Optimal Worst-Case QoS Routing in Constrained AWGN Channel Network

In this paper, we extend the optimal worst-case QoS routing algorithm and metric definition given in [1]. We prove that in addition to the q-ary symmetric and q-ary erasure channel model, the necessary and sufficient conditions defined in [2] for the Generalized Dijkstra's Algorithm (GDA) can be used with a constrained non-negative-mean AWGN channel. The generalization allowed the computation of the worst-case QoS metric value for a given edge weight density. The worst-case value can then be used as the routing metric in networks where some nodes have error correcting capabilities. The result is an optimal worst-case QoS routing algorithm that uses the Generalized Dijkstra's Algorithm as a subroutine with a polynomial time complexity of O(V^3)

Operator Calculus Algorithms for Multi-Constrained Paths

Classical approaches to multi-constrained routing problems generally require construction of trees and the use of heuristics to prevent combinatorial explosion. Introduced here is the notion of constrained path algebras and their application to multi-constrained path problems. The inherent combinatorial properties of these algebras make them useful for routing problems by implicitly pruning the underlying tree structures. Operator calculus (OC) methods are generalized to multiple non-additive constraints in order to develop algorithms for the multi constrained path problem and multi constrained optimization problem. Theoretical underpinnings are developed first, then algorithms are presented. These algorithms demonstrate the tremendous simplicity, flexibility and speed of the OC approach. Algorithms are implemented in Mathematica and Java and applied to a problem first proposed by Ben Slimane et al. as an example

Finding the Best QoS Path in a Gilbert Channel Network

Many different types of modern wired and wireless communication links can be mathematically described as discrete- time Gilbert channels. In this extended abstract, we present an exact method of calculating the best path in a network of discrete- time Gilbert channels, each of which is defined as a Markov chain with two states. In the "Good" state of the chain, the channel produces no erasure, and in the "Bad" state of the chain, the channel produces an erasure. Our method relies on a modified version of the Dijkstra's algorithm, which we customize to operate on sets of Gilbert channel parameters, instead of real numbers. We prove that the Gilbert channels obeys a certain set of algebraic properties which makes it compatible with our algorithm

Bandwidth sensitive routing in diffServ networks with heterogeneous bandwidth requirements

This paper studies the problem of finding optimal routes for premium class traffic in a DiffServ network such that (1) loop-freedom is guaranteed in the entire network under hop-by-hop routing assumption; and (2) the maximum relative congestion among all links is minimized. This problem is called the Extended Optimal Premium Routing (eOPR) problem, which is proven to be NP-hard. We use the integer programming method to mathematically formulate the eOPR problem and find the optimal solutions for small scale networks. We also study heuristic algorithms in order to handle large scale networks. Simulation results are compared with the optimal solutions obtained by solving the integer programming models. The results show that the Bandwidth-inversion Shortest Path (BSP) algorithm can be a good candidate to route premium traffic in DiffServ networks.published_or_final_versio

Finding the best path in a binary Block Interference network

A binary block interference channel (BIC) is model of binary channels with memory that allows for a mathematically tractable computation of channel capacity. One can easily imagine interconnecting such channels into a network that allows point-to-point communication between any two nodes in the network. Given a pair of network nodes, finding the path with the highest capacity is quite trivial if we can assume that all participating nodes in any path connecting the two nodes can perform coding at arbitrary complexity such that at each link capacity is achieved. However, even if the complexity assumption is not taken into account, in most real-life networks (such as the current Internet), only a minimum amount of coding is performed at the link layer. In most networks, coding is performed five or six layers up in the OSI network model, i.e., on either the presentation or the application layer. Under such realistic circumstances, finding the path with the highest capacity is no longer trivial. In this paper, we propose a solution based on a modified version of the Dijkstrapsilas Algorithm

Theories and Models for Internet Quality of Service

We survey recent advances in theories and models for Internet Quality of Service (QoS). We start with the theory of network calculus, which lays the foundation for support of deterministic performance guarantees in networks, and illustrate its applications to integrated services, differentiated services, and streaming media playback delays. We also present mechanisms and architecture for scalable support of guaranteed services in the Internet, based on the concept of a stateless core. Methods for scalable control operations are also briefly discussed. We then turn our attention to statistical performance guarantees, and describe several new probabilistic results that can be used for a statistical dimensioning of differentiated services. Lastly, we review recent proposals and results in supporting performance guarantees in a best effort context. These include models for elastic throughput guarantees based on TCP performance modeling, techniques for some quality of service differentiation without access control, and methods that allow an application to control the performance it receives, in the absence of network support

