Model checking spatial reachability specifications of public transport networks

Well-designed spatial configurations of public transport stops and routes in big cities contribute to enhancing daily travel services for citizens, effectively mitigating traffic congestion, and addressing other pertinent challenges. When examining spatial layouts of public transport networks (PTNs), various reachability demands between stops or urban Points of Interest (POIs) are crucial issues should be firstly taken into account. Existing methods to investigate spatial reachability properties of PTNs generally need to construct some evaluation functions, or survey reachability metrics through some network analysis techniques. These methods are often impractical, as the functional relations always cannot be accurately defined, or some global network metrics cannot provide explicit evidences for PTN layout planning or optimization.

In this paper, we introduce spatial model checking techniques to the formal verification of the reachability specifications of PTN to guarantee the rationality of PTN layout. First, we extend closure space structure by incorporating attribute labeling functions and logical propositions for public transport stops and routes to develop a formal spatial verification model for PTN spatial layout. Second, we propose several novel reachability operators based on the logical operators of the Spatial Logic for Closure Space (SLCS) to facilitate the logical characterization of reachability specifications. Third, we perform the verification of the transformed reachability formulas by the spatial model checker topochecker. Examples demonstrate the effectiveness of our approach and indicate that it can perform automatic, descriptive and comprehensible verification of the reachability properties PTN layouts.