Delay Propagation in Temporal Networks close to Criticality

Abstract

Timeliness — goods and services being at the right place at the right time — is essential for transport networks to function properly. To ensure timeliness, transport networks must anticipate random delays and include temporal buffers in their schedules to diminish them. Determining the ideal buffer allocation is a difficult task, since a balance must be struck between system efficiency and timeliness. This thesis provides a framework to process and analyze delay propagation by using a temporal network as a model, in order to enhance our understanding of spreading effects in complex systems such as transport networks. Temporal network analysis reveals a second-order phase transition in delay propagation, occurring at a critical uniform buffer size where the mean delay propagation is zero. In other words, temporal networks experience a temporal criticality — a criticality in the temporal dimension. In sparse networks, this transition becomes an infinite-order transition. When delay in the system interacts with the topology of the network, the transition also becomes of infinite order. At the critical buffer size Bc, the mean delay auto- correlation diverges, and the mean delay noise exhibits 1/f 1.5 noise. Consequently, at criticality, the system demonstrates optimal conditions for information transfer.