Which bike-train integration strategy is most suitable in a city? A cost comparison using continuous approximation

This paper studies which bike–train integration strategy minimizes total cost under varying city conditions. Assuming a uniform service area where travelers access a single train station, we develop continuous approximation models for three strategies: (i) shared bikes, (ii) private bike parking near stations, and (iii) boarding bikes on trains. Key decision variables depend on the modeled strategy, including the bike parking location, the number of bike-sharing stations, and the number of slots. The formulations show how demand, values of time, cycling and walking speeds, egress distance, land cost, truck speed, service-area size, and rail capacity affect optimal design and cost. Analytical comparisons are complemented by case studies in Parramatta (Australia) and Pasig City (Philippines). Results indicate: at low demand, boarding bikes on trains is attractive if there is enough train space and space cost is low; otherwise, parking private bikes is more favorable. At high demand, shared bikes dominate through reuse and smaller fleets. High time values make shared and private bikes costly due to rebalancing and security, making boarding bikes strategy favorable unless rail operating costs or crowding are high. Faster walking speeds mainly affect the shared bikes and private bike strategy. Faster cycling and long egress distances favor biking the last leg which is done when boarding bikes. High land costs favor smaller parking areas (from shared bikes). Slower streets and larger service areas result to avoiding shared bikes, and boarding can be infeasible under tight rail capacity. The framework guides cities on selecting cost-effective bike–train integration.