Intra-domain Level Research Articles

Solving security constraints for 5G slice embedding: A proof-of-concept

Network slicing is a prominent feature of 5G, which allow tenants to rent network and computing virtual resources from one or more Infrastructure Providers (InPs). Those resources are allocated according to tenants requirements, not only in terms of QoS but also in terms of security. In this paper, we build on our previous work to propose and evaluate a security-aware slice embedding implementation which enables tenants to declare security-oriented requirements, while limiting InP network information disclosure. To do so we improve our requirement model so that it becomes compatible with an Satisfiability Modulo Theories (SMT) formulation. Our implementation distinguishes two sub-problems, one for the intra-domain level (inside each InP) and one for the inter-domain level (in between the InPs). We leverage those sub-problems in a multi-level resolution algorithm to generate all multi-domain slice embeddings.

Component-based reduced basis for parametrized symmetric eigenproblems

A component-based approach is introduced for fast and flexible solution of parameter-dependent symmetric eigenproblems. Considering a generalized eigenproblem with symmetric stiffness and mass operators, we start by introducing a “ σ-shifted” eigenproblem where the left hand side operator corresponds to an equilibrium between the stiffness operator and a weighted mass operator, with weight-parameter σ>0. Assuming that σ=λ n >0, the nth real positive eigenvalue of the original eigenproblem, then the shifted eigenproblem reduces to the solution of a homogeneous linear problem. In this context, we can apply the static condensation reduced basis element (SCRBE) method, a domain synthesis approach with reduced basis (RB) approximation at the intradomain level to populate a Schur complement at the interdomain level. In the Offline stage, for a library of archetype subdomains we train RB spaces for a family of linear problems; these linear problems correspond to various equilibriums between the stiffness operator and the weighted mass operator. In the Online stage we assemble instantiated subdomains and perform static condensation to obtain the “ σ-shifted” eigenproblem for the full system. We then perform a direct search to find the values of σ that yield singular systems, corresponding to the eigenvalues of the original eigenproblem. We provide eigenvalue a posteriori error estimators and we present various numerical results to demonstrate the accuracy, flexibility and computational efficiency of our approach. We are able to obtain large speed and memory improvements compared to a classical Finite Element Method (FEM), making our method very suitable for large models commonly considered in an engineering context.

The Static Condensation Reduced Basis Element Method for a Mixed-Mean Conjugate Heat Exchanger Model

We propose a new approach for the simulation of conjugate heat exchangers. First, we introduce a dimensionality-reduced mathematical model for conjugate (fluid-solid) heat transfer: in the fluid channels, we consider a mixed-mean temperature defined on one-dimensional filaments; in the solid we consider a detailed partial differential equation conduction representation. We then propose a Petrov--Galerkin finite element (FE) numerical approximation which provides suitable stability and accuracy for our mathematical model. We next apply the static condensation reduced basis element (scRBE) method: a domain synthesis approach with parametric model order reduction at the intradomain level to populate a Schur complement at the interdomain level. We first build a library of “components,” each corresponding to a subdomain with a simple fluid channel geometry; for each component, we prepare Petrov--Galerkin reduced basis bubble approximations (and error bounds). We then assemble the system equations by static condensation and solve for the temperature distribution in the full domain. System-level error bounds are derived from matrix perturbation arguments; we also introduce a new output error bound which is sharper than the original scRBE estimator. We present numerical results for a two-dimensional automotive radiator model which demonstrate the flexibility, accuracy, and computational efficiency of our approach.

A static condensation reduced basis element method: Complex problems

We extend the static condensation reduced basis element (scRBE) method to treat the class of parametrized complex Helmholtz partial differential equations. The main ingredients are (i) static condensation at the interdomain level, (ii) a conforming eigenfunction “port” representation at the interface level, (iii) the reduced basis (RB) approximation of finite element (FE) bubble functions at the intradomain level, and (iv) rigorous system-level error bounds which reflect RB perturbation of the FE Schur complement. We then incorporate these ingredients in an Offline–Online computational strategy to achieve rapid and accurate prediction of parametric systems formed from instantiations of interoperable parametrized archetype components from a Library. We introduce a number of extensions with respect to the original scRBE framework: first, primal–dual RB methods for general non-symmetric (complex) problems; second, stability constant procedures for weakly coercive problems (at both the interdomain level and intradomain level); third, treatment of non-port linear–functional outputs (as well as functions of outputs); fourth, consideration of particular components and outputs relevant to acoustic applications. We consider several numerical examples in acoustics (in particular focused on mufflers and horns) to demonstrate that the approach can handle models with many parameters and/or topology variations with particular reference to waveguide-like applications.

