Network calculus for parallel processing

In this note, we present preliminary results on the use of "network calculus" for parallel processing systems, specifically MapReduce

ОБ ОДНОМ ПРИМЕНЕНИИ ДРОБНОГО ДВИЖЕНИЯ ЛЕВИ К МОДЕЛИРОВАНИЮ СЕТЕВОГО ТРАФИКА

Марковские процессы, хорошо зарекомендовавшие себя при моделировании текстовых и голосовых потоков информации, не способны отразить высокую вариабельность пакетного трафика вкупе с наличием долгой памяти. Эти модели существенно недооценивают реальную нагрузку и характеристики производительности систем. Поэтому построение более адекватных моделей трафика и исследование их свойств остается на сегодняшний день весьма актуальной задачей. В настоящей работе найдена неасимптотическая верхняя граница для длины очереди в системе с неограниченным накопителем и входящим трафиком, характеризующимся фрактальным движением Леви. Расчеты опираются на принципы сетевого анализа с помощью огибающих кривых и не предполагают стационарных режимов функционирования или асимптотик «большого буфера» и «большого числа источников

Stochastic Service Curve and Delay Bound Analysis: A Single Node Case

A packet-switched network node with constant capacity (in bps) is considered, where packets within each flow are served in the first in first out (FIFO) manner. While this single node system is perhaps the simplest computer communication system, its stochastic service curve characterization and independent case analysis in the context of stochastic network calculus (snetcal) are still basic and many crucial questions surprisingly remain open. Specifically, when the input is a single flow, what stochastic service curve and delay bound does the node provide? When the considered flow shares the node with another flow, what stochastic service curve and delay bound does the node provide to the considered flow, and if the two flows are independent, can this independence be made use of and how? The aim of this paper is to provide answers to these fundamental questions

Delay Bound: Fractal Traffic Passes through Network Servers

Delay analysis plays a role in real-time systems in computer communication networks. This paper gives our results in the aspect of delay analysis of fractal traffic passing through servers. There are three contributions presented in this paper. First, we will explain the reasons why conventional theory of queuing systems ceases in the general sense when arrival traffic is fractal. Then, we will propose a concise method of delay computation for hard real-time systems as shown in this paper. Finally, the delay computation of fractal traffic passing through severs is presented

Non-stationary service curves : model and estimation method with application to cellular sleep scheduling

In today’s computer networks, short-lived flows are predominant. Consequently, transient start-up effects such as the connection establishment in cellular networks have a significant impact on the performance. Although various solutions are derived in the fields of queuing theory, available bandwidths, and network calculus, the focus is, e.g., about the mean wake-up times, estimates of the available bandwidth, which consist either out of a single value or a stationary function and steady-state solutions for backlog and delay. Contrary, the analysis during transient phases presents fundamental challenges that have only been partially solved and is therefore understood to a much lesser extent. To better comprehend systems with transient characteristics and to explain their behavior, this thesis contributes a concept of non-stationary service curves that belong to the framework of stochastic network calculus. Thereby, we derive models of sleep scheduling including time-variant performance bounds for backlog and delay. We investigate the impact of arrival rates and different duration of wake-up times, where the metrics of interest are the transient overshoot and relaxation time. We compare a time-variant and a time-invariant description of the service with an exact solution. To avoid probabilistic and maybe unpredictable effects from random services, we first choose a deterministic description of the service and present results that illustrate that only the time-variant service curve can follow the progression of the exact solution. In contrast, the time-invariant service curve remains in the worst-case value. Since in real cellular networks, it is well known that the service and sleep scheduling procedure is random, we extend the theory to the stochastic case and derive a model with a non-stationary service curve based on regenerative processes. Further, the estimation of cellular network’s capacity/ available bandwidth from measurements is an important topic that attracts research, and several works exist that obtain an estimate from measurements. Assuming a system without any knowledge about its internals, we investigate existing measurement methods such as the prevalent rate scanning and the burst response method. We find fundamental limitations to estimate the service accurately in a time-variant way, which can be explained by the non-convexity of transient services and their super-additive network processes. In order to overcome these limitations, we derive a novel two-phase probing technique. In the first step, the shape of a minimal probe is identified, which we then use to obtain an accurate estimate of the unknown service. To demonstrate the minimal probing method’s applicability, we perform a comprehensive measurement campaign in cellular networks with sleep scheduling (2G, 3G, and 4G). Here, we observe significant transient backlogs and delay overshoots that persist for long relaxation times by sending constant-bit-rate traffic, which matches the findings from our theoretical model. Contrary, the minimal probing method shows another strength: sending the minimal probe eliminates the transient overshoots and relaxation times