Delays in public transport are common, often impacting users through prolonged travel times and missed transfers. Existing solutions for handling delays remain limited; backup plans based on historical data miss opportunities for earlier arrivals, while snapshot planning accounts for current delays but not future ones. With the growing availability of live delay data, users can adjust their journeys in real-time. However, the literature lacks a framework that fully exploits this advantage for system-scale dynamic replanning. To address this, we formalise the dynamic replanning problem in public transport routing and propose two solutions: a "pull" approach, where users manually request replanning, and a novel "push" approach, where the server proactively monitors and adjusts journeys. Our experiments show that the push approach outperforms the pull approach, achieving significant speedups. The results also reveal substantial arrival time savings enabled by dynamic replanning.

We explore the earliest arrival time problem in public transport journey planning. A journey typically consists of multiple scheduled public transport legs. The actual time required to transfer between these legs can substantially influence route planning. Therefore, we properly model transfers by incorporating their exact costs. We then introduce a novel oracle-based routing algorithm that constructs an efficient transfer database, considering the proposed transfer model. The database is leveraged online to quickly reconstruct the optimal journey in response to an earliest arrival time query. Our experimental results show that neglecting exact transfer costs often lead to either infeasible or suboptimal route plans. Furthermore, the findings highlight the efficiency of our algorithm in handling queries, demonstrated by response times within mere microseconds.