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

TL;DR

This paper introduces a non-stationary service curve model to analyze transient effects of sleep scheduling in cellular networks, providing new measurement methods and revealing significant backlog and delay overshoots.

Contribution

It develops a novel non-stationary service curve framework and a two-phase probing method for accurately estimating transient service in cellular networks with sleep scheduling.

Findings

Transient backlog and delay overshoots are significant in cellular sleep scheduling.

The proposed measurement method effectively estimates transient service behavior.

Cellular networks exhibit long relaxation times after sleep scheduling events.

Abstract

While steady-state solutions of backlog and delay have been derived for essential wireless systems, the analysis of transient phases still poses significant challenges. Considering the majority of short-lived and interactive flows, transient startup effects, as caused by sleep scheduling in cellular networks, have, however, a substantial impact on the performance. To facilitate reasoning about the transient behavior of systems, this paper contributes a notion of non-stationary service curves. Models of systems with sleep scheduling are derived and transient backlogs and delays are analyzed. Further, measurement methods that estimate the service of an unknown system from observations of selected probe traffic are developed. Fundamental limitations of existing measurement methods are explained by the non-convexity of the transient service and further difficulties are shown to be due to the super-additivity of network service processes. A novel two-phase probing technique is devised that first determines the shape of a minimal probe and subsequently obtains an accurate estimate of the unknown service. In a comprehensive measurement campaign, the method is used to evaluate the service of cellular networks with sleep scheduling (2G, 3G, and 4G), revealing considerable transient backlog and delay overshoots that persist for long relaxation times.