Bounding the inefficiency of logit-based stochastic user equilibrium

Abstract

Abstract. Bounding the inefficiency of selfish routing has become an emerging research subject. A central result obtained in the literature is that the inefficiency of deterministic User Equilibrium (UE) is bounded and the bound is independent of network topology. This paper makes a contribution to the literature by bounding the inefficiency of the logit-based Stochastic User Equilibrium (SUE). In a stochastic environment there are two different definitions of system optimization: one is the traditional System Optimum (SO) which minimizes the total actual system travel time, and the other is the Stochastic System Optimum (SSO) which minimizes the total perceived travel time of all users. Thus there are two ways to define the inefficiency of SUE, i.e. to compare SUE with SO in terms of total actual system travel time, or to compare SUE with SSO in terms of total perceived travel time.We establish upper bounds on the inefficiency of SUE in both situations.

Inefficiency of Logit-Based Stochastic User Equilibrium in a Traffic Network Under ATIS

“…(17), and thereby bound the overall cost inefficiency of the two-user class SUE. Before doing this, we first introduce a lemma which has been proven in Guo and Yang (2005) and Yang and Huang (2005). …”

“…In this paper, we extend the works of Guo and Yang (2005) and Yang and Huang (2005) that dealt with single user class only, to the two-user class case in which one class is equipped with ATIS and another without. All drivers are divided into two classes, both of which follow the SUE principle in route choices.…”

“…Following this line of thinking, Guo and Yang (2005) and Yang and Huang (2005) investigated the bound of the cost inefficiency of a SUE flow pattern in relation to the Wardropian system optimum.…”

Efficiency Loss of Mixed Equilibrium Associated with Altruistic Users and Logit-based Stochastic Users in Transportation Network

“…Based on the results of Ledyard [17], Chen and Kempe [19], and the definition of the perceived cost of altruistic user with altruism coefficient AU b^h is as follows: 6 @. The AU aim to minimize their personal perceived travel cost under the current routing decisions of the LSU, which is equivalent to solve…”

“…After that, quantifying the efficiency loss of user's selfish behaviour in the transportation context has been an important aspect in the traffic science. The researchers have extended the above works in different aspects [3][4][5][6][7][8][9].…”