A Scalable Approach for Service Chain (SC) Mapping with Multiple SC Instances in a Wide-Area Network

Network Function Virtualization (NFV) aims to simplify deployment of network services by running Virtual Network Functions (VNFs) on commercial off-the-shelf servers. Service deployment involves placement of VNFs and in-sequence routing of traffic flows through VNFs comprising a Service Chain (SC). The joint VNF placement and traffic routing is called SC mapping. In a Wide-Area Network (WAN), a situation may arise where several traffic flows, generated by many distributed node pairs, require the same SC; then, a single instance (or occurrence) of that SC might not be enough. SC mapping with multiple SC instances for the same SC turns out to be a very complex problem, since the sequential traversal of VNFs has to be maintained while accounting for traffic flows in various directions. Our study is the first to deal with the problem of SC mapping with multiple SC instances to minimize network resource consumption. We first propose an Integer Linear Program (ILP) to solve this problem. Since ILP does not scale to large networks, we develop a column-generation-based ILP (CG-ILP) model. However, we find that exact mathematical modeling of the problem results in quadratic constraints in our CG-ILP. The quadratic constraints are made linear but even the scalability of CG-ILP is limited. Hence, we also propose a two-phase column-generation-based approach to get results over large network topologies within reasonable computational times. Using such an approach, we observe that an appropriate choice of only a small set of SC instances can lead to a solution very close to the minimum bandwidth consumption. Further, this approach also helps us to analyze the effects of number of VNF replicas and number of NFV nodes on bandwidth consumption when deploying these minimum number of SC instances.Comment: arXiv admin note: substantial text overlap with arXiv:1704.0671

Service Chain (SC) Mapping with Multiple SC Instances in a Wide Area Network

Network Function Virtualization (NFV) aims to simplify deployment of network services by running Virtual Network Functions (VNFs) on commercial off-the-shelf servers. Service deployment involves placement of VNFs and in-sequence routing of traffic flows through VNFs comprising a Service Chain (SC). The joint VNF placement and traffic routing is usually referred as SC mapping. In a Wide Area Network (WAN), a situation may arise where several traffic flows, generated by many distributed node pairs, require the same SC, one single instance (or occurrence) of that SC might not be enough. SC mapping with multiple SC instances for the same SC turns out to be a very complex problem, since the sequential traversal of VNFs has to be maintained while accounting for traffic flows in various directions. Our study is the first to deal with SC mapping with multiple SC instances to minimize network resource consumption. Exact mathematical modeling of this problem results in a quadratic formulation. We propose a two-phase column-generation-based model and solution in order to get results over large network topologies within reasonable computational times. Using such an approach, we observe that an appropriate choice of only a small set of SC instances can lead to solution very close to the minimum bandwidth consumption

A tutorial on recursive models for analyzing and predicting path choice behavior

The problem at the heart of this tutorial consists in modeling the path choice behavior of network users. This problem has been extensively studied in transportation science, where it is known as the route choice problem. In this literature, individuals' choice of paths are typically predicted using discrete choice models. This article is a tutorial on a specific category of discrete choice models called recursive, and it makes three main contributions: First, for the purpose of assisting future research on route choice, we provide a comprehensive background on the problem, linking it to different fields including inverse optimization and inverse reinforcement learning. Second, we formally introduce the problem and the recursive modeling idea along with an overview of existing models, their properties and applications. Third, we extensively analyze illustrative examples from different angles so that a novice reader can gain intuition on the problem and the advantages provided by recursive models in comparison to path-based ones

Chaining Test Cases for Reactive System Testing (extended version)

Testing of synchronous reactive systems is challenging because long input sequences are often needed to drive them into a state at which a desired feature can be tested. This is particularly problematic in on-target testing, where a system is tested in its real-life application environment and the time required for resetting is high. This paper presents an approach to discovering a test case chain---a single software execution that covers a group of test goals and minimises overall test execution time. Our technique targets the scenario in which test goals for the requirements are given as safety properties. We give conditions for the existence and minimality of a single test case chain and minimise the number of test chains if a single test chain is infeasible. We report experimental results with a prototype tool for C code generated from Simulink models and compare it to state-of-the-art test suite generators.Comment: extended version of paper published at ICTSS'1

Pseudo-Separation for Assessment of Structural Vulnerability of a Network

Based upon the idea that network functionality is impaired if two nodes in a network are sufficiently separated in terms of a given metric, we introduce two combinatorial \emph{pseudocut} problems generalizing the classical min-cut and multi-cut problems. We expect the pseudocut problems will find broad relevance to the study of network reliability. We comprehensively analyze the computational complexity of the pseudocut problems and provide three approximation algorithms for these problems. Motivated by applications in communication networks with strict Quality-of-Service (QoS) requirements, we demonstrate the utility of the pseudocut problems by proposing a targeted vulnerability assessment for the structure of communication networks using QoS metrics; we perform experimental evaluations of our proposed approximation algorithms in this context

Blocked All-Pairs Shortest Paths Algorithm on Intel Xeon Phi KNL Processor: A Case Study

Manycores are consolidating in HPC community as a way of improving performance while keeping power efficiency. Knights Landing is the recently released second generation of Intel Xeon Phi architecture. While optimizing applications on CPUs, GPUs and first Xeon Phi's has been largely studied in the last years, the new features in Knights Landing processors require the revision of programming and optimization techniques for these devices. In this work, we selected the Floyd-Warshall algorithm as a representative case study of graph and memory-bound applications. Starting from the default serial version, we show how data, thread and compiler level optimizations help the parallel implementation to reach 338 GFLOPS.Comment: Computer Science - CACIC 2017. Springer Communications in Computer and Information Science, vol 79