  Understanding the detailed queueing behavior of a networking session is
critical in enabling low-latency services over the Internet. Especially when
the packet arrival and service rates at the queue of a link vary over time and
moreover when the session is short-lived, analyzing the corresponding queue
behavior as a function of time, which involves a transient analysis, becomes
extremely challenging. In this paper, we propose and develop a new analytical
framework that anatomizes the transient queue behavior under time-varying
arrival and service rates even under unstable conditions. Our framework is
capable of answering key questions in designing low-latency services such as
the time-dependent probability distribution of the queue length; the
instantaneous or time-averaged violation probability that the queue length
exceeds a certain threshold; and the fraction of time during an interval $[0,
t]$ at which the queue length exceeds a certain threshold. We validate our
framework by comparing its prediction results over time with the statistical
simulation results and confirm that our analysis is accurate enough. Our
extensive demonstrations on the efficacy of the analytical framework in
designing low-latency services reveal that its prediction ability for the
transient queue behavior in diverse time-varying packet arrival and service
patterns can be of a high practical value.
