A unified network performance measure with importance identification and the ranking of network components

In this paper, we propose the first network performance measure that can be used to assess the efficiency of a network in the case of either fixed or elastic demands. Such a measure is needed for many different applications since only when the performance of a network can be quantifiably measured can the network be appropriately managed. Moreover, as we demonstrate, the proposed performance measure, which captures flow information and behavior, allows one to determine the criticality of various nodes (as well as links) through the identification of their importance and ranking. We present specific networks for which the performance/efficiency is computed along with the importance rankings of the nodes and links. The new measure can be applied to transportation networks, supply chains, financial networks, electric power generation and distribution networks as well as to the Internet and can be used to assess the vulnerability of a network to disruptions.     

Perturbations of finite networks and asymptotic periodicity of flow semigroups

We consider a transport process on a finite network and introduce a new special transformation of the underlying graph that is then used to yield an alternative proof of the main theorem on asymptotic periodicity of the flow semigroup proven in Kramar and Sikolya (Math. Z. 249:139–162, 2005). The perturbation technique we develop allows us to prove this theorem starting from a special case, thus greatly simplifying the proof. This technique is in Kunszenti-Kovács (Perturbations of networks and asymptotic periodicity of recurrent flows: the infinite case, Preprint, 2008) adapted to infinite networks, where it allows for significant generalisations of previous results.     

Financial Networks with Intermediation and Transportation Network Equilibria: A Supernetwork Equivalence and Reinterpretation of the Equilibrium Conditions with Computations

In this paper, we consider two distinct classes of network problems – financial networks with intermediation and with electronic transactions and transportation network equilibrium problems, which have been modeled and studied independently. We then prove that the former problem can be reformulated as the latter problem through an appropriately constructed abstract network i.e., a supernetwork. The established equivalence allows one to then transfer the methodological tools, in particular, algorithms, that have been developed for transportation network equilibria to the financial network domain. In addition, this connection provides us with a novel interpretation of the financial network equilibrium conditions in terms of paths and path flows and a direct existence result. We further show how the theoretical results obtained in this paper can be exploited computationally through several numerical examples.      

Bandwidth allocation for guaranteed versus best effort service categories

Modern communication networks evolve towards integration of guaranteed-performance and best-effort service types. The coexistence of these two service types offers substantial benefits, such as resource sharing between service classes, and the ability of the user to select an appropriate service class according to its individual requirements and preferences. Notwithstanding, such interaction gives rise to more complicated system behavior and related performance issues, which need to be explored and understood in order to allow efficient network operation. In this paper we examine potential congestion phenomena, which arise due to the combined effect of bandwidth sharing and user migration between service classes. We propose a simplified fluid model for session flow, consisting of two coupled queues with state-dependent flows, which captures the essential ingredients of service-class interaction. Our analysis shows that the system might exhibit bistable behavior, in the sense that transient congestion may stir the system from a stable and efficient operating point to an inefficient and congested one. We identify conditions which give rise to bistability, and propose a call admission control scheme which prevents the system from getting trapped in a congested-type equilibrium, while not interfering with normal system operation. This revised version was published online in June 2006 with corrections to the Cover Date.     

An investigation of synchrony in transport networks

The cumulative degree distributions of transport networks, such as air transportation networks and respiratory neuronal networks, follow power laws. The significance of power laws with respect to other network performance measures, such as throughput and synchronization, remains an open question. Evolving methods for the analysis and design of air transportation networks must be able to address network performance in the face of increasing demands and the need to contain and control local network disturbances, such as congestion. Toward this end, we investigate functional relationships that govern the performance of transport networks; for example, the links between the first nontrivial eigenvalue, λ₂, of a network's Laplacian matrix—a quantitative measure of network synchronizability—and other global network parameters. In particular, among networks with a fixed degree distribution and fixed network assortativity (a measure of a network's preference to attach nodes based on a similarity or difference), those with small λ₂ are shown to be poor synchronizers, to have much longer shortest paths and to have greater clustering in comparison to those with large λ₂. A simulation of a respiratory network adds data to our investigation. This study is a beginning step in developing metrics and design variables for the analysis and active design of air transport networks. © 2008 Wiley Periodicals, Inc. Complexity, 2009     

Capacity and flow assignment of data networks by generalized Benders decomposition

A mixed-integer non-linear model is proposed to optimize jointly the assignment of capacities and flows (the CFA problem) in a communication network. Discrete capacities are considered and the cost function combines the installation cost with a measure of the Quality of Service (QoS) of the resulting network for a given traffic. Generalized Benders decomposition induces convex subproblems which are multicommodity flow problems on different topologies with fixed capacities. These are solved by an efficient proximal decomposition method. Numerical tests on small to medium-size networks show the ability of the decomposition approach to obtain global optimal solutions of the CFA problem.     

