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

A Hierarchical Path View Model for Path Finding in Intelligent Transportation Systems

Effective path finding has been identified as an important requirement for dynamic route guidance in Intelligent Transportation Systems (ITS). Path finding is most efficient if the all-pair (shortest) paths are precomputed because path search requires only simple lookups of the precomputed path views. Such an approach however incurs path view maintenance (computation and update) and storage costs which can be unrealistically high for large ITS networks. To lower these costs, we propose a Hierarchical Path View Model (HPVM) that partitions an ITS road map, and then creates a hierarchical structure based on the road type classification. HPVM includes a map partition algorithm for creating the hierarchy, path view maintenance algorithms, and a heuristic hierarchical path finding algorithm that searches paths by traversing the hierarchy. HPVM captures the dynamicity of traffic change patterns better than the ITS path finding systems that use the hierarchical A * approach because: (1) during path search, HPVM traverses the hierarchy by dynamically selecting the connection points between two levels based on up-to-date traffic, and (2) HPVM can reroute the high-speed road traffic through local streets if needed. In this paper, we also present experimental results used to benchmark HPVM and to compare HPVM with alternative ITS path finding approaches, using both synthetic and real ITS maps that include a large Detroit map (> 28,000 nodes). The results show that the HPVM incurs much lower costs in path view maintenance and storage than the non-hierarchical path precomputation approach, and is more efficient in path search than the traditional ITS path finding using A * or hierarchical A * algorithms.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45593/1/10707_2004_Article_142477.pd

Extending TRANSIMS Technology to an Integrated Multilevel Representation

The TRANSIMS system developed at Los Alamos in the USA over the past decade is a world leader in providing an integrated land-use transportation dynamical model for large areas with a million or more inhabitants. TRANSIMS uses standard survey data to create synthetic micropopulations, including family structure, to simulate trip making and emergent traffic dynamics. We propose to extend TRANSIMS by adapting it to a new multi-level representation, allowing dynamics to be algebraically integrated at the micro-, meso- and macro-levels. The new representation builds a lattice hierarchy in a way that integrates non-partitional hierarchies of links and routes based on the usual hierarchy of geographical zones, e.g. neighbourhoods, districts, cities, counties and countries. Applying the representation to a big city starts by defining sets of zones at different levels. At the first level, N, is the street. This can be subdivided to building plots at level N-1, buildings at level N-2, and even rooms at level N-3. At level N+1 are the neighbourhoods, at level N+2 is the set of district zones (each of them containing the different neighbourhoods in the previous level), and at the top level N+3 (in this case), is just one zone, the city itself. If a larger study area is to be considered, we would have a whole set of N+3 zones defining N+4-level areas, and so on, extending to the level of counties, countries or even continents. This paper will explain the fundamentals of TRANSIMS technology and compare it to other systems. We will show how TRANSIMS and the new multi-level representation can be brought together to give new insights into the macro-dynamics of very large road systems such as London, England and even the whole of Europe

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