I assume each carrier takes turns switching the customer at a juntion?[^o)]
The answer is not simple, especially in the present context of a shipper demand for government regulations to add fairness to railroad pricing of service. Here is a short thread in which the third post addresses your question:
Reciprocal Switching: A mutual interchange of inbound and outbound carload freight which is switched to or from a siding/spur/backtrack of another carrier under a regular switching charge. The charge is usually absorbed by the carrier receiving the line haul. -Railway Age’s Comprehensive Railroad Dictionary.