Order Estimation of Markov-Chain Processes in Complex Mobility Network Embedded in Vehicle Traces

Vehicle mobility in urban traffic systems is complex, partly because it reflects mobility of a human who drives a vehicle, and partly because it depends on many roles which the vehicle plays. Previous studies on human mobility revealed that it includes Levy-flights-like motions and memoryless deterministic walks as well as random walks, but the mobility of vehicles may be more biased due to their functions. Focusing our research target on a sightseeing vehicle with sufficiently limited functions, we show a method to measure regularity of visitation patterns, quantified by order(s) of Markov chains in their mobility. Graphs of higher-order Markov chains, which are representatives of mobility in a network style, possess statistical properties; in our observation dataset, they include degree distributions similar to scale-free networks. The detection of mobility in real social experiments, which is also assumed on these graphs, yields the order of Markov chains inside it with its comparison with the results of agent-based simulations. Centrality indices of the mobility networks well coincide with prediction of these analytical and numerical results.