Coupling Spatio-Temporal Graph Forecasting with Wardrop Equilibrium: Measuring the Network-Wide Cost of Emergency Vehicle Priority

Granting an emergency vehicle priority on a road network — through signal preemption or a reserved lane — reduces the capacity available to other traffic along its route. The resulting delay has been measured at the intersections the vehicle passes through, but not as a network-wide quantity, even though drivers far from the emergency route also change their paths in response. This paper measures that wider cost. A temporal graph convolu- tional network forecasts traffic conditions on the METR-LA sensor network; these forecasts set the link costs of a Wardrop user equilibrium, which is solved with the Frank–Wolfe algorithm before and after capacity is reserved along the emergency route. The difference in total system travel time between the two equilibria is termed the price of priority. Across 92 valid trials, each combining a forecast condition with a simulated link failure, reserving a fifth of the capacity along the emergency route increased background travel time in everytrial, by 0.195% on average; the effect remained positive in all 87 valid trials of a sensitivity analysis spanning a fourfold range of the capacity assumption. Two further observations emerge: congestion-aware routing improved on congestion-blind routing only where an alternative path existed, in roughly two-thirds of trials, and neither capacity utilisation nor betweenness centrality reliably predicted which failures caused the greatest disruption. The measurement uses synthetic travel demand on a single network, and its magnitude should be read accordingly.