Personalised incentives for demand management of congested public transport systems: A reverse-engineering approach and application

To reduce congestion, public transport service providers can offer incentives that encourage passengers to choose alternative routes and travel times (RTs). To the best of the authors’ knowledge, no existing study on incentive design evaluates scheme performance by explicitly quantifying the deviation of the incentivised system from the exact system-optimal (SO) benchmark. To fill this gap, we develop RE-ESO: a Reverse-Engineering framework using the Exact SO solution for incentive design in public transport. Our algorithm systematically determines specific incentive amounts for each RT combination by iteratively analysing the discrepancies between the current incentivised assignment flows and the exact SO assignment flows. In particular we show, for the first time, incentives that as nearly as possible result in SO passenger choices. The effectiveness of RE-ESO for reducing congestion costs is demonstrated through a case study on the Hong Kong Mass Transit Railway network. In our experiments, RE-ESO achieves a 32.74% reduction in congestion costs, substantially outperforming two comparative baselines: incentive optimisation without a globally optimal target (IO-NGT), which appears popularly in the literature (bi-level method; 22.18% cost reduction), and time-based shifting, which is popular with the industry (off-peak fare reward; 10.90% cost reduction). Notably, our result approaches the theoretical maximum of 36.35% congestion reduction indicated by the exact SO system. Another key finding is that departure time shifting accounts for 82% of the total congestion relief, indicating broad potential for applicability in transit networks like Hong Kong and Stockholm, where route-shifting options are limited.