Description:

In this talk, I introduce a dynamic percolation model designed to describe resource consumption and depletion in networks: the minimum-cost percolation (MCP) model.  In the model, rational agents progressively consume resources allocated on the edges of a network along demanded minimum-cost paths. As a result, the network undergoes a transition between a percolating phase where it can properly serve demand to a non-percolating phase where demand can no longer be supplied. First, I investigate the MCP transition on Erd\H{o}s–Rényi (ER) and uncorrelated scale-free (SF) networks. On ER graphs, the nature of the phase transition changes depending on the budget available to the agents. Finite budget leads to a standard continuous percolation phase transition; the transition becomes weakly discontinuous if budget is unbounded. On SF graphs, the power-law degree distribution is responsible for an anomalous phase transition only if paths of length one can be requested; for larger budget values instead, one recovers the same behavior as in ER graphs, displaying a continuous transition for finite budget and a weakly discontinuous transition in the infinite-budget case. Second, I apply the MCP model to a weighted, directed, temporal, multi-layer network representation of the air transportation system that can be generated using real schedules of commercial flights operated by US carriers. I study how cooperation among different carriers could improve the ability of the overall air transportation system in serving the demand of passengers, finding that unrestricted cooperation could lead to a 30% efficiency increase compared to the non-cooperative scenario. Cooperation would require major airlines to share a significant portion of their market, but it would also allow for an increased robustness of the system against perturbations causing flight cancellations. My findings underscore some key benefits that could emerge by simply promoting code-share arrangements among US airlines without altering their current cost of operation.

Filippo Radicchi, Professor, Indiana University

Host; Istvan Kovacs