Dynamic mode control for transit services in disaster evacuations using a Hawkes-based jump diffusion process

This paper introduces a new strategic decision architecture for dynamic transportation mode and vehicle size switching during mass evacuations, driven by a Hawkes-based jump diffusion process (HB-JDP) and evaluated against deterministic cost models, a concept previously unexplored in the evacuation literature. The control benchmark is the Pointwise Cost-Minimizing Lower-Bound Policy (PCMLB): at each decision instant the lower-cost configuration is selected. For deployment, we enact Intensity-Band Hysteresis (IBH), a day-schedulable controller defined on the distribution of fitted daily intensities; service-type changes occur only when the daily intensity exits pre-set quantile bands, aiming to minimize system cost while preserving operational auditability and switching stability. We implement: a linear Hawkes backbone with exponential memory, a nonnegative exogenous jump channel at detected days, a Negative Binomial (NB) observation model, a scalar least-squares scale to 5-minute proxies, and a two-threshold hysteresis policy defined on daily intensity . An empirical case study uses INRIX daily trip counts for Hurricane Sally (Escambia County, 2020) within a dual-control design that combines a temporal control (same region, same calendar window in the prior year) with spatial control (contemporaneous unaffected Florida region matched on urban/coastal characteristics). The storm-period fit is ridge-tethered to control-season anchors and enforces subcriticality of the endogenous mechanism; the estimated branching ratio is strictly below one with a tight moving-block-bootstrap interval, providing a stability certificate. Enabling the exogenous jump channel reallocates spike mass without disturbing the Hawkes memory scale; parameter estimates remain stable across jump modes, while the baseline level adjusts coherently. A closed-form daily-to–5-minute scale produces deterministic operational proxies that feed the cost layer unchanged, allowing direct comparison among service types, the PCMLB, and the IBH policy. Calibrated outcomes show that IBH tracks the lower bound closely while confining flips to day boundaries with gap fractions in the 0.25–0.38 range across fixed, flexible, and variant architectures that jump reallocation reduces short-lag residual correlation without degrading best-achievable costs; and that control-based calibration yields reproducible parameters suitable for operational governance. Additional multi-event validation across Hurricanes Sally, Ian, Idalia, Milton, and Helene further demonstrates structural robustness of the HB-JDP/IBH architecture under heterogeneous evacuation-demand environments, while perturbation-based sensitivity diagnostics show stable regime geometry and switching behavior under coupled stress variations in spatial concentration and operational penalty structure. The resulting pipeline, PCMLB as formal benchmark and IBH as deployable surrogate on a calibrated HB-JDP driver, provides an applied, policy-grade mechanism for triggering mode/size reconfiguration under real hurricane demand.