We study the problem of computing all Pareto-optimal journeys in a public transit network regarding the two criteria of arrival time and number of transfers taken. We take a novel approach, focusing on trips and transfers between them, allowing fine-grained modeling. Our experiments on the metropolitan network of London show that the algorithm computes full 24-hour profiles in 70ms after a preprocessing phase of 30s, allowing fast queries in dynamic scenarios.
Other approaches do not use graphs at all. (Round-bAsed Public Transit Optimized Router) @cite_16 is a dynamic program. In each round, it computes earliest arrival times for journeys with @math transfers, where @math is the current round number. It does this by scanning along lines and, at each stop, checking for the earliest trip of that line that can be reached. It outperforms Dijkstra-based approaches in practice. The @cite_6 operates on (trip segments of length @math ). It orders them by departure time into a single array. During queries, this array is then scanned once, which is very fast in practice due to the linear memory access pattern.
@cite_16 @cite_6
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We study the problem of computing all Pareto-optimal journeys in a dynamic public transit network for multiple criteria, such as arrival time and number of transfers. Existing algorithms consider this as a graph problem and solve it using various graph search algorithms. Unfortunately, this leads to either high query times or suboptimal solutions. We take a different approach. We introduce RAPTOR, our novel round-based public transit router. Unlike previous algorithms, it is not Dijkstra-based, looks at each route such as a bus line in the network at most once per round, and can be made even faster with simple pruning rules and parallelization using multiple cores. Because it does not rely on preprocessing, RAPTOR works in fully dynamic scenarios. Starting from arrival time and number of transfers as criteria, it can be easily extended to handle flexible departure times or arbitrary additional criteria. As practical examples we consider fare zones and reliability of transfers. When run on complex public transportation networks such as London, RAPTOR computes all Pareto-optimal journeys between two random locations an order of magnitude faster than previous approaches, which easily enables interactive applications. This paper studies the problem of computing optimal journeys in dynamic public transit networks. We introduce a novel algorithmic framework, called Connection Scan Algorithm (CSA), to compute journeys. It organizes data as a single array of connections, which it scans once per query. Despite its simplicity, our algorithm is very versatile. We use it to solve earliest arrival and multi-criteria profile queries. Moreover, we extend it to handle the minimum expected arrival time (MEAT) problem, which incorporates stochastic delays on the vehicles and asks for a set of (alternative) journeys that in its entirety minimizes the user’s expected arrival time at the destination. Our experiments on the dense metropolitan network of London show that CSA computes MEAT queries, our most complex scenario, in 272 ms on average.