Parallel Network Flow Allocation in Repeated Routing Games via LQR Optimal Control

TL;DR

This paper models repeated routing games on parallel networks using LQR optimal control, providing a control-theoretic analysis and an explicit MPC algorithm to optimize flow allocation and ensure convergence.

Contribution

It introduces a novel control framework for repeated routing games, applying LQR and explicit MPC to analyze and optimize flow dynamics on parallel networks.

Findings

Control parameters ensure flow conservation.

Explicit MPC provides optimal flow solutions.

Numerical results show parameter impact on solutions.

Abstract

In this article, we study the repeated routing game problem on a parallel network with affine latency functions on each edge. We cast the game setup in a LQR control theoretic framework, leveraging the Rosenthal potential formulation. We use control techniques to analyze the convergence of the game dynamics with specific cases that lend themselves to optimal control. We design proper dynamics parameters so that the conservation of flow is guaranteed. We provide an algorithmic solution for the general optimal control setup using a multiparametric quadratic programming approach (explicit MPC). Finally we illustrate with numerics the impact of varying system parameters on the solutions.