Fluctuation-driven capacity distribution in complex networks

TL;DR

This paper studies how real-world infrastructure networks allocate capacity relative to load, revealing a nonlinear relationship influenced by cost considerations and highlighting differences from traditional linear models.

Contribution

It provides empirical evidence of capacity-load relations in infrastructure networks and introduces a model explaining how capacity allocation depends on cost constraints and network fluctuations.

Findings

Capacity tends to match maximum available when cost constraints are weak.

Higher cost emphasis leads to capacities approaching loads nonlinearly.

Networks have evolved to prevent local failures but not necessarily global cascades.

Abstract

Maximizing robustness and minimizing cost are common objectives in the design of infrastructure networks. However, most infrastructure networks evolve and operate in a highly decentralized fashion, which may significantly impact the allocation of resources across the system. Here, we investigate this question by focusing on the relation between capacity and load in different types of real-world communication and transportation networks. We find strong empirical evidence that the actual capacity of the network elements tends to be similar to the maximum available capacity, if the cost is not strongly constraining. As more weight is given to the cost, however, the capacity approaches the load nonlinearly. In particular, all systems analyzed show larger unoccupied portions of the capacities on network elements subjected to smaller loads, which is in sharp contrast with the assumptions involved in (linear) models proposed in previous theoretical studies. We describe the observed behavior of the capacity-load relation as a function of the relative importance of the cost by using a model that optimizes capacities to cope with network traffic fluctuations. These results suggest that infrastructure systems have evolved under pressure to minimize local failures, but not necessarily global failures that can be caused by the spread of local damage through cascading processes.