A network service curve approach for the stochastic analysis of networks

Abstract

The stochastic network calculus is an evolving new methodology for backlog and delay analysis of networks that can account for statistical multiplexing gain. This paper advances the stochastic network calculus by deriving a network service curve, which expresses the service given to a flow by the network as a whole in terms of a probabilistic bound. The presented network service curve permits the calculation of statistical end-to-end delay and backlog bounds for broad classes of arrival and service distributions. The benefits of the derived service curve are illustrated for the exponentially bounded burstiness (EBB) traffic model. It is shown that end-to-end performance measures computed with a network service curve are bounded by O ( H log H ), where H is the number of nodes traversed by a flow. Using currently available techniques that compute end-to-end bounds by adding single node results, the corresponding performance measures are bounded by O ( H 3 ).

Toward statistical QoS guarantees in a differentiated services network

“…In [15], the same framework is used to address bounds on the rate-variance envelope for regulated, adversarial traffic sources. In [2,7,13,18], various stochastic service curves were developed to perform delay analysis with stochastic network calculus.…”

“…A number of projects ( [5,15]) address the problem associated with Vertex C in Fig. 1, while studies of [2,7,13,17,18,28] are for the case of Vertex D. For the cases related to Vertex F, solutions have been discussed in [23,24]. The problems associated with statistical services within the diffserv model seem to be particularly challenging.…”

Multi-layer Resource Optimization and QoS Guarantee for Inter-working Wireless Networks

“…Usually, in stochastic NetCal, the input and output traffic in a network are defined as two stochastic processes which are the cumulative arrival process: A = A(t) for all t≥0 and the departure process: D = D(t) for all t≥0 [10]. If ε is defined as the probability bound, then, the function WN ε (t) is an effective stochastic service curve for an arrival process A if equation 1 is satisfied for all t ≥ 0 [10].…”

A calculus for stochastic QoS analysis

“…However, due to some difficulties as mentioned in the same paper, an estimation of the busy period is needed for the analysis. Recently, Ciucu, Burchard and Liebeherr in [11] derived various performance bounds using a variation of the definition of stochastic service curve from [14] by adding a positivity requirement. Another service model by adding a supremum to the definition of the stochastic service curve has been proposed in [19] to obtain an end-to-end stochastic network service curve.…”