9,964 research outputs found
Stochastic on-time arrival problem in transit networks
This article considers the stochastic on-time arrival problem in transit
networks where both the travel time and the waiting time for transit services
are stochastic. A specific challenge of this problem is the combinatorial
solution space due to the unknown ordering of transit line arrivals. We propose
a network structure appropriate to the online decision-making of a passenger,
including boarding, waiting and transferring. In this framework, we design a
dynamic programming algorithm that is pseudo-polynomial in the number of
transit stations and travel time budget, and exponential in the number of
transit lines at a station, which is a small number in practice. To reduce the
search space, we propose a definition of transit line dominance, and techniques
to identify dominance, which decrease the computation time by up to 90% in
numerical experiments. Extensive numerical experiments are conducted on both a
synthetic network and the Chicago transit network.Comment: 29 pages; 12 figures. This manuscript version is made available under
the CC-BY-NC-ND 4.0 license
https://creativecommons.org/licenses/by-nc-nd/4.0
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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
A dynamic ridesharing dispatch and idle vehicle repositioning strategy with integrated transit transfers
We propose a ridesharing strategy with integrated transit in which a private
on-demand mobility service operator may drop off a passenger directly
door-to-door, commit to dropping them at a transit station or picking up from a
transit station, or to both pickup and drop off at two different stations with
different vehicles. We study the effectiveness of online solution algorithms
for this proposed strategy. Queueing-theoretic vehicle dispatch and idle
vehicle relocation algorithms are customized for the problem. Several
experiments are conducted first with a synthetic instance to design and test
the effectiveness of this integrated solution method, the influence of
different model parameters, and measure the benefit of such cooperation.
Results suggest that rideshare vehicle travel time can drop by 40-60%
consistently while passenger journey times can be reduced by 50-60% when demand
is high. A case study of Long Island commuters to New York City (NYC) suggests
having the proposed operating strategy can substantially cut user journey times
and operating costs by up to 54% and 60% each for a range of 10-30 taxis
initiated per zone. This result shows that there are settings where such
service is highly warranted
Timely Data Delivery in a Realistic Bus Network
AbstractâWiFi-enabled buses and stops may form the backbone of a metropolitan delay tolerant network, that exploits nearby communications, temporary storage at stops, and predictable bus mobility to deliver non-real time information. This paper studies the problem of how to route data from its source to its destination in order to maximize the delivery probability by a given deadline. We assume to know the bus schedule, but we take into account that randomness, due to road traffic conditions or passengers boarding and alighting, affects bus mobility. We propose a simple stochastic model for bus arrivals at stops, supported by a study of real-life traces collected in a large urban network. A succinct graph representation of this model allows us to devise an optimal (under our model) single-copy routing algorithm and then extend it to cases where several copies of the same data are permitted. Through an extensive simulation study, we compare the optimal routing algorithm with three other approaches: minimizing the expected traversal time over our graph, minimizing the number of hops a packet can travel, and a recently-proposed heuristic based on bus frequencies. Our optimal algorithm outperforms all of them, but most of the times it essentially reduces to minimizing the expected traversal time. For values of deadlines close to the expected delivery time, the multi-copy extension requires only 10 copies to reach almost the performance of the costly flooding approach. I
Tractable Pathfinding for the Stochastic On-Time Arrival Problem
We present a new and more efficient technique for computing the route that
maximizes the probability of on-time arrival in stochastic networks, also known
as the path-based stochastic on-time arrival (SOTA) problem. Our primary
contribution is a pathfinding algorithm that uses the solution to the
policy-based SOTA problem---which is of pseudo-polynomial-time complexity in
the time budget of the journey---as a search heuristic for the optimal path. In
particular, we show that this heuristic can be exceptionally efficient in
practice, effectively making it possible to solve the path-based SOTA problem
as quickly as the policy-based SOTA problem. Our secondary contribution is the
extension of policy-based preprocessing to path-based preprocessing for the
SOTA problem. In the process, we also introduce Arc-Potentials, a more
efficient generalization of Stochastic Arc-Flags that can be used for both
policy- and path-based SOTA. After developing the pathfinding and preprocessing
algorithms, we evaluate their performance on two different real-world networks.
To the best of our knowledge, these techniques provide the most efficient
computation strategy for the path-based SOTA problem for general probability
distributions, both with and without preprocessing.Comment: Submission accepted by the International Symposium on Experimental
Algorithms 2016 and published by Springer in the Lecture Notes in Computer
Science series on June 1, 2016. Includes typographical corrections and
modifications to pre-processing made after the initial submission to SODA'15
(July 7, 2014
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Accommodating user preferences in the optimization of public transport travel
Maximizing Service Reliability in Distributed Computing Systems with Random Node Failures: Theory and Implementation
In distributed computing systems (DCSs) where server nodes can fail permanently with nonzero probability, the system performance can be assessed by means of the service reliability, defined as the probability of serving all the tasks queued in the DCS before all the nodes fail. This paper presents a rigorous probabilistic framework to analytically characterize the service reliability of a DCS in the presence of communication uncertainties and stochastic topological changes due to node deletions. The framework considers a system composed of heterogeneous nodes with stochastic service and failure times and a communication network imposing random tangible delays. The framework also permits arbitrarily specified, distributed load-balancing actions to be taken by the individual nodes in order to improve the service reliability. The presented analysis is based upon a novel use of the concept of stochastic regeneration, which is exploited to derive a system of difference-differential equations characterizing the service reliability. The theory is further utilized to optimize certain load-balancing policies for maximal service reliability; the optimization is carried out by means of an algorithm that scales linearly with the number of nodes in the system. The analytical model is validated using both Monte Carlo simulations and experimental data collected from a DCS testbed
An optimization model for line planning and timetabling in automated urban metro subway networks
In this paper we present a Mixed Integer Nonlinear Programming model that we
developed as part of a pilot study requested by the R&D company Metrolab in
order to design tools for finding solutions for line planning and timetable
situations in automated urban metro subway networks. Our model incorporates
important factors in public transportation systems from both, a cost-oriented
and a passenger-oriented perspective, as time-dependent demands, interchange
stations, short-turns and technical features of the trains in use. The incoming
flows of passengers are modeled by means of piecewise linear demand functions
which are parameterized in terms of arrival rates and bulk arrivals. Decisions
about frequencies, train capacities, short-turning and timetables for a given
planning horizon are jointly integrated to be optimized in our model. Finally,
a novel Math-Heuristic approach is proposed to solve the problem. The results
of extensive computational experiments are reported to show its applicability
and effectiveness to handle real-world subway networksComment: 30 pages, 6 figures, 9 table
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