A Boundedly Rational Day-to-Day Rerouting Model with Dynamic Indifference Band and Net Marginal Cost Preference

Abstract

This paper suggests factoring both dynamic indifference band (DIB) and marginal decision rule into boundedly rational day-to-day traffic dynamics modeling. To this purpose, a relative indifference band based DIB is employed to capture the variation of indifference band against dynamical network traffic conditions, and the net marginal cost preference (NetMCP) is newly introduced and quantified to replace the routine marginal cost preference as an amended behavior criterion for rerouting decision. To concentrate on the essence, DIB and NetMCP are mathematically formulated into the traffic evolution equation of the classical proportional-switch adjustment process with a new revision protocol, leading to the present dynamically bounded rational swapping process with NetMCP (DBRSP-NetMCP), of which the stationary state is defined and proved. It is also proved that DBRSP-NetMCP is a bounded rational behavior swapping process; and given separable link travel times, DBRSP-NetMCP is globally stable. It is numerically demonstrated that i) an object-oriented modelling approach may cause obvious deviation in rerouting behavior from the behavior-oriented one, and thus is inadvisable to model the day-to-day traffic dynamics; and ii) both DIB and NetMCP show striking effect on traffic evolution, and NetMCP helps to shorten the evolution path towards the stationary states, which may contribute to better the performance of a swapping algorithm to solve the deterministic traffic equilibrium.