Publishing transport data on the Web for consumption by others poses several challenges for data publishers. In addition to planned schedules, access to live schedule updates (e.g. delays or cancellations) and historical data is fundamental to enable reliable applications and to support machine learning use cases. However publishing such dynamic data further increases the computational burden for data publishers, resulting in often unavailable historical data and live schedule updates for most public transport networks. In this paper we apply and extend the current Linked Connections approach for static data to also support cost-efficient live and historical public transport data publishing on the Web. Our contributions include (i) a reference specification and system architecture to support cost-efficient publishing of dynamic public transport schedules and historical data; (ii) empirical evaluations on route planning query performance based on data fragmentation size, publishing costs and a comparison with a traditional route planning engine such as OpenTripPlanner; (iii) an analysis of potential correlations of query performance with particular public transport network characteristics such as size, average degree, density, clustering coefficient and average connection duration. Results confirm that fragmentation size influences route planning query performance and converges on an optimal fragment size per network. Size (stops), density and connection duration also show correlation with route planning query performance. Our approach proves to be more cost-efficient and in some cases outperforms OpenTripPlanner when supporting the earliest arrival time route planning use case. Moreover, the cost of publishing live and historical schedules remains in the same order of magnitude for server-side resources compared to publishing planned schedules only. Yet, further optimizations are needed for larger networks (>1000 stops) to be useful in practice. Additional dataset fragmentation strategies (e.g. geospatial) may be studied for designing more scalable and performant Web apis that adapt to particular use cases, not only limited to the public transport domain.