This paper introduces a stylized model of delay propagation on temporal networks to study the functionality of schedule-based systems where timing is crucial. The model exhibits timeliness criticality, a novel critical behavior where the magnitude of the delay-mitigating buffer acts as a control parameter. The authors characterize fluctuations near criticality (avalanches) and identify corresponding critical exponents. The model is applied to real-world temporal systems like production networks, and potential connections to the mode-coupling theory of glasses, depinning transition, and the directed polymer problem are explored.

José Moran, Matthijs Romeijnders, Pierre Le Doussal, Frank P. Pijpers, Utz Weitzel, Debabrata Panja, Jean-Philippe Bouchaud