Multi-Scale Equilibrium under Variable Indicator Dimensionality: Faithful Reduction of Dynamic Attractors in Urban Mobility Systems
Multiagent Systems
Summary
The authors study how to analyze complex urban mobility systems using many different performance indicators, but recognize that data availability often varies across cities. They develop a model showing how fast and slow layers of urban mobility performance interact during disruptions, and define when simpler, lower-dimensional indicators can still accurately capture the system's state. Their work includes mathematical conditions for these simplifications and shows a tendency to underestimate recovery times when monitoring is reduced. Simulations in example city setups support their findings, helping city planners decide which mobility indicators are most important to track.
Authors
Ali Ghoroghi, Yacine Rezgui, Afrouz Ghaemi, Cristina De Nardi, Andrei Hodorog
Abstract
Equilibrium analysis of urban mobility systems is formulated in a high-dimensional indicator space, whilst data availability varies sharply across cities and disruption contexts. This paper gives a formal treatment of that mismatch. It presents a dynamic multi-layer equilibrium attractor for disrupted urban mobility, in which a fast performance layer relaxes towards an indicator-dependent target, a slow strategic layer supplies a joint traffic, modal and learning fixed point, and antifragility is classified through a statistical decision rule on the post-to-baseline performance ratio. It then characterises when a lower-dimensional indicator projection is faithful to this equilibrium structure, establishing four results: conditions for exact and approximate projectability of the attractor with an explicit error bound; preservation of the coupled two-layer fixed point up to a contraction boundary; the retained Fisher information and decision power of any indicator support under a measurement model on observable urban indicators; and a one-sided restoration-time bias, whereby reduced monitoring can only understate recovery duration. A simulation study on three stylised pilot-city configurations verifies each result, and shows that two observable channels suffice for the candidate classification target where the indicator catalogue permits. The framework gives city authorities a principled basis for deciding which indicators must be maintained.