Biological version of Braess' paradox arising from perturbed homeostasis

Abstract

Braess' paradox is an observation in traffic networks in which changes to the structure of the network-such as the addition of a road-which are intended to enhance flow can often instead have the paradoxical effect of reducing flow through the network. Versions of Braess' paradox have subsequently been observed in many other network types. Homeostasis is a seemingly unrelated biological concept in which interacting regulatory mechanisms work in concert to regulate a particular system output such that it is relatively insensitive to changes in input. A classic example is the broad range of ambient temperatures (input) over which mammalian body temperature (output) is close to constant. In this work, we propose a connection between these concepts using the mathematical formulation of infinitesimal homeostasis and argue that perturbations of homeostatic systems in disease may often lead to observations of paradoxical behavior via the universal unfoldings of infinitesimal homeostasis. We illustrate the concept with an example system drawn from the study of the pathophysiology and treatment of asthma; as a network flow model, this exhibits a form of paradoxical behavior akin to Braess' paradox which we argue arises from perturbation of homeostasis due to disease.

On Braess's paradox and routing algorithms

“…Recently, studies have investigated the paradox in new areas. Penchina and Penchina 3 described for mechanical network, Donovan demonstrated the biology version 4 and Baillieul et al for smart microgrids. 5 Bruce et al 17 consider the paradox in queueing networks with state-dependent routing and parallel routes.…”

“…The creation of a new road can lead drivers to use this new road and increase the overall time in traffic. Many studies have investigated the paradox in the context of game theory, 2 road traffic network, 1 mechanical network, 3 biology, 4 smart microgrids 5 and even data network. 6 However, they looked at the congestion cases and latency edge networks.…”

Reducing urban traffic congestion due to localized routing decisions

“…It suggests that newly introduced shortcuts, being attractive to users, create congestion in the shortcut edges and nearby areas. The phenomenon is reminiscent of Braess's paradox in the static routing game [32] and other complex systems [33][34][35], where adding resources can possibly lead to a degradation of system performance. In our model, drivers have limited knowledge and are unaware of the long-distance traffic condition, so that the myopic decisions make the system more prone to congestion.…”