On Average Distortion of Embedding Metrics into the Line

We introduce and study the notion of the average distortion of a nonexpanding embedding of one metric space into another. Less sensitive than the multiplicative metric distortion, the average distortion captures well the global picture and, overall, is a quite interesting new measure of metric proximity, related to the concentration of measure phenomenon. The paper mostly deals with embeddings into the real line with a low (as much as it is possible) average distortion. Our main technical contribution is that the shortest-path metrics of special (e.g., planar, bounded treewidth, etc.) undirected weighted graphs can be embedded into the line with constant average distortion. This has implications, e.g., on the value of the MinCut–MaxFlow gap in uniform-demand multicommodity flows on such graphs. A preliminary version of this paper has appeared at STOC’03, pp. 156–162. Supported in part by a grant ISF-247-02-10.5.     

A fast heuristic method for minimizing traffic congestion on reconfigurable ring topologies

We describe the development of fast heuristics and methodologies for congestion minimization problems in directional wireless networks, and we compare their performance with optimal solutions. The focus is on the network layer topology control problem (NLTCP) defined by selecting an optimal ring topology as well as the flows on it. Solutions to NLTCP need to be computed in near realtime due to changing weather and other transient conditions and which generally preclude traditional optimization strategies. Using a mixed-integer linear programming formulation, we present both new constraints for this problem and fast heuristics to solve it. The new constraints are used to increase the lower bound from the linear programming relaxation and hence speed up the solution of the optimization problem by branch and bound. The upper and lower bounds for the optimal objective function to the mixed integer problem then serve to evaluate new node-swapping heuristics which we also present. Through a series of tests on different sized networks with different traffic demands, we show that our new heuristics achieve within about 0.5% of the optimal value within seconds.     

Markovian traffic equilibrium

We analyze an equilibrium model for traffic networks based on stochastic dynamic programming. In this model passengers move towards their destinations by a sequential process of arc selection based on a discrete choice model at every intermediate node in their trip. Route selection is the outcome of this sequential process while network flows correspond to the invariant measures of the underlying Markov chains. The approach may handle different discrete choice models at every node, including the possibility of mixing deterministic and stochastic distribution rules. It can also be used over a multi-modal network in order to model the simultaneous selection of mode and route, as well as to treat the case of elastic demands. We establish the existence of a unique equilibrium, which is characterized as the solution of an unconstrained strictly convex minimization problem of low dimension. We report some numerical experiences comparing the performance of the method of successive averages (MSA) and Newton’s method on one small and one large network, providing a formal convergence proof for MSA. Dedicated to Clovis Gonzaga on the occassion of his 60th birthday.     

Insensitive Bandwidth Sharing in Data Networks

We represent a data network as a set of links shared by a dynamic number of competing flows. These flows are generated within sessions and correspond to the transfer of a random volume of data on a pre-defined network route. The evolution of the stochastic process describing the number of flows on all routes, which determines the performance of the data transfers, depends on how link capacity is allocated between competing flows. We use some key properties of Whittle queueing networks to characterize the class of allocations which are insensitive in the sense that the stationary distribution of this stochastic process does not depend on any traffic characteristics (session structure, data volume distribution) except the traffic intensity on each route. We show in particular that this insensitivity property does not hold in general for well-known allocations such as max-min fairness or proportional fairness. These results are ilustrated by several examples on a number of network topologies.     

Stable network topologies using the notion of covering

An alternative perspective to evaluate networks and network evolution is introduced, based on the notion of covering. For a particular node in a network covering captures the idea of being outperformed by another node in terms of, for example, visibility and possibility of information gathering. In this paper, we focus on networks where these subdued network positions do not exist. We call these networks stable. Within this set we identify the minimal stable networks, which frequently have a ‘bubble-like’ structure. Severing a link in such a network results in at least one of the nodes being covered. In a minimal stable network therefore all nodes cooperate to avoid that one of the nodes ends up in a subdued position. Our results can be applied to, for example, the design of (covert) communication networks and the dynamics of social and information networks.     

Maximum flow problem on dynamic generative network flows with time-varying bounds

This paper considers a new class of network flows, called dynamic generative network flows in which, the flow commodity is dynamically generated at a source node and dynamically consumed at a sink node and the arc-flow bounds are time dependent. Then the maximum dynamic flow problem in such networks for a pre-specified time horizon T is defined and mathematically formulated in both arc flow and path flow presentations. By exploiting the special structure of the problem, an efficient algorithm is developed to solve the general form of the dynamic problem as a minimum cost static flow problem.     

Optimum synthesis of discrete capacitated networks with multi-terminal commodity flow requirements

Network design problems arise in a wide range of applied areas including telecommunications, computer networks, and transportation. In this paper, we address the following discrete capacitated multi-terminal network design problem. Given a connected digraph G = (V,A), a set of L potential facilities to be installed on each arc, and a set of K multi-terminal (non-simultaneous) commodity flow requirements, the problem is to find a set of facilities to install in order to route the K nonsimultaneous flows while minimizing the total fixed plus variable costs. We describe an exact procedure for solving this problem based on Benders decomposition. Our algorithm includes