The pressing necessity to renew infrastructure assets in developed railway systems leads to an increased number of activities to be scheduled annually. Scheduling of renewal activities for a railway network is a critical task since these activities often require a significant amount of time and create a capacity conflict in operation scheduling. This paper discusses economic and technological aspects, opportunities, and constraints in the renewals of multiple rail infrastructure components at several locations in a railway network. We address and model a challenging situation that there are interrelationships between different track lines, and thus, possession of a track line can have impacts on the other track lines and prevent renewal works on them. A mathematical formulation for the railway infrastructure renewal scheduling problem in the network context is presented to minimize the total renewal and unavailability costs. A method based on a triple-prioritization rule and an optimal sharing of renewal times allocated for different types of rail infrastructure components in a possession is proposed to solve the problem. The method is applied to a real case of a regional railway network in Northern Netherlands and it is shown that up to 13% of total costs can be saved compared to the current scheduling practice.