AbstractThis paper presents a mathematical model of a single‐lane bridge serving two‐way traffic in alternating directions (with an FIFO rule observed within each directional queue). While the bridge serves cars moving in one direction, cars approaching from the opposite direction wait in a queue at its foot. When cars in the current direction finish crossing the bridge, it begins serving cars from the other direction, if any are present. A newly‐arrived car finding an empty bridge mounts it immediately. Several cars moving in the same direction may occupy the bridge simultaneously. The crossing speed is assumed to be constant, and the arrival processes in both directions are assumed to be independent, homogeneous Poisson processes. A generalization of the alternating‐priority models [1, 2] is developed to arrive at the Laplace‐Stieltjes transform and the expected value of the flow time (the time interval between the moments of arrival at the bridge and departure from it) for steady state conditions. The results are discussed and some examples are presented gr