Analysis of Stochastic Service Guarantees in Communication Networks: A Server Model

Abstract

A basic calculus is presented for stochastic service guarantee analysis in communication networks. Central to the calculus are two definitions, maximum-(virtual)-backlog-centric (m.b.c) stochastic arrival curve and stochastic service curve, which respectively generalize arrival curve and service curve in the deterministic network calculus framework. With m.b.c stochastic arrival curve and stochastic service curve, various basic results are derived under the (min, +) algebra for the general case analysis, which are crucial to the development of stochastic network calculus. These results include (i) superposition of flows, (ii) concatenation of servers, (iii) output characterization, (iv) per-flow service under aggregation, and (v) stochastic backlog and delay guarantees. In addition, to perform independent case analysis, stochastic strict server is defined, which uses an ideal service process and an impairment process to characterize a server. The concept of stochastic strict server not only allows us to improve the basic results (i) -(v) under the independent case, but also provides a convenient way to find the stochastic service curve of a serve. Moreover, an approach is introduced to find the m.b.c stochastic arrival curve of a flow and the stochastic service curve of a server.

A calculus for stochastic QoS analysis

“…Note that there exists a relationship between gSBB and SBB as shown in Theorem 1 where the bounding function needs to be within F In fact, following the same proof steps of Theorem 1 in [40], it can be proved that this relationship also holds for bounding functions not within F (e.g. see Theorem 3 in [20]). In either case, the right part of (14) could become larger than 1, so a restriction on it is enforced in Theorem 9 to meet the requirement on the bounding function based on the definition of gSBB.…”

“…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. Furthermore, Cruz [14] did some preliminary work to derive the stochastic backlog bound and delay bound for a stochastic input flow after passing through a stochastic server.…”

“…An example for this is α-stable traffic [21]. Although this type of traffic has gSBB [20], it does not have SBB [45].…”

On Superlinear Scaling of Network Delays

“…Examples of the former can be found in [23], where delays at each node are assumed to satisfy a priori delay bounds, in [2], where it is assumed that a node discards traffic that exceeds a threshold, and in [13], which assumes that service at subsequent nodes is statistically independent. Examples of the latter include [8], which assumes that the statistical service description is made over time intervals, and [17,18], which assumes sample path guarantees for service. In [11], it was shown that a composition of per-node service curves becomes feasible without such assumptions for a broad class of traffic types, by accounting for a rate penalty at each traversed node.…”

Modeling and analysis of Rayleigh fading channels using stochastic network calculus

“…Ciucu et al [12] extended the stochastic network calculus by providing a network service curve formulation which is capable of calculating stochastic end-to-end delay and backlog bounds for a number of arrival and service distributions. In [16], Jiang and Emstad proposed a server model to facilitate stochastic service guarantee analysis and address the challenges of delay guarantee, backlog guarantee, output characterization and concatenation property. There are a lot of works providing theoretic fundamentals of stochastic network calculus, but few of them study the problem of mapping the theory to a specific application.…”