arXiv subjects

Ulrich Killat

Publications and source records attributed to Ulrich Killat.

3 recordsLinked to original sources

arXiv2012

A Simple Proof of Linear Scaling of End-to-End Probabilistic Bounds using Network Calculus

Statistical network calculus is the probabilistic extension of network calculus, which uses a simple envelope approach to describe arrival traffic and service available for the arrival traffic in a node. One of the key features of network calculus is the possibility to describe the service available in a network using a network service envelope constructed from the service envelopes of the individual nodes constituting the network. It have been shown that the end-to-end worst case performance measures computed using the network service envelope is bounded by $ {\cal O} (H) $, where $H$ is the number of nodes traversed by a flow. There have been many attempts to achieve a similar linear scaling for end-to-end probabilistic performance measures but with limited success. In this paper, we present a simple general proof of computing end-to-end probabilistic performance measures using network calculus that grow linearly in the number of nodes ($H$).

cs.NI↗

arXiv2012

An Approach using Demisubmartingales for the Stochastic Analysis of Networks

Stochastic network calculus is the probabilistic version of the network calculus, which uses envelopes to perform probabilistic analysis of queueing networks. The accuracy of probabilistic end-to-end delay or backlog bounds computed using network calculus has always been a concern. In this paper, we propose novel end-to-end probabilistic bounds based on demisubmartingale inequalities which improve the existing bounds for the tandem networks of GI/GI/1 queues. In particular, we show that reasonably accurate bounds are achieved by comparing the new bounds with the existing results for a network of M/M/1 queues.

cs.NI↗

arXiv2011

Probabilistic Performance Analysis of Networks using an Improved Network Service Envelope Approach

Stochastic network calculus is an evolving theory which accounts for statistical multiplexing and uses an envelope approach for probabilistic delay and backlog analysis of networks. One of the key ideas of stochastic network calculus is the possibility to describe service offered at network node as a stochastic service envelope, which in turn can be used to describe the stochastic service available in a network of nodes and determine end-to-end probabilistic delay and backlog bounds. This paper introduces a new definition of stochastic service envelopes which yield a simple network service envelope and tighter end-to-end performance bounds. It is shown for ($σ(θ), ρ(θ)$) - constrained traffic model that the end-to-end performance measures computed using the new stochastic network service envelope are tight in comparison to the ones obtained using the existing start-of-the-art definition of statistical network service envelope and are bounded by ${\cal O}(H \log{H})$, where $H$ is the number of nodes traversed by the arrival traffic.

cs.NI↗