A Stochastic Network Calculus

The issue of Quality of Service (QoS) performance analysis in packet switched networks has drawn a lot of attention in the networking community in recent years. There is a lot of work including an elegant theory under the name of network calculus focusing on analysis of deterministic worst case QoS performance bounds. In the meantime, other researchers have studied the stochastic QoS performance for specific schedulers. As yet, there has been no systematic investigation and analysis of end-to-end stochastic QoS performance. On the other hand, most of the previous work on deterministic QoS analysis or stochastic QoS analysis only considered a server which provides deterministic service, i.e. deterministically bounded rate service. Few works have considered the behavior of a stochastic server providing input flows with variable rate service. In this paper, we propose a stochastic network calculus to systematically analyze the end-to-end stochastic QoS performance of a system with stochastically bounded input traffic over a series of deterministic and stochastic servers. The proposed framework is also applied to analyze per-flow stochastic QoS performance since a server serving an aggregate of flows can be regarded as a stochastic server for individual flows within the aggregate under aggregate scheduling.