  We study the rare event behavior of the workload process in a transitory
queue, where the arrival epochs (or points) of a finite number of jobs are
assumed to be the ordered statistics of independent and identically distributed
(i.i.d.) random variables. The service times (or marks) of the jobs are assumed
to be i.i.d. random variables with a general distribution, that are jointly
independent of the arrival epochs. Under the assumption that the service times
are strictly positive, we derive the large deviations principle (LDP) satisfied
by the workload process. The analysis leverages the connection between ordered
statistics and self-normalized sums of exponential random variables to
establish the LDP. This paper presents the first analysis of rare events in
transitory queueing models, supplementing prior work that has focused on fluid
and diffusion approximations.
