Sample-path Large deviations for Scheduled Arrival Processes with Unpunctuality

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 $D([0,T])$, 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.