Tolling traffic links under stochastic assignment: Modelling the relationship between the number and price level of tolled links and optimal traffic flows

Stewart, Kathryn

doi:10.1016/j.tra.2006.09.015

Cited by 14 publications

(14 citation statements)

References 21 publications

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“…The logit SUE model is an important one in transportation science that addresses suboptimal user route choices or difference in the costs perceived by different users. Before discussing the inefficiency of SUE, we should mention that there are two different system optimum definitions in a stochastic environment: one is the aforementioned conventional 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 (Maher et al, 2005;Stewart, 2007), or equivalently maximizes the net economic benefit (Yang, 1999). As a result, there are two ways to define the inefficiency of SUE, i.e.…”

Section: Bounding the Inefficiency Of Logit-based Stochastic User Equmentioning

confidence: 99%

Bounding the inefficiency of logit-based stochastic user equilibrium

Guo

Yang

Liu

2010

European Journal of Operational Research

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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.

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Section: Bounding the Inefficiency Of Logit-based Stochastic User Equmentioning

confidence: 99%

Bounding the inefficiency of logit-based stochastic user equilibrium

Guo

Yang

Liu

2010

European Journal of Operational Research

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“…Marcotte 1986;Patriksson & Rockafellar 2002); it could also represent maximum allowed travel times, exhaust emissions, or constraints defined by equity measures in a multi-class model (e.g. Eliasson & Mattsson 2006;Stewart 2007), or equilibrium travel times (e.g. Sumalee et al 2006), which are examples of joint upper-level constraints.…”

Section: (C ) Stochastic Mathematical Programmes With Equilibrium Conmentioning

confidence: 99%

Robust bi-level optimization models in transportation science

Patriksson

2008

Phil. Trans. R. Soc. A.

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Mathematical programmes with equilibrium constraints (MPECs) constitute important modelling tools for network flow problems, as they place 'what-if' analyses in a proper mathematical framework. We consider a class of stochastic MPEC traffic models that explicitly incorporate possible uncertainties in travel costs and demands. In stochastic programming terminology, we consider 'here-and-now' models where decisions must be made before observing the uncertain parameter values and the responses of the network users; the objective is to minimize the expectation of the upper-level objective function. Such a model could, for example, be used to derive a fixed toll pricing scheme that provides the best revenue for a given network over a time period, where variations in traffic conditions and demand elasticities are described by distributions of parameters in the travel time and demand functions.We present new results on the stability of globally optimal solutions to perturbations in the probability distribution, establishing the robustness of the model. We also discuss penalization and discretization algorithms, the latter enabling the use of standard MPEC algorithms, and provide many future research avenues.

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“…This paper will focus on within-day DCC and the congestion charging toll will be imposed on each path. Figure 1 illustrates the DCC framework we have defined for use in this research; this is the same framework as that presented in Stewart andGe (2010 and. Each component of the framework is further discussed below.…”

Section: Model Formulationmentioning

confidence: 99%

“…Previous papers examining low-revenue tolls (Stewart andGe (2010,2011)) to reduce overall Total Network Travel Cost (TNTC) have examined the entire time [0, T], so as to avoid boundary issue complications; this paper however examines tolling solutions which have better network benefit than those presented in Stewart (2010b, 2012) and simultaneously examines the boundary issues of these relative to predetermined tolls.…”

Section: Tolling Schemementioning

confidence: 99%

“…In the static case, the minimal revenue toll problem is capable of solution by various methods, such as linear programming (Bergendorff et al, 1997) and heuristically by reduction to a multicommodity max-flow problem (Dial, 2000). Previous work by Stewart (Stewart andMaher, 2006, Stewart, 2007) in a static stochastic environment has developed heuristics to determine low revenue tolls that produce good sub-optimal flow patterns where total network costs approach the system optimal. Extending to the dynamic case produces a large range of additional further objectives; primarily the tolls levied can vary with time and hence may be flat or profiled, there is usually a desired arrival-window imposed and tolling periods do not have to extend throughout the entire modelling period.…”

Section: Introductionmentioning

confidence: 99%

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