Network Flows Under Thermal Restrictions

TL;DR

This paper introduces thermal networks where node capacity depends on temperature, analyzing maximum flow under heating and cooling dynamics, providing closed-form solutions for optimal flow.

Contribution

It models thermal networks with temperature-dependent node capacities and derives closed-form solutions for maximum flow, extending traditional flow models.

Findings

Closed-form maximum flow solutions for thermal networks.

Thermal network properties and behavior analyzed.

Impact of cooling on flow capacity studied.

Abstract

We define a \emph{thermal network}, which is a network where the flow functionality of a node depends upon its temperature. This model is inspired by several types of real-life networks, and generalizes some conventional network models wherein nodes have fixed capacities and the problem is to maximize the flow through the network. In a thermal network, the temperature of a node increases as traffic moves through it, and nodes may also cool spontaneously over time, or by employing cooling packets. We analyze the problems of maximizing the flow from a source to a sink for both these cases, for a holistic view with respect to the single-source-single-sink dynamic flow problem in a thermal network. We have studied certain properties such a thermal network exhibits, and give closed-form solutions for the maximum flow that can be achieved through such a network.