18,785 research outputs found
Ranking paths in stochastic time-dependent networks
In this paper we address optimal routing problems in networks where travel times are both stochastic and time-dependent.
In these networks, the best route choice is not necessarily a path, but rather a "time-adaptive strategy" that assigns successors to nodes as a function of time.
Nevertheless, in some particular cases an origin-destination path must be chosen "a priori", since time-adaptive choices are not allowed. Unfortunately, finding the a priori shortest path is an NP-hard problem.
In this paper, we propose a solution method for the a priori shortest path problem, and we show that it can be easily extended to the ranking of the first K shortest paths. Our method exploits the solution of the time-adaptive routing problem as a relaxation of the a priori problem.
Computational results are presented showing that, under realistic distributions of travel times and costs, our solution methods are effective and robust
K shortest paths in stochastic time-dependent networks
A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks, the best route choice is not necessarily a path, but rather a time-adaptive strategy that assigns successors to nodes as a function of time. In some particular cases, the shortest origin-destination path must nevertheless be chosen a priori, since time-adaptive choices are not allowed. Unfortunately, finding the a priori shortest path is NP-hard, while the best time-adaptive strategy can be found in polynomial time. In this paper, we propose a solution method for the a priori shortest path problem, and we show that it can be easily adapted to the ranking of the first K shortest paths. Moreover, we present a computational comparison of time-adaptive and a priori route choices, pointing out the effect of travel time and cost distributions. The reported results show that, under realistic distributions, our solution methods are effectiveShortest paths; K shortest paths; stochastic time-dependent networks; routing; directed hypergraphs
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Accommodating user preferences in the optimization of public transport travel
Bicriterion a priori route choice in stochastic time-dependent networks.
In recent years there has been a growing interest in using stochastic time-dependent (STD) networks as a modelling tool for a number of applications within such areas as transportation and telecommunications. It is known that an optimal routing policy does not necessarily correspond to a path, but rather to a time-adaptive strategy. In some applications, however, it makes good sense to require that the routing policy corresponds to a loopless path in the network, that is, the time-adaptive aspect disappears and a priori route choice is considered. In this paper we consider bicriterion a priori route choice in STD networks, i.e. the problem of finding the set of efficient paths. Both expectation and min-max criteria are considered and a solution method based on the two-phase approach is devised. Experimental results reveal that the full set of efficient solutions can be determined on rather large test instances, which is in contrast to previously reported results for the time-adaptive caseStochastic time-dependent networks; Bicriterion shortest path; A priori route choice; Two-phase method
Dominant transport pathways in an atmospheric blocking event
A Lagrangian flow network is constructed for the atmospheric blocking of
eastern Europe and western Russia in summer 2010. We compute the most probable
paths followed by fluid particles which reveal the {\it Omega}-block skeleton
of the event. A hierarchy of sets of highly probable paths is introduced to
describe transport pathways when the most probable path alone is not
representative enough. These sets of paths have the shape of narrow coherent
tubes flowing close to the most probable one. Thus, even when the most probable
path is not very significant in terms of its probability, it still identifies
the geometry of the transport pathways.Comment: Appendix added with path calculations for a simple kinematic model
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Classes of random walks on temporal networks with competing timescales
Random walks find applications in many areas of science and are the heart of
essential network analytic tools. When defined on temporal networks, even basic
random walk models may exhibit a rich spectrum of behaviours, due to the
co-existence of different timescales in the system. Here, we introduce random
walks on general stochastic temporal networks allowing for lasting
interactions, with up to three competing timescales. We then compare the mean
resting time and stationary state of different models. We also discuss the
accuracy of the mathematical analysis depending on the random walk model and
the structure of the underlying network, and pay particular attention to the
emergence of non-Markovian behaviour, even when all dynamical entities are
governed by memoryless distributions.Comment: 16 pages, 5 figure
PageRank: Standing on the shoulders of giants
PageRank is a Web page ranking technique that has been a fundamental
ingredient in the development and success of the Google search engine. The
method is still one of the many signals that Google uses to determine which
pages are most important. The main idea behind PageRank is to determine the
importance of a Web page in terms of the importance assigned to the pages
hyperlinking to it. In fact, this thesis is not new, and has been previously
successfully exploited in different contexts. We review the PageRank method and
link it to some renowned previous techniques that we have found in the fields
of Web information retrieval, bibliometrics, sociometry, and econometrics
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