# A Physarum-inspired model for the probit-based stochastic user equilibrium problem

## TL;DR

This paper introduces a Physarum-inspired model tailored for the probit-based stochastic user equilibrium problem in traffic networks, offering a novel approach to find equilibrium flows considering two-way traffic and normal distribution of perceived costs.

## Contribution

The work modifies the Physarum model to handle two-way traffic networks and probabilistic cost perception, providing a new method for stochastic user equilibrium computation.

## Key findings

- The proposed model effectively finds equilibrium flows in traffic networks.
- It performs favorably compared to the Method of Successive Averages.
- Numerical examples demonstrate its applicability and efficiency.

## Abstract

Stochastic user equilibrium is an important issue in the traffic assignment problems, tradition models for the stochastic user equilibrium problem are designed as mathematical programming problems. In this article, a Physarum-inspired model for the probit-based stochastic user equilibrium problem is proposed. There are two main contributions of our work. On the one hand, the origin Physarum model is modified to find the shortest path in traffic direction networks with the properties of two-way traffic characteristic. On the other hand, the modified Physarum-inspired model could get the equilibrium flows when traveller's perceived transportation cost complies with normal distribution. The proposed method is constituted with a two-step procedure. First, the modified Physarum model is applied to get the auxiliary flows. Second, the auxiliary flows are averaged to obtain the equilibrium flows. Numerical examples are conducted to illustrate the performance of the proposed method, which is compared with the Method of Successive Average method.