Approximating earliest arrival flows with flow-dependent transit times

Baumann, Nadine; Köhler, Ekkehard

doi:10.1016/j.dam.2006.04.030

Cited by 19 publications

(7 citation statements)

References 10 publications

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“…The travel time depends on the amount of traffic inflow and is modeled with an alternative time-expanded network, where exactly one arc of finite different time-space arcs emerging from a time copy of a node has to be chosen. The earliest arrival flows, where the flow is defined according to the above-mentioned approaches of the inflow-dependent (Köhler et al, 2002) andload-dependent (Köhler andSkutella, 2005) travel times, are investigated in Baumann and Köhler (2007). A similar alternative time-expanded network is introduced by Carey (2001) to capture the flow behavior of traffic flow more realistically.…”

Section: Dynamic Network Flows With Flow-dependent Travel Timementioning

confidence: 99%

Mathematical Models for Evacuation Planning in Urban Areas

Bretschneider¹

2013

Lecture Notes in Economics and Mathematical Systems

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Section: Dynamic Network Flows With Flow-dependent Travel Timementioning

confidence: 99%

Mathematical Models for Evacuation Planning in Urban Areas

Bretschneider¹

2013

Lecture Notes in Economics and Mathematical Systems

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“…We are able to show that earliest arrival flows and the approximations developed in do not exist in this setting. Theorem There are undirected networks over time

N = (G, u, b, τ)

for which an earliest arrival flow exists, but that do not allow for an earliest arrival contraflow.…”

Section: The Price Of Orientationmentioning

confidence: 95%

“…For multiple sinks, that is usually not the case if the sinks have a finite demand (see Fig. 10), but approximations are still possible [2,9]. β .…”

Section: Earliest Arrival Flowsmentioning

confidence: 99%

Graph orientation and flows over time

2015

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Flows over time are used to model many real-world logistic and routing problems. The networks underlying such problems - streets, tracks, etc. - are inherently undirected and directions are only imposed on them to reduce the danger of colliding vehicles and similar problems. Thus, the question arises, what influence the orientation of the network has on the network flow over time problem that is being solved on the oriented network. In the literature, this is also referred to as the contraflow or lane reversal problem. We introduce and analyze the price of orientation: How much flow is lost in any orientation of the network if the time horizon remains fixed? We prove that there is always an orientation where we can still send one-third of the flow and this bound is tight. For the special case of networks with a single source or sink, this fraction is half, which is again tight. We present more results of similar flavor and also show nonapproximability results for finding the best orientation for single and multicommodity maximum flows over time

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“…Fleischer (2001) presented an instance in a network with two sources and two sinks where the EAF does not exist. Baumann and Kohler (2007) further showed that for load-dependent transit time, the earliest arrival s − t flow does not exist. For a single-sink network with multiple sources and predefined parameters, however, the EAF does always exist (Fleischer and Skutella 2007;Richardson and Tardos 2002).…”

Section: Earliest Arrival Flowmentioning

confidence: 95%

A Network Flow Algorithm for the Cell-Based Single-Destination System Optimal Dynamic Traffic Assignment Problem

Zheng

Chiu

2011

Transportation Science

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T he cell-transmission model-based single-destination system optimal dynamic traffic assignment problem proposed by Ziliaskopoulos was mostly solved by standard linear programming (LP) methods, e.g., simplex and interior point methods, which produce link-based flows involving vehicle-holding phenomenon. In this paper we present a network flow algorithm for this problem. We show that the problem is equivalent to the earliest arrival flow and then solve the earliest arrival flow on a time-expanded network. In particular, a scaled flow scheme is proposed to deal with the situation in which the ratio of backward wave speed to forward wave speed is less than one. The proposed algorithm produces path-based flows exhibiting realistic nonvehicleholding properties. Complexity and numerical analyses show that the algorithm runs more efficiently than LP.

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Approximating earliest arrival flows with flow-dependent transit times

Cited by 19 publications

References 10 publications

Mathematical Models for Evacuation Planning in Urban Areas

Mathematical Models for Evacuation Planning in Urban Areas

Graph orientation and flows over time

A Network Flow Algorithm for the Cell-Based Single-Destination System Optimal Dynamic Traffic Assignment Problem

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