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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
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Accommodating user preferences in the optimization of public transport travel
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
IMPROVED PUBLIC TRANSIT ROUTING ALGORITHM FOR FINDING THE SHORTEST K-PATH
Most of the existing public transit routing algorithms were developed on the basis of graph theory. Recently, algorithms are being developed that can compute for O-D public transit paths by using timetable information only, not using network structure consisting of nodes and links. The timetable-based public transit routing algorithm produces one shortest path to destination, using departure time and arrival time by stop. But it has limitations in reflecting additional factors, such as transfer penalty and alternative path selection, in the process of path calculation. In addition, since public transit passengers tend to choose one among various alternative paths, it is necessary to calculate multiple paths rather than a single path as in the existing methods. Therefore, this study proposes an improved RAPTOR algorithm that can consider transfer penalty and produce multiple paths, while it is based on RAPTOR, the existing timetable-based public transit routing algorithm. The transfer penalty was applied at the point of transfer, and differently according to transfer types. As a result of analyzing computed paths of the algorithms before and after improvement, it was found that computed paths with the improved RAPTOR algorithm proposed by this study were more similar to Seoul public transit passengers' actual travel paths than computed paths by the existing RAPTOR alone
Analysis of the Airport Network of India as a complex weighted network
Transportation infrastructure of a country is one of the most important
indicators of its economic growth. Here we study the Airport Network of India
(ANI), which represents India's domestic civil aviation infrastructure, as a
complex network. We find that ANI, a network of domestic airports connected by
air links, is a small-world network characterized by a truncated power-law
degree distribution, and has a signature of hierarchy. We investigate ANI as a
weighted network to explore its various properties and compare them with their
topological counterparts. The traffic in ANI, as in the World-wide Airport
Network (WAN), is found to be accumulated on interconnected groups of airports
and is concentrated between large airports. In contrast to WAN, ANI is found to
be having disassortative mixing which is offset by the traffic dynamics. The
analysis indicates toward possible mechanism of formation of a national
transportation network, which is different from that on a global scale.Comment: 6 pages, 6 figure
The Price of Robustness in Timetable Information
In timetable information in public transport the goal is to search for a good passenger\u27s path between an origin and a destination. Usually, the travel time and the number of transfers shall be minimized. In this paper, we consider robust timetable information, i.e. we want to identify a path which will bring the passenger to the planned destination even in the case of delays. The classic notion of strict robustness leads to the problem of identifying those changing activities which will never break in any of the expected delay scenarios. We show that this is in general a strongly NP-hard problem. Therefore, we propose a conservative heuristic which identifies a large subset of these robust changing activities in polynomial time by dynamic programming and so allows us to find strictly robust paths efficiently. We also transfer the notion of light robustness, originally introduced for timetabling, to timetable information. In computational experiments we then study the price of strict and light robustness: How much longer is the travel time of a robust path than of a shortest one according to the published schedule? Based on the schedule of high-speed trains within Germany of 2011, we quantitatively explore the trade-off between the level of guaranteed robustness and the increase in travel time. Strict robustness turns out to be too conservative, while light robustness is promising: a modest level of guarantees is achievable at a reasonable price for the majority of passengers
Trip-Based Public Transit Routing Using Condensed Search Trees
We study the problem of planning Pareto-optimal journeys in public transit
networks. Most existing algorithms and speed-up techniques work by computing
subjourneys to intermediary stops until the destination is reached. In
contrast, the trip-based model focuses on trips and transfers between them,
constructing journeys as a sequence of trips. In this paper, we develop a
speed-up technique for this model inspired by principles behind existing
state-of-the-art speed-up techniques, Transfer Pattern and Hub Labelling. The
resulting algorithm allows us to compute Pareto-optimal (with respect to
arrival time and number of transfers) 24-hour profiles on very large real-world
networks in less than half a millisecond. Compared to the current state of the
art for bicriteria queries on public transit networks, this is up to two orders
of magnitude faster, while increasing preprocessing overhead by at most one
order of magnitude
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