A Static condensation Reduced Basis Element method : approximation anda posteriorierror estimation

We propose a new reduced basis element-cum-component mode synthesis approach for parametrized elliptic coercive partial differential equations. In the Offline stage we construct a Library of interoperable parametrized reference components relevant to some family of problems; in the Online stage we instantiate and connect reference components (at ports) to rapidly form and query parametric systems. The method is based on static condensation at the interdomain level, a conforming eigen- function port representation at the interface level, and finally Reduced Basis (RB) approximation of Finite Element (FE) bubble functions at the intradomain level. We show under suitable hypotheses that the RB Schur complement is close to the FE Schur complement: we can thus demonstrate the stability of the discrete equations; furthermore, we can develop inexpensive and rigorous (system-level) a posteriori error bounds. We present numerical results for model many-parameter heat transfer and elasticity problems with particular emphasis on the Online stage; we discuss flexibility, accuracy, com- putational performance, and also the effectivity of the a posteriori error bounds.

Bandwidth Broker

Research community has been showing an immense interest for more than a decade in issues related to providing better than best effort service guarantees on the Internet. A number of options have been explored in this regard. Differentiated Services architecture is one of the proposed solutions that treat traffic flows based on their pre-assigned classes to eliminate scalability issue, otherwise a difficult and non trivial problem to solve. Bandwidth Broker is a logical resource management entity in Differentiated Services domain that performs a number of important functions at inter and intra-domain level to optimize resource utilization. Optimal resource management is not only complex but is tricky in this scenario, as the networks service providing ability is greatly affected by the optimality of domain management. Hence, Bandwidth Broker has been a focus of a lot of research efforts. This paper: a) provides a brief but concise discussion on different functions and modules of Bandwidth Broker, b) points out some advance features proposed for BBs performance enhancements and, c) reviews recent patents directly and indirectly related to Bandwidth Broker. Keywords: Bandwidth broker, DiffServ, QoS, Resource management, Integrated Services (IntServ), Differentiated Services (DiffServ), DiffServ domain, Service Level Agreements (SLA)s, Policy Enforcement Points (PEP)s, Information Acquisition

On the challenges of establishing disjoint QoS IP/MPLS paths across multiple domains

MPLS is being actively adopted as the core switching infrastructure at the intradomain level. This trend is mainly attributable to the undeniable potential of MPLS in terms of virtual private networks (VPNs) management, traffic engineering (TE), QoS delivery, path protection, and fast recovery from network failures. However, little progress has been made to attain the expected extension of MPLS label-switched paths (LSPs) across domain boundaries. Among the problems that remain unsolved is how to efficiently find and establish primary and protection interdomain LSPs for mission-critical services subject to QoS constraints. This article explores the major limitations hindering the deployment of these kinds of LSPs across multiple domains, in the context of the current interdomain network model. We describe the critical problems faced by the research community, and present our vision on how to rationally overcome some of the problems exposed. Our perspective is that we should be prepared for rather coarse-grained solutions as long as we need to coexist with the current interdomain network model

Locating internet bottlenecks

The ability to locate network bottlenecks along end-to-end paths on the Internet is of great interest to both network operators and researchers. For example, knowing where bottleneck links are, network operators can apply traffic engineering either at the interdomain or intradomain level to improve routing. Existing tools either fail to identify the location of bottlenecks, or generate a large amount of probing packets. In addition, they often require access to both end points. In this paper we present Pathneck , a tool that allows end users to efficiently and accurately locate the bottleneck link on an Internet path. Pathneck is based on a novel probing technique called Recursive Packet Train (RPT) and does not require access to the destination. We evaluate Pathneck using wide area Internet experiments and trace-driven emulation. In addition, we present the results of an extensive study on bottlenecks in the Internet using carefully selected, geographically diverse probing sources and destinations. We found that Pathneck can successfully detect bottlenecks for almost 80% of the Internet paths we probed. We also report our success in using the bottleneck location and bandwidth bounds provided by Pathneck to infer bottlenecks and to avoid bottlenecks in multihoming and overlay routing.