A Nonlinear Pairwise Swapping Dynamics to Model the Selfish Rerouting Evolutionary Game

TL;DR

This paper introduces a nonlinear pairwise swapping dynamics (NPSD) model for selfish rerouting in traffic networks, demonstrating its advantages over classical methods in preventing over-swapping, ensuring convergence, and simplifying the step-length selection process.

Contribution

The paper develops a novel nonlinear pairwise swapping dynamics model that improves traffic evolution modeling by ensuring convergence and eliminating over-swapping issues.

Findings

NPSD and PAP require similar network information for route-swaps.

NPSD prevents over-swapping in traffic rerouting.

NPSD guarantees global convergence in continuous time.

Abstract

In this paper, a nonlinear revision protocol is proposed and embedded into the traffic evolution equation of the classical proportional-switch adjustment process (PAP), developing the present nonlinear pairwise swapping dynamics (NPSD) to describe the selfish rerouting evolutionary game. It is demonstrated that i) NPSD and PAP require the same amount of network information acquisition in the route-swaps, ii) NPSD is able to prevent the over-swapping deficiency under a plausible behavior description; iii) NPSD can maintain the solution invariance, which makes the trial and error process to identify a feasible step-length in a NPSD-based swapping algorithm is unnecessary, and iv) NPSD is a rational behavior swapping process and the continuous-time NPSD is globally convergent. Using the day-to-day NPSD, a numerical example is conducted to explore the effects of the reaction sensitivity on traffic evolution and characterize the convergence of discrete-time NPSD.