Slope-Based Path Shift Propensity Algorithm for the Static Traffic Assignment Problem

Abstract

This paper presents a path-based traffic assignment algorithm for solving the static deterministic user equilibrium traffic assignment problem. It uses the concepts of the path shift-propensity factor and the sensitivity of path costs with respect to path flows in the flow update process, and is labeled as the slope-based path shift-propensity algorithm (SPSA). It seeks to enable faster convergence, incorporates behavioral realism in the flow update process, and maintains simplicity of execution for easy deployment in practice. The behavioral rationale behind the proposed algorithm is explained. The mathematical exposition of the algorithm and its proof of convergence are articulated. Numerical experiments are conducted using test networks to benchmark the performance of SPSA. The computational performance of the SPSA is compared with those of two versions of the recently developed path-based algorithm labeled slope-based multipath algorithm (SMPA), the widely-used Frank-Wolfe (F-W) algorithm, and a variant of the F-W algorithm labeled the social pressure algorithm (SPA). They illustrate that the rate of convergence of the SPSA is very close to that of the SMPA and significantly better than those of the F-W algorithm and the SPA. One version of the SMPA performs better than the SPSA in terms of convergence, though the latter is easier to implement and hence a potential substitute for SMPA in practice. Further, the results vindicate the notion that the SPSA is a feasible deployment option under the computational capabilities available today.

A day-to-day dynamical model for the evolution of path flows under disequilibrium of traffic networks with fixed demand

“…Hence, when drivers shift from expensive paths, they are likely to shift to a set of potentially attractive paths rather than just to the cheapest path. This behavioral perspective is motivated by Smith and Mounce (2011) and Kumar and Peeta (2014), and the proposed DTD model can be viewed as the generalization of the static traffic assignment model by Kumar and Peeta (2014).…”

Topological-Based Measures with Flow Attributes to Identify Critical Links in a Transportation Network

“…For the numerical experiments, MATLAB R2016a on a quad-core 3.5GHz CPU desktop computer with 16GB of memory was used. The traffic assignment algorithm used was the Slope-Based Path Shift Propensity Algorithm (SPSA) ( 34 ). The computational time for estimating the hybrid and traffic-based measures is shown in Table 6.…”

Trip Assignment Modelling for an Indian City to Assess the Benefits of Proposing Ring Roads

“…This study evaluated and calibrated travel demand model using Cube software and its relation to fuel consumption, for the city of Shiraz, Iran. Kumar and Peeta (2014) introduced a path-based traffic assignment algorithm for solving the static deterministic user equ i l ibr iu m t ra f f ic assig n ment problem. It used the concepts of the path shift-propensity factor and the sensitivity of path costs with respect to path f lows in the flow update process It was labelled as the slope-based path shift-propensity algorithm (SPSA).…”