A Non-stationary Service Curve Model for Performance Analysis of Transient Phases

摘要

Steady-state solutions for a variety of relevant queueing systems are known today, e.g., from queueing theory, effective bandwidths, and network calculus. The behavior during transient phases, on the other hand, is understood to a much lesser extent as its analysis poses significant challenges. Considering the majority of short-lived flows, transient effects that have diverse causes, such as TCP slow start, sleep scheduling in wireless networks, or signalling in cellular networks, are, however, predominant. This paper contributes a general model of regenerative service processes to characterize the transient behavior of systems. The model leads to a notion of non-stationary service curves that can be conveniently integrated into the framework of the stochastic network calculus. We derive respective models of sleep scheduling and show the significant impact of transient phases on backlogs and delays. We also consider measurement methods that estimate the service of an unknown system from observations of selected probe traffic. We find that the prevailing rate scanning method does not recover the service during transient phases well. This limitation is fundamental as it is explained by the non-convexity of nonstationary service curves. A second key difficulty is proven to be due to the super-additivity of network service processes. We devise a novel two-phase probing technique that first determines a minimal pattern of probe traffic. This probe is used to obtain an accurate estimate of the unknown transient service.