Study, evaluation and contributions to new algorithms for the embedding problem in a network virtualization environment

Network virtualization is recognized as an enabling technology for the future Internet. It aims to overcome the resistance of the current Internet to architectural change and to enable a new business model decoupling the network services from the underlying infrastructure. The problem of embedding virtual networks in a substrate network is the main resource allocation challenge in network virtualization and is usually referred to as the Virtual Network Embedding (VNE) problem. VNE deals with the allocation of virtual resources both in nodes and links. Therefore, it can be divided into two sub-problems: Virtual Node Mapping where virtual nodes have to be allocated in physical nodes and Virtual Link Mapping where virtual links connecting these virtual nodes have to be mapped to paths connecting the corresponding nodes in the substrate network. Application of network virtualization relies on algorithms that can instantiate virtualized networks on a substrate infrastructure, optimizing the layout for service-relevant metrics. This class of algorithms is commonly known as VNE algorithms. This thesis proposes a set of contributions to solve the research challenges of the VNE that have not been tackled by the research community. To do that, it performs a deep and comprehensive survey of virtual network embedding. The first research challenge identified is the lack of proposals to solve the virtual link mapping stage of VNE using single path in the physical network. As this problem is NP-hard, existing proposals solve it using well known shortest path algorithms that limit the mapping considering just one constraint. This thesis proposes the use of a mathematical multi-constraint routing framework called paths algebra to solve the virtual link mapping stage. Besides, the thesis introduces a new demand caused by virtual link demands into physical nodes acting as intermediate (hidden) hops in a path of the physical network. Most of the current VNE approaches are centralized. They suffer of scalability issues and provide a single point of failure. In addition, they are not able to embed virtual network requests arriving at the same time in parallel. To solve this challenge, this thesis proposes a distributed, parallel and universal virtual network embedding framework. The proposed framework can be used to run any existing embedding algorithm in a distributed way. Thereby, computational load for embedding multiple virtual networks is spread across the substrate network Energy efficiency is one of the main challenges in future networking environments. Network virtualization can be used to tackle this problem by sharing hardware, instead of requiring dedicated hardware for each instance. Until now, VNE algorithms do not consider energy as a factor for the mapping. This thesis introduces the energy aware VNE where the main objective is to switch off as many network nodes and interfaces as possible by allocating the virtual demands to a consolidated subset of active physical networking equipment. To evaluate and validate the aforementioned VNE proposals, this thesis helped in the development of a software framework called ALgorithms for Embedding VIrtual Networks (ALEVIN). ALEVIN allows to easily implement, evaluate and compare different VNE algorithms according to a set of metrics, which evaluate the algorithms and compute their results on a given scenario for arbitrary parameters

Advances in Internet Quality of Service

We describe recent advances in theories and architecture that support performance guarantees needed for quality of service networks. We start with deterministic computations and give applications to integrated services, differentiated services, and playback delays. We review the methods used for obtaining a scalable integrated services support, based on the concept of a stateless core. New probabilistic results that can be used for a statistical dimensioning of differentiated services are explained; some are based on classical queuing theory, while others capitalize on the deterministic results. Then we discuss performance guarantees in a best effort context; we review: methods to provide some quality of service in a pure best effort environment; methods to provide some quality of service differentiation without access control, and methods that allow an application to control the performance it receives, in the absence of network support

Hop-by-hop computing for green Internet routing

In this paper we study energy conservation in the Internet. We observe that different traffic volumes on a link can result in different energy consumption; this is mainly due to such technologies as trunking (IEEE 802.1AX), adaptive link rates, etc. We design a green Internet routing scheme, where the routing can lead traffic in a way that is green. We differ from previous studies where they switch network components, such as line cards and routers, into sleep mode. We do not prune the Internet topology. We first develop a power model, and validate it using real commercial routers. Instead of developing a centralized optimization algorithm, which requires additional protocols such as MPLS to materialize in the Internet, we choose a hop-by-hop approach. It is thus much easier to integrate our scheme into the current Internet. We progressively develop three algorithms, which are loop-free, maximize energy conservation, and jointly consider green and QoS requirements such as path stretch. We comprehensively evaluate our algorithms through simulations on synthetic and real topologies and traffic traces. We show that the power saving in the line cards can be as much as 50%.Department of ComputingRefereed conference pape