Xiaolei Guo

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.

The price of anarchy of cournot oligopoly

Cournot oligopoly is typically inefficient in maximizing social welfare which is total surplus of consumer and producer. This paper quantifies the inefficiency of Cournot oligopoly with the term “price of anarchy”, i.e. the worst-case ratio of the maximum possible social welfare to the social welfare at equilibrium. With a parameterization of the equilibrium market share distribution, the inefficiency bounds are dependent on equilibrium market shares as well as market demand and number of firms. Equilibrium market share parameters are practically observable and analytically manageable. As a result, the price of anarchy of Cournot oligopoly established in this paper is applicable to both practical estimation and theoretical analysis.

Build-operate-transfer Schemes for Road Franchising with Road Deterioration and Maintenance Effects

Private provision of public roads through build-operate-transfer (BOT) approaches is increasing around the world. By considering both social welfare gain and profitability, the BOT problem is to determine the optimal BOT contract which can be viewed as a combination of three primary variables of concession period, road capacity and toll charge. This paper models the BOT problem as the isoperimetric problem in calculus of variations to maximize the social welfare with a profit constraint. The model explicitly incorporates the effect of road deterioration and maintenance over the years, which is assumed to depend on the traffic loads, road capacity and road natural deterioration. We find that an optimal pricing policy requires toll increase over calendar time to reduce traffic load due to time-increasing and load-increasing maintenance cost. If, however, the marginal user damage on road is independent of time, then the optimal toll charge is free from the effect of road natural deterioration and thus time-invariant. We also discuss how to reach an optimal contract through government regulations and investigate the effects of economic growth on the solution properties of the problem.

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.