms in both accuracy and computational performance.

Local search heuristics for very large-scale vehicle routing problems (VRPs) have made remarkable advances in recent years. However, few local search heuristics have focused on the use of the spatial neighborhood in Voronoi diagrams to improve local searches. Based on the concept of a k-ring shaped Voronoi neighbor, we propose a Voronoi spatial neighborhood-based search heuristic and algorithm to solve very large-scale VRPs. In this algorithm, k-ring Voronoi neighbors of a customer are limited to building and updating local routings, and rearranging local routings with improper links. This algorithm was evaluated using four sets of benchmark tests for 200–8683 customers. Solutions were compared with specific examples in the literature, such as the one-depot VRP. This algorithm produced better solutions than some of the best-known benchmark VRP solutions and requires less computational time. The algorithm outperformed previous methods used to solve very large-scale, real-world distance constrained capacitated VRP.

This article proposes an efficient solution algorithm to aid travelers' route choice decisions in road network with travel time uncertainty, in the context of advanced traveler information systems (ATIS). In this article, the travel time of a link is assumed to be spatially correlated only to the neighboring links within a local ‘impact area.’ Based on this assumption, the spatially dependent reliable shortest path problem (SD-RSPP) is formulated as a multicriteria shortest path-finding problem. The dominant conditions for the SD-RSPP are established in this article. A new multicriteria A* algorithm is proposed to solve the SD-RSPP in an equivalent two-level hierarchical network. A case study using real-world data shows that link travel times are, indeed, only strongly correlated within the local impact areas; and the proposed limited spatial dependence assumption can well approximate path travel time variance when the size of the impact area is sufficiently large. Computational results demonstrate that the size of the impact area would have a significant impact on both accuracy and computational performance of the proposed solution algorithm.