A mixed integer linear programming formulation of the dynamic traffic assignment problem

Kaufman, David W.; Nonis, Jason; Smith, Robert L.

doi:10.1109/icsmc.1992.271771

Cited by 3 publications

(3 citation statements)

References 9 publications

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“…The nature of the assignment mapping A is very general; our definition is intended to encompass everything from deterministic mathematical models based on link impedance functions (e.g., Janson (1991), Kaufman, Nonis, and Smith (1996), and Lafortune et al (1994)) to deterministic traffic simulations (e.g., Santiago and Rathi (1990), Van Aerde et al (1989), and Wong (1990)). …”

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confidence: 99%

User-equilibrium properties of fixed points in dynamic traffic assignment

Kaufman

Smith

Wunderlich

1998

Transportation Research Part C: Emerging Technologies

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This paper considers the problem of dynamic traffic assignment under the principle that individual drivers will choose fastest paths, in the dynamic situation where path durations consist of time-dependent link travel times. Rather than constructing a unified model encompassing traffic dynamics and route choice, we decompose the model into an assignment mapping, which identifies the link travel times resulting from an input routing policy, and a routing mapping, which yields fastest-path routings associated with input link travel times. Since time-dynamic link travel times are influenced by route choice, this dynamic situation therefore encompasses predictive routing strategies.We establish that user-equilibrium routing policies are fixed points of the composition of the routing and assignment functions. After discussing difficulties associated with establishing existence of fixed points under discrete-time modeling and all-ornothing routing, we present instead new iterative routing mappings for continuous-time multipath routing (the splitting of a single-class flow onto multiple paths), which adjust routing policies more incrementally. We provide sufficient conditions for existence of fixed points in various routing policy domains and offer some suggestions on the computation of these fixed-point policies.

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Section: Insert Figure 1 About Herementioning

confidence: 99%

User-equilibrium properties of fixed points in dynamic traffic assignment

Kaufman

Smith

Wunderlich

1998

Transportation Research Part C: Emerging Technologies

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“…We build the assumption that vehicles entering in a link i j ( , ) later from node i should not leave earlier from node j, which means the ATs do not pass on another. These constraints were established by Kaufman et al (1992). Constraints (18)-(22) define the domain for the decision variables.…”

Section: Decision Variables P Evtmentioning

confidence: 99%

Automated taxis’ dial-a-ride problem with ride-sharing considering congestion-based dynamic travel times

Xiao

Correia

2020

Transportation Research Part C: Emerging Technologies

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In this paper, we study the dial-a-ride problem of ride-sharing automated taxis (ATs) in an urban road network, considering the traffic congestion caused by the ATs. This shared automated mobility system is expected to provide a seamless door-to-door service for urban travellers, much like what the existing transportation network companies (TNC) do, but with decreased labour cost and more flexible relocation operations due to the vehicles' automation. We propose an integer non-linear programming (INLP) model that optimizes the routing of the ATs to maximize the system profit, depending on dynamic travel times, which are a non-linear function of the ATs' flows. It is important to involve traffic congestion in such a routing problem since for a growing number of ATs circulating in the city their number will lead to delays. The model is embedded within a rolling horizon framework, which divides a typical day into several horizons to deal with the real-time travel demand. In each horizon, the routing model is solved with the demand at that interval and assuring the continuity of the trips between horizons. Nevertheless, each horizon model is hard to solve given its number of constraints and decision variables. Therefore, we propose a solution approach based on a customized Lagrangian relaxation algorithm, which allows identifying a near-optimal solution for this difficult problem. Numerical experiments for the city of Delft, The Netherlands, are used to demonstrate the solution quality of the proposed algorithm as well as obtaining insights about the AT system performance. Results show that the solution algorithm can solve the proposed model for hard instances. Ride-sharing makes the AT system more capable to provide better service regarding delay time and the number of requests that can be attended by the system. The delay penalty on the profit objective function is an effective control parameter on guaranteeing the service quality while maintaining system profitability.

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“…It is assumed that vehicles entering on a link ( i , j ) later from node i should not leave earlier from node j , which means the ATs do not pass one another. These constraints were established by Kaufman et al ( 15 ):…”

Section: Integer Programming Modelmentioning

confidence: 99%

Applying a Model for Trip Assignment and Dynamic Routing of Automated Taxis with Congestion: System Performance in the City of Delft, The Netherlands

Xiao

Correia

Arem

2018

Transportation Research Record: Journal of the Transportation R

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This paper proposes a method of assigning trips to automated taxis (ATs) and designing the routes of those vehicles in an urban road network, and also considering the traffic congestion caused by this dynamic responsive service. The system is envisioned to provide a seamless door-to-door service within a city area for all passenger origins and destinations. An integer programming model is proposed to define the routing of the vehicles according to a profit maximization function, depending on the dynamic travel times, which varies with the ATs’ flow. This will be especially important when the number of automated vehicles (AVs) circulating on the roads is high enough that their routing will cause delays. This system should be able to serve not only the reserved travel requests, but also some real-time requests. A rolling horizon scheme is used to divide one day into several periods in which both the real-time and the booked demand will be considered together. The model was applied to the real size case study city of Delft, the Netherlands. The results allow assessing of the impact of the ATs movements on traffic congestion and the profitability of the system. From this case-study, it is possible to conclude that taking into account the effect of the vehicle flows on travel time leads to changes in the system profit, the satisfied percentage and the driving distance of the vehicles, which highlights the importance of this type of model in the assessment of the operational effects of ATs in the future.

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A mixed integer linear programming formulation of the dynamic traffic assignment problem

Cited by 3 publications

References 9 publications

User-equilibrium properties of fixed points in dynamic traffic assignment

User-equilibrium properties of fixed points in dynamic traffic assignment

Automated taxis’ dial-a-ride problem with ride-sharing considering congestion-based dynamic travel times

Applying a Model for Trip Assignment and Dynamic Routing of Automated Taxis with Congestion: System Performance in the City of Delft, The Netherlands

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