Sample-path Large deviations for Scheduled Arrival Processes with Unpunctuality
arXiv:2607.12666
The paper analyzes a counting process where scheduled arrival times are randomly perturbed, proving a sample‑path large deviations principle for its empirical mean and applying the results to workload processes in both deterministic and random service settings.
Abstract
We study a scheduled-arrival process in which deterministic arrival times are perturbed by i.i.d. unpunctuality random variables. For the empirical mean of independent copies of the resulting counting process, we prove a sample-path large deviations principle on , equipped with the Skorokhod topology. As an application, we derive large deviation principles for the corresponding workload process under deterministic and random service setting. In the deterministic service case, we also identify the exponentially tilted arrival path associated with a rare workload overflow event.