Stochastic Network Calculus Models under Max-Plus Algebra

A challenging research issue of analyzing networks where packets are served probabilistically, such as multi-access networks and wireless networks, is to characterize the stochastic nature of service provided to users. This paper proposes a server model for characterizing a service process with the consideration of the stochastic nature of service. The proposed server model is defined based on a probabilistic bound on the cumulative packet service time. In addition, two traffic models characterizing the arrival process by the cumulative packet inter-arrival time are defined. Based on the proposed models, stochastic service guarantees including delay bound and backlog bound and the output characterization are explored. A two-class Probabilistic Priority server system, a generic server model which can model systems serving packets probabilistically, is analyzed to illustrate that the proposed models can facilitate performance analysis.