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Time-dependent stochastic shortest path(s) algorithms for a scheduled transportation network
Following on from our work concerning travellersâ preferences in public transportation networks (Wu and Hartley, 2004), we introduce the concept of stochasticity to our algorithms. Stochasticity greatly increases the complexity of the route finding problem, so greater algorithmic efficiency becomes imperative. Public transportation networks (buses, trains) have two important features: edges can only be traversed at certain points in time and the weights of these edges change in a day and have an uncertainty associated with them. These features determine that a public transportation network is a stochastic and time-dependent network. Finding multiple shortest paths in a both stochastic and time-dependent network is currently regarded as the most difficult task in the route finding problems (Loui, 1983). This paper discusses the use of k-shortest-paths (KSP) algorithms to find optimal route(s) through a network in which the edge weights are defined by probability distributions. A comprehensive review of shortest path(s) algorithms with probabilistic graphs was conducted
Route Planning in Transportation Networks
We survey recent advances in algorithms for route planning in transportation
networks. For road networks, we show that one can compute driving directions in
milliseconds or less even at continental scale. A variety of techniques provide
different trade-offs between preprocessing effort, space requirements, and
query time. Some algorithms can answer queries in a fraction of a microsecond,
while others can deal efficiently with real-time traffic. Journey planning on
public transportation systems, although conceptually similar, is a
significantly harder problem due to its inherent time-dependent and
multicriteria nature. Although exact algorithms are fast enough for interactive
queries on metropolitan transit systems, dealing with continent-sized instances
requires simplifications or heavy preprocessing. The multimodal route planning
problem, which seeks journeys combining schedule-based transportation (buses,
trains) with unrestricted modes (walking, driving), is even harder, relying on
approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4,
previously published by Microsoft Research. This work was mostly done while
the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at
Microsoft Research Silicon Valle
Selfish Routing on Dynamic Flows
Selfish routing on dynamic flows over time is used to model scenarios that
vary with time in which individual agents act in their best interest. In this
paper we provide a survey of a particular dynamic model, the deterministic
queuing model, and discuss how the model can be adjusted and applied to
different real-life scenarios. We then examine how these adjustments affect the
computability, optimality, and existence of selfish routings.Comment: Oberlin College Computer Science Honors Thesis. Supervisor: Alexa
Sharp, Oberlin Colleg
Graph Orientation and Flows Over Time
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 of the
flow and this bound is tight. For the special case of networks with a single
source or sink, this fraction is which is again tight. We present
more results of similar flavor and also show non-approximability results for
finding the best orientation for single and multicommodity maximum flows over
time
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