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While steady-state solutions of backlog and delay have been derived foressential wireless systems, the analysis of transient phases still posessignificant challenges. Considering the majority of short-lived and interactiveflows, transient startup effects, as caused by sleep scheduling in cellularnetworks, have, however, a substantial impact on the performance. To facilitatereasoning about the transient behavior of systems, this paper contributes anotion of non-stationary service curves. Models of systems with sleepscheduling are derived and transient backlogs and delays are analyzed. Further,measurement methods that estimate the service of an unknown system fromobservations of selected probe traffic are developed. Fundamental limitationsof existing measurement methods are explained by the non-convexity of thetransient service and further difficulties are shown to be due to thesuper-additivity of network service processes. A novel two-phase probingtechnique is devised that first determines the shape of a minimal probe andsubsequently obtains an accurate estimate of the unknown service. In acomprehensive measurement campaign, the method is used to evaluate the serviceof cellular networks with sleep scheduling (2G, 3G, and 4G), revealingconsiderable transient backlog and delay overshoots that persist for longrelaxation times.

A Non-stationary Service Curve Model for Estimation of Cellular Sleep Scheduling