Spatio-temporal Networks: Modeling, Storing, and Querying Temporally-Detailed Roadmaps

Given spatio-temporal networks (e.g., roadmaps with traffic speed reported as a time-series in 5 min increments over a typical day for each road-segment) and operators (e.g., network snapshot, shortest path or path evaluation), a spatio-temporal network model provides a computer representation to facilitate reasoning, analysis and algorithm design for important societal applications. For example, next generation routing services are estimated to save consumers hundreds of billions of dollars in terms of time and fuel saved by 2020. Developing a model for spatio-temporal networks is challenging due to potentially conflicting requirements of expressiveness and model simplicity. Related work in Time Geography models spatio-temporal movement and relationships via dimension-based representations such as space-time prisms and space-time trajectories. These representations are not adequate for many STN use-cases, such as spatio-temporal routing queries. To address these limitations, we discuss a novel model called time-aggregated graph (TAG) that allows the properties of the network to be modeled as a time series. This model retains spatial network information while reducing the temporal replication needed in other models, thus resulting in a much more efficient model for several computational techniques for routing problems. In this chapter, we discuss spatio-temporal networks as represented by time-aggregated graphs at a conceptual, logical, and physical level. This chapter also focuses on shortest path algorithms for spatio-temporal networks. We develop the topics via case studies using TAGs in context of Lagrangian shortest-path queries and evacuation route planning.