Improved heuristic to reduce oscillations in transit assignment on refined networks

Frequency-based transit assignment supports planning and evaluation for high-frequency public transport. Two practical issues persist: expanded network representations can generate re-boarding flows at transfer stations, and when effective frequency depends on passenger flow, standard iterative solvers may oscillate or converge slowly. This study implements a pre-line marked (PLM) representation that conditions choices on the previously arriving line and treats any strategy that re-boards the arriving line as an on-board decision during dwell time. This yields a different interpretation of transfers and a finer station-level flow decomposition. To address algorithmic instability, we examine the fixed-point relation induced by effective frequency and characterise the instability of the flow loading process. Building on this analysis, we embed an oscillation detection algorithm (ODA) into the method of successive averages to flag period-two oscillations and apply damping without altering the main loop. Tests on a small network show that the PLM representation eliminates re-boarding at transfer stations and yields a more interpretable station-level flow decomposition. On the Winnipeg bus network, the proposed ODA achieves more stable convergence and lower per-iteration cost than a quasi-Newton inner fixed-point solver, while attaining comparable solution accuracy.