A Transient Queueing Analysis under Time-varying Arrival and Service Rates for Enabling Low-Latency Services

ABSTRACT 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 con€rm that our analysis is accurate enough. Our extensive demonstrations on the ecacy 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 paŠerns can be of a high practical value.