Towards the analysis of transient phases with stochastic network calculus

Current analysis methods for queueing systems mostly aim at steady-state results. However, many applications demand results for systems with a transient behavior. In communication networks such transient phases arise from sleep scheduling or the slow-start phase of TCP. In both examples the service offered is separated into a transient and a steady-state phase. In a larger context also the arrivals to a queueing system can show transient behavior. The demand or availability of energy in smart grids, the pool of data generated after the map phase in big data applications, or the arrivals in public transportation networks are a few examples. Analyzing these kind of systems in a steady-state fashion (for example via queueing theory) ignores their behavior in the transient phases. On the other side the analysis of transient phases bears additional challenges. This paper uses stochastic network calculus to describe the non-stationary behavior of queueing systems. With the help of bivariate arrival- and service envelopes time-variant performance bounds are constructed. Two numerical examples exemplify the framework created by these envelopes and compare it to the time-invariant analysis.