Reliable Network Design Problem: Case with Uncertain Demand and Total Travel Time Reliability

Sumalee, Agachai; Watling, David; Nakayama, Shinichi

doi:10.3141/1964-10

Cited by 92 publications

(62 citation statements)

References 29 publications

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“…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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“…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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“…(7), n a E V     is the n th raw moment of the normally distributed link flow. The method of moment generating function (MGF) applied in (11) and (17) …”

Section: Link and Path Travel Timesmentioning

confidence: 99%

“…Since travel times are stochastic, the perceived expected travel time is considered to be the deterministic dis-utility term of each path, following (11). The perceived expected travel cost for path k is defined as ; Σ , which can be determined from link travel time perception errors and the link path incident matrix, see e.g.…”

Section: Path Choice Modelmentioning

confidence: 99%

“…The model is then incorporated into FNDP by optimizing the link capacity investments in the future so as to maximize the M-SD network capacity. An analytical approach to solve the proposed model, following the implicit programming approach (6,10,11), is developed. The method of sensitivity analysis (SA) (12,13) is employed to calculate both the gradient of the objective function, and Jacobian of the constraints with respect to changes in the design parameters, namely the mean and SD demand multipliers, and link capacity investments.…”

Section: Introductionmentioning

confidence: 99%

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Evaluation and Design of Transport Network Capacity under Demand Uncertainty

Sumalee

Luathep

Lam

et al. 2009

Transportation Research Record: Journal of the Transportation R

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This paper proposes a flexible transport network capacity evaluation and design problem (FNDP) under demand variability. The future stochastic demand is assumed to follow a normal distribution. Travellers' path choice behaviour is assumed to follow the Probit Stochastic User Equilibrium (SUE). The network reserve capacity is used to evaluate the performance of the network. Since the future demand is stochastic, the reserve capacity is measured by possible increases in both mean and standard deviation (SD) of the base demand distribution. The proposed model therefore represents the flexibility of the network in its robustness to OD demand variation (i.e. high SD). The proposed model can also determine an optimal network design to maximize the reserve capacity of the network in terms of both the mean and SD of the increased demand distribution. The paper applies the implicit programming approach to solve the FNDP. Sensitivity analysis is adopted to provide all necessary derivatives. The model and algorithm are tested with a hypothetical network to illustrate the merits of the proposed model.

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“…However, in a more general situation, each driver's perceptions can be modelled through individual learning models, which are called disaggregate memory models, but at the cost of significant computing time (8). It is also noted that OD demand is assumed to be constant, but could be readily extended to the case of uncertain demand as in (11) and ( 12).…”

Section: Stochastic Process Modelmentioning

confidence: 99%

Doubly Dynamic Traffic Assignment

Balijepalli

Watling

Liu

2007

Transportation Research Record: Journal of the Transportation R

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This paper presents, and investigates properties of, a doubly dynamic simulation assignment model which involves specifying a day-to-day route choice model as a discrete time stochastic process, combining a between-day driver learning and adjusting model with a continuous time, within-day dynamic network loading. Such a simulation model may be regarded as the realisation of a stochastic process, which under certain mild conditions, admits a unique stationary probability distribution (i.e. an invariant probability distribution over time of network flows and travel times). Such a stationary state of the stochastic process is of interest to transport modellers, as one can then describe the stochastic process by its moments such as the means, variances and covariances of the flow and travel time profiles. The results of a simulation experiment are reported in which the process of individual drivers' day-to-day route choices are based on the aggregate learning of the experienced within-day route costs by all drivers departing in the same period. Experimental results of the stationarity of the stochastic process are discussed, along with an analysis of the sensitivity of autocorrelations of the route flows to the route choice model parameters. The results also illustrate the consistency of the link flow model with properties such as First-In, First-Out (FIFO), and a simple network is used to illustrate the properties.

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Reliable Network Design Problem: Case with Uncertain Demand and Total Travel Time Reliability

Cited by 92 publications

References 29 publications

Robust bi-level optimization models in transportation science

Robust bi-level optimization models in transportation science

Evaluation and Design of Transport Network Capacity under Demand Uncertainty

Doubly Dynamic Traffic Assignment

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