An algorithm for the stochastic user equilibrium problem

Damberg, Olof; Lundgren, Jan T.; Patriksson, Michael

doi:10.1016/0191-2615(95)00026-7

Cited by 80 publications

(51 citation statements)

References 18 publications

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“…However, Carey and Ge (2012) provide numerical evidence of promising convergence in the DUE case, which matches with our own experience of applying these methods in an RSUE setting to the transformed costs (section 6). Some of the other path-based DUE and SUE solution algorithms (such as the SUE DSD proposed by Damberg et al (1996)) have been proven to converge under certain assumptions, and thus applying e.g. the Damberg et al (1996) algorithm for the Restricted master problem phase (…”

Section: Convergence Of Proposed Solution Methodsmentioning

confidence: 99%

“…Consequently, a one-to-one mapping exists between path and link flows for SUE solutions, making link-or path-based methods in this sense equally attractive. Many link-and path-based solution methods have been proposed for SUE (e.g., Sheffi and Powell, 1982;Damberg et al, 1996;Bekhor and Toledo, 2005;Zhou et al, 2012;Akamatsu, 1996;Bell et al, 1997;Leurent, 1997;Maher and Hughes, 1997).…”

Section: Solving In the Space Of Link-or Path Flowsmentioning

confidence: 99%

“…These have been modified to apply to SUE with an MNL choice model (Damberg et al, 1996;Bekhor and Toledo, 2005) and a Cross-Nested Logit model (Bekhor et al, 2008;Zhou et al, 2012).…”

Section: The Restricted Master Problem Phasementioning

confidence: 99%

“…While the latter three references use a pre-defined choice set (which in the adaptation to the RSUE solution algorithm would be defined by the routes generated by the Column generation phase), it is worth noting that the algorithm proposed by Damberg et al (1996) allows augmenting the choice set. Damberg et al (1996) noted that this augmentation can be achieved by following one of many strategies.…”

Section: The Restricted Master Problem Phasementioning

confidence: 99%

“…Damberg et al (1996) noted that this augmentation can be achieved by following one of many strategies. Indeed, even though the RSUE model had not then been defined, one of their suggested strategies generates a solution fulfilling the MNL RSUE(min) conditions!…”

Section: The Restricted Master Problem Phasementioning

confidence: 99%

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Stochastic user equilibrium with equilibrated choice sets: Part II – Solving the restricted SUE for the logit family

Rasmussen

Watling

Prato

et al. 2015

Transportation Research Part B: Methodological

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We propose a new class of path-based solution algorithms to solve the Restricted Stochastic User Equilibrium (RSUE), as introduced in Watling et al (2014). The class allows a flexible specification of how the choice sets are 'systematically' grown by considering congestion effects and how the flows are allocated among routes. The specification allows adapting traditional pathbased stochastic user equilibrium flow allocation methods (designed for pre-specified choice sets) to the generic solution algorithm. We also propose a cost transformation function and show that by using this we can, for certain Logit-type choice models, modify existing path-based Deterministic User Equilibrium solution methods to fit the RSUE solution algorithm. The transformation function also leads to a two-part relative gap measure for consistently monitoring convergence to a RSUE solution. Numerical tests are reported on two real-life cases, in which we explore convergence patterns and choice set composition and size, for alternative specifications of the RSUE solution algorithm.

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Section: Convergence Of Proposed Solution Methodsmentioning

confidence: 99%

Section: Solving In the Space Of Link-or Path Flowsmentioning

confidence: 99%

“…These have been modified to apply to SUE with an MNL choice model (Damberg et al, 1996;Bekhor and Toledo, 2005) and a Cross-Nested Logit model (Bekhor et al, 2008;Zhou et al, 2012).…”

Section: The Restricted Master Problem Phasementioning

confidence: 99%

Section: The Restricted Master Problem Phasementioning

confidence: 99%

Section: The Restricted Master Problem Phasementioning

confidence: 99%

See 3 more Smart Citations

Stochastic user equilibrium with equilibrated choice sets: Part II – Solving the restricted SUE for the logit family

Rasmussen

Watling

Prato

et al. 2015

Transportation Research Part B: Methodological

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Network equilibrium for congested multi‐mode networks with elastic demand

Lam

2003

J of Advced Transportation

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This paper proposes an elastic demand network equilibrium model for networks with transit and walking modes. In Hong Kong, the multi-mode transit system services over 90% of the total journeys and the demand on it is continuously increasing. Transit and walking modes are related to each other as transit passengers have to walk to and from transit stops. In this paper, the multi-mode elastic-demand network equilibrium problem is formulated as a variational inequality problem where the combined mode and route choices are modeled in a hierarchical logit structures and the total travel demand for each origin-destination pair is explicitly given by an elastic demand function. In addition, the capacity constraint for transit vehicles and the effects of bi-directional flows on walkways are considered in the proposed model. All these congestion effects are taken into account for modeling the travel choices. A solution algorithm is developed to solve the multi-mode elastic-demand network equilibrium model. It is based on a Block Gauss-Seidel decomposition approach coupled with the method of successive averages. A numerical example is used to illustrate the application of the proposed model and solution algorithm.Public transport or transit systems are generally considered to be economically, financially, environmentally and socially sustainable forms of urban transportation in major cities (World Bank, 1996). Recently, substantial research has been devoted to the methodological developments (Wong and Lam, 200 1) and practical applications (Lam and Wong, 2001) of efficient public transit systems. The modeling of public transit systems can be broadly classified into five stages (Lam and

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Algorithms for Traffic Assignment to Transportation Networks

Cascetta

2001

Applied Optimization

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An algorithm for the stochastic user equilibrium problem

Cited by 80 publications

References 18 publications

Stochastic user equilibrium with equilibrated choice sets: Part II – Solving the restricted SUE for the logit family

Stochastic user equilibrium with equilibrated choice sets: Part II – Solving the restricted SUE for the logit family

Network equilibrium for congested multi‐mode networks with elastic demand

Algorithms for Traffic Assignment to Transportation Networks

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