Kaiserslautern - Fachbereich Informatik
Refine
Document Type
- Doctoral Thesis (2)
Language
- English (2)
Has Fulltext
- yes (2)
Keywords
- Network Calculus (2) (remove)
Faculty / Organisational entity
Dealing with Dependence in the End-to-End Performance Analysis in Stochastic Network Calculus
(2022)
Communication networks, in particular the Internet, have become a pivotal part of our life. Since their beginnings, a key aspect of their applicability has been the performance. Safety-critical applications, for example, can sometimes only be implemented in a responsible manner if guarantees about their end-to-end delay can be made. A mathematical modeling and performance evaluation of communication networks requires a powerful set of tools that is able to incorporate their increasing complexity.
The stochastic network calculus (SNC) is a versatile, mathematical framework that allows for a calculation of probabilistic end-to-end performance bounds of distributed systems. Its flexibility enables to incorporate a large class of different schedulers as well as different models of traffic processes beyond the assumption of Poisson arrivals that is predominant in queueing theory-based analyses. It originates in the so-called deterministic network analysis (DNC) in the 90's of the 20th century that was introduced to provide deterministic, ``hard'' guarantees that are of relevance, e.g., in the context of real-time systems. While the DNC of today can be used to calculate fast and accurate delay bounds of arbitrary feedforward networks, the SNC is still in a significantly earlier stage. In particular, method-pertinent dependencies, i.e., a phenomenon that occurs when independent flows become stochastically dependent after sharing resources in the network, can be considered a major challenge in the SNC with moment-generating functions (MGFs).
This thesis argues to contribute to the SNC in several ways. First, we show that the ``pay multiplexing only once'' (PMOO) analysis known from the DNC is also possible in the SNC. Not only does it significantly improve end-to-end delay bounds, it also needs to consider less method-pertinent dependencies. Therefore, complexity and runtimes of the calculation are greatly reduced. Second, we introduce the concept of negative dependence to the SNC with MGFs and give numerical evidence that this can further lead to better performance bounds. Third, for the larger problem of end-to-end performance bounds of tree networks, we introduce so-called ''h-mitigators'', a modification in the calculation of MGF output bounds. It is minimally invasive, all existing results and procedures are still applicable, and improves performance bounds. As a fourth contribution, we conduct extensive numerical evaluations to substantiate our claims. Moreover, we made the respective code, the ''SNC MGF toolbox'', publicly available to ensure that the results are reproducible. At last, we conduct different stochastic analyses of a popular fair scheduler, generalized processor sharing (GPS). We give an overview of the state-of-the-art analyses in the SNC and substantiate the comparison through numerical evaluations.
Distributed systems are omnipresent nowadays and networking them is fundamental for the continuous dissemination and thus availability of data. Provision of data in real-time is one of the most important non-functional aspects that safety-critical networks must guarantee. Formal verification of data communication against worst-case deadline requirements is key to certification of emerging x-by-wire systems. Verification allows aircraft to take off, cars to steer by wire, and safety-critical industrial facilities to operate. Therefore, different methodologies for worst-case modeling and analysis of real-time systems have been established. Among them is deterministic Network Calculus (NC), a versatile technique that is applicable across multiple domains such as packet switching, task scheduling, system on chip, software-defined networking, data center networking and network virtualization. NC is a methodology to derive deterministic bounds on two crucial performance metrics of communication systems:
(a) the end-to-end delay data flows experience and
(b) the buffer space required by a server to queue all incoming data.
NC has already seen application in the industry, for instance, basic results have been used to certify the backbone network of the Airbus A380 aircraft.
The NC methodology for worst-case performance analysis of distributed real-time systems consists of two branches. Both share the NC network model but diverge regarding their respective derivation of performance bounds, i.e., their analysis principle. NC was created as a deterministic system theory for queueing analysis and its operations were later cast in a (min,+)-algebraic framework. This branch is known as algebraic Network Calculus (algNC). While algNC can efficiently compute bounds on delay and backlog, the algebraic manipulations do not allow NC to attain the most accurate bounds achievable for the given network model. These tight performance bounds can only be attained with the other, newly established branch of NC, the optimization-based analysis (optNC). However, the only optNC analysis that can currently derive tight bounds was proven to be computationally infeasible even for the analysis of moderately sized networks other than simple sequences of servers.
This thesis makes various contributions in the area of algNC: accuracy within the existing framework is improved, distributivity of the sensor network calculus analysis is established, and most significantly the algNC is extended with optimization principles. They allow algNC to derive performance bounds that are competitive with optNC. Moreover, the computational efficiency of the new NC approach is improved such that this thesis presents the first NC analysis that is both accurate and computationally feasible at the same time. It allows NC to scale to larger, more complex systems that require formal verification of their real-time capabilities.