Timeliness criticality in complex systems

TL;DR

This paper introduces a stylized model of delay propagation in temporal networks, revealing a new form of critical behavior called timeliness criticality, with implications for real-world systems and connections to established theories.

Contribution

It proposes a novel model demonstrating timeliness criticality in delay propagation, characterizes its critical exponents, and links it to existing physical theories.

Findings

Identification of timeliness criticality as a new critical phenomenon.

Characterization of fluctuations and critical exponents near criticality.

Validation of the model on real-world production networks.

Abstract

In complex systems, external parameters often determine the phase in which the system operates, i.e., its macroscopic behavior. For nearly a century, statistical physics has extensively studied systems' transitions across phases, (universal) critical exponents, and related dynamical properties. Here we consider the functionality of systems, notably operations in socio-technical ones, production in economic ones and, more generally, any schedule-based system, where timing is of crucial importance. We introduce a stylized model of delay propagation on temporal networks, where the magnitude of delay-mitigating buffer acts as a control parameter. The model exhibits {\it timeliness criticality}, a novel form of critical behavior. We characterize fluctuations near criticality, commonly referred to as ``avalanches'', and identify the corresponding critical exponents. The model exhibits timeliness criticality also when run on real-world temporal systems such as production networks. Additionally, we explore potential connections with the Mode-Coupling Theory of glasses, the depinning transition and the directed polymer problem.