On Emergent Traffic Patterns in Synthetic Road Network Ensembles
: An Experimental Mathematics Approach

  • Alonso Espinosa Mireles De Villafranca

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


This thesis presents a computational investigation of traffic equilibrium models on synthetic networks that represent stylised street maps. Borrowing from statistical physics and complexity science, a network ensemble approach is used to examine the relationship between network structure and traffic equilibria. The network family constructed (αβ-networks) capture node distributions that range from square grids to networks with uniformly randomly distributed nodes. Cost-function parameters for roads are defined according to an endogenous supply provision heuristic that incorporates local network structure, and the static traffic assignment problem (STAP) is solved for ensembles of αβ -networks with a range of morphologies. How the networks’ griddedness and road density affect the performance of traffic equilibria is explored. A key finding is that traditional network theory statistics do not correlate well with transportation
efficiency. Also, less grid-like networks are more sensitive to the choice of demand structure. For mixtures of selfish and altruistic vehicles, the road density and network size are found to be key features determining the pathway to optimal performance. Finally, the αβ -networks are used to investigate how to recover a network fundamental diagram (NFD). It is found that combining the STAP with an ensemble approach is enough to determine how the uncongested branch of the NFD depends on network morphology. Finally, a method is proposed for recovering the congested branch of the NFD by using projected dynamical systems and Filippov systems, in order to capture dynamics of congestion that that lie beyond the STAP’s scope.
Date of Award26 Nov 2020
Original languageEnglish
Awarding Institution
  • The University of Bristol
SupervisorR E Wilson (Supervisor)

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