Tian-Liang Liu

Bounding the inefficiency of logit-based stochastic user equilibrium

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.

Mixed Travel Behavior in Networks with ATIS and Upper Bound of Efficiency Loss

Abstract In a transportation network supported by the Advanced Traveler Information Systems (ATIS), the drivers equipped with ATIS are directed by a control center to select their routes so as to minimize the total network travel time, while the unequipped ones make the route choice decisions on the base of minimizing their individual travel times. This article presents a variational inequality model to formulate the mixed travel behavior associated with both system optimum and user equilibrium, and derives a general formula for the upper bound of efficiency loss of the mixed behavior. The upper bounds when all link travel cost functions are polynomial are examined against different ATIS market penetrations. It is found that the upper bound is related to the ATIS market penetration and the corresponding mixed equilibrium flow pattern.

Equilibria and Inefficiency in Traffic Networks with Stochastic Capacity and Information Provision

In this paper, we study the inefficiencies of various behavior equilibria in traffic networks with stochastic capacity and information provision. Variational inequality models are presented to formulate the travel behaviors associated with user equilibrium (UE) with imperfect information, system optimum (SO) with imperfect information and system optimum with perfect information, respectively. The tight upper bounds of inefficiencies caused by UE selfish behavior with imperfect information are analytically discussed in detail. It is found that when link travel time functions are all polynomial, the worst-case inefficiencies against the SOs with imperfect or perfect information are dependent upon the steepness degree of link time functions and independent of the network topology. The upper bound of inefficiency against the SO with perfect information is yet dependent upon the degradation degree and occurring probability density of link capacity. Furthermore, it is also found that perfect information can always improve the traffic network performance whilst imperfect information has the same worst-case efficiency as zero information.