Railway traffic management requires a timely and accurate redefinition of routes and schedules in response to detected perturbations of the original timetable. To date, most of the (automated) solutions to this problem require a central authority to make decisions for all the trains in a given control area. An appealing alternative is to consider trains as intelligent agents able to self-organize and determine the best traffic management strategy. This could lead to more scalable and resilient approaches, that can also take into account the real-time mobility demand. In this paper, we formalize the concept of railway traffic self-organization and we present an original design that enables its real-world deployment. We detail the principles at the basis of the sub-processes brought forth by the trains in a decentralized way, explaining their sequence and interaction. Moreover, we propose a preliminary proof of concept based on a realistic setting representing traffic in a French control area. The results allow conjecturing that self-organizing railway traffic management may be a viable option, and foster further research in this direction.