Freight rail traffic assignment with interline transfers: a Generalized Nash Equilibrium approach

Competition among railroad carriers is inherent in the US Class I freight rail network. Prior studies of rail equilibrium have focused on path choice or shipper-carrier interactions, largely overlooking strategic interactions among carriers. Interline service, where trainloads move across multiple carriers’ networks, is also common but absent from existing competitive assignment models. This paper develops an equilibrium framework for freight rail traffic assignment that captures profit-maximizing competition among carriers with interline transfer. Freight demand is assigned over a network formed by the union of individual carrier networks. Because carriers jointly affect shared capacity, interline operations create endogenous constraints linking their decisions. We formulate the problem as a Generalized Nash Equilibrium Problem and reformulate it as a nonlinear complementarity problem solved by a non-smooth Newton method. Applications to synthetic and US Class I networks show how carrier interactions and capacity allocation influence traffic patterns, congestion, and profitability.