A Stochastic Network Calculus

The issue of Quality of Service (QoS) performance analysis in packet switching networkshas drawn a lot of attention in the networking community in recent years. There is a lot ofwork including an elegant theory under the name of network calculus focusing on analysisof deterministic worst case QoS performance bounds. In the meantime, other researchershave studied the stochastic QoS performance for specific schedulers. As yet, there has beenno systematic investigation and analysis of end-to-end stochastic QoS performance. On theother hand, most of the previous work on deterministic QoS analysis or stochastic QoSanalysis only considered a server which provides deterministic service, i.e. deterministicallybounded rate service. Few works have considered the behavior of a stochastic server provid-ing input flows with variable rate service. In this paper, we propose a stochastic networkcalculus to systematically analyze the end-to-end stochastic QoS performance of a systemwith 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 sincea server serving an aggregate of flows can be regarded as a stochastic server for individualflows within the aggregate under aggregate scheduling.