Time of arrival cumulative probability in public transportation travel assistance

In travel planning/assistance applications, the Estimated Time of Arrival (ETA) is defined as a single time value that indicates the expected time it will take for a traveler to reach her destination. While this value conveys much information with as little data as possible, it is valuable insofar the user catches all the proposed connections in the travel and, more generally, it lacks information on the effects of haphazard factors like traffic jams or disruptions. In this paper we propose a generalization of the ETA concept: the Estimated Time of Arrival Cumulative Probability (ETACP) for a route is defined as the cumulative probability to arrive within a given time, considering the specific features and sources of variability of a route (e.g., number of connections, traffic probability in a line, walking time between connecting stations, ...). ETACP is useful in when for a user it is not important to choose the fastest route, but the one that guarantees with high probability to reach the desired destination within a given time (e.g., take a train, arrive to a office that is closing soon). We show how to compute ETACP in real world scenarios, and propose ways to effectively represent its information content to the users.