An end-to-end stochastic network calculus with effective bandwidth and effective capacity

Abstract

Network calculus is an elegant theory which uses envelopes to determine the worst-case performance bounds in a network. Statistical network calculus is the probabilistic version of network calculus, which strives to retain the simplicity of envelope approach from network calculus and use the arguments of statistical multiplexing to determine probabilistic performance bounds in a network. The tightness of the determined probabilistic bounds depends on the efficiency of modelling stochastic properties of the arrival traffic and the service available to the traffic at a network node. The notion of effective bandwidth from large deviations theory is a well known statistical descriptor of arrival traffic. Similarly, the notion of effective capacity summarizes the time varying resource availability to the arrival traffic at a network node. The main contribution of this paper is to establish an end-to-end stochastic network calculus with the notions of effective bandwidth and effective capacity which provides efficient end-to-end delay and backlog bounds that grows linearly in the number of nodes (H) traversed by the arrival traffic, under the assumption of independence.

Capacity–Delay–Error Boundaries: A Composable Model of Sources and Systems

“…Despite their similarity, the two models are essentially researched independently, i.e., a significant body of literature focuses either on deriving the effective bandwidth of sources, e.g., Markovian, On-Off, and fractional Brownian motion, or the effective capacity of wireless systems, e.g., fading channels. The composition of statistically independent sources and systems that are characterized by MGFs has mainly been considered in the stochastic network calculus, see e.g., [7], [14], [33], [52]. Compared to these works, Thm.…”

Using demisubmartingales for the stochastic analysis of networks

“…(2) and (4) with the error function ε( ) = e −Â . The main advantage of using network calculus to do performance analysis of networks is that the network calculus allows to model a network of nodes as a single virtual node.…”

“…However, the bounds on probabilistic performance measures of the network in [17] are computed using Boole's inequality and also require a bound on busy period of the scheduler. In [2], we have used effective bandwidth and effective capacity to compute end-to-end probabilitic performance bounds using Boole's inequality in a more general setting without the requirements on arrival and service processes to have stationary and independent increments. The rest of the paper is structured as follows: In Section 2, we introduce the notion and assumptions used in the paper.…”

Overlaying delay-tolerant service using SDN

“…Extensive simulations highlight the accuracy of this method. In stochastic network calculus, the closest notion to what we are investigating is that of leftover capacity, studied in [2], where the focus is still on obtaining bounds rather than on approaching the actual value. The contribution of this paper is then a method to estimate the usable capacity for given quality constraints given the characteristics of the nondeferrable traffic using it, and its extension in a very simple manner to the network case: it is indeed sufficient to apply the single-link method independently on each link of a network.…”