Using the growing volumes of vehicle trajectory data, it becomes increasingly possible to capture time-varying and uncertain travel costs in a road network, including travel time and fuel consumption. The current paradigm represents a road network as a graph, assigns weights to the graph's edges by fragmenting trajectories into small pieces that fit the underlying edges, and then applies a routing algorithm to the resulting graph. We propose a new paradigm that targets more accurate and more efficient estimation of the costs of paths by associating weights with sub-paths in the road network. The paper provides a solution to a foundational problem in this paradigm, namely that of computing the time-varying cost distribution of a path. The solution consists of several steps. We first learn a set of random variables that capture the joint distributions of sub-paths that are covered by sufficient trajectories. Then, given a departure time and a path, we select an optimal subset of learned random variables such that the random variables' corresponding paths together cover the path. This enables accurate joint distribution estimation of the path, and by transferring the joint distribution into a marginal distribution, the travel cost distribution of the path is obtained. The use of multiple learned random variables contends with data sparseness, the use of multi-dimensional histograms enables compact representation of arbitrary joint distributions that fully capture the travel cost dependencies among the edges in paths. Empirical studies with substantial trajectory data from two different cities offer insight into the design properties of the proposed solution and suggest that the solution is effective in real-world settings.
When all edges have travel costs, it is possible to estimate the travel cost of any path, i.e., by summing up the travel costs of the edges in the paths @cite_14 @cite_15 @cite_11 . However, a recent study @cite_1 shows that using the sum of travel costs of edges as the travel cost of a path can be inaccurate because it ignores hard-to-formalize aspects of travel, such as turn costs. Instead, a method is proposed to identify an optimal set of sub-paths that can be concatenated into a path. The path's travel cost is then the sum of travel costs of the sub-paths, which can be obtained from trajectories. However, this method does not support travel cost distributions, and it assumes independence among sub-paths.
@cite_15 @cite_14 @cite_1 @cite_11
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With the growing volumes of vehicle trajectory data, it becomes increasingly possible to capture time-varying and uncertain travel costs in a road network, including travel time and fuel consumption. The current paradigm represents a road network as a weighted graph; it blasts trajectories into small fragments that fit the under-lying edges to assign weights to edges; and it then applies a routing algorithm to the resulting graph. We propose a new paradigm, the hybrid graph, that targets more accurate and more efficient path cost distribution estimation. The new paradigm avoids blasting trajectories into small fragments and instead assigns weights to paths rather than simply to the edges. We show how to compute path weights using trajectory data while taking into account the travel cost dependencies among the edges in the paths. Given a departure time and a query path, we show how to select an optimal set of weights with associated paths that cover the query path and such that the weights enable the most accurate joint cost distribution estimation for the query path. The cost distribution of the query path is then computed accurately using the joint distribution. Finally, we show how the resulting method for computing cost distributions of paths can be integrated into existing routing algorithms. Empirical studies with substantial trajectory data from two different cities offer insight into the design properties of the proposed method and confirm that the method is effective in real-world settings. In this paper a model that handles costs of turns in route planning is defined, investigated and discussed. Costs are traditionally attached to edges in a graph. For some important route planning problems other costs can be identified, namely costs that appear when leaving one edge and entering the next. Examples are turn restrictions, the turning angle, or the simple necessity to turn. Such costs cannot be stored as attributes of nodes or edges in the graph, and they cannot be handled correctly by shortest path algorithms without modifications. Turn costs can be represented by a pseudo-dual graph in a way that shortest path algorithms run without modifications. Although the idea is not new, it has not found much interest in the literature. The pseudo-dual graph is defined here in a new way, it is systematically investigated, and some practical applications are shown. Concentrating strictly on topology, it turns out that the pseudo-dual graph is conceptually cleaner and more efficient in route planning than alternative, currently used ways to deal with turn costs. The discussed applications are from the field of pedestrian navigation, which gave rise to this research. We address the problem of choosing the best paths among a set of candidate paths between the same origin–destination pair. This functionality is used extensively when constructing origin–destination matrices in logistics and flex transportation. Because the cost of a path, e.g., travel time, varies over time and is uncertain, there is generally no single best path. We partition time into intervals and represent the cost of a path during an interval as a random variable, resulting in an uncertain time series for each path. When facing uncertainties, users generally have different risk preferences, e.g., risk-loving or risk-averse, and thus prefer different paths. We develop techniques that, for each time interval, are able to find paths with non-dominated lowest costs while taking the users’ risk preferences into account. We represent risk by means of utility function categories and show how the use of first-order and two kinds of second-order stochastic dominance relationships among random variables makes it possible to find all paths with non-dominated lowest costs. We report on empirical studies with large uncertain time series collections derived from a 2-year GPS data set. The study offers insight into the performance of the proposed techniques, and it indicates that the best techniques combine to offer an efficient and robust solution. When planning routes, drivers usually consider a multitude of different travel costs, e.g., distances, travel times, and fuel consumption. Different drivers may choose different routes between the same source and destination because they may have different driving preferences (e.g., time-efficient driving v.s. fuel-efficient driving). However, existing routing services support little in modeling multiple travel costs and personalization—they usually deliver the same routes that minimize a single travel cost (e.g., the shortest routes or the fastest routes) to all drivers. We study the problem of how to recommend personalized routes to individual drivers using big trajectory data. First, we provide techniques capable of modeling and updating different drivers' driving preferences from the drivers' trajectories while considering multiple travel costs. To recommend personalized routes, we provide techniques that enable efficient selection of a subset of trajectories from all trajectories according to a driver's preference and the source, destination, and departure time specified by the driver. Next, we provide techniques that enable the construction of a small graph with appropriate edge weights reflecting how the driver would like to use the edges based on the selected trajectories. Finally, we recommend the shortest route in the small graph as the personalized route to the driver. Empirical studies with a large, real trajectory data set from 52,211 taxis in Beijing offer insight into the design properties of the proposed techniques and suggest that they are efficient and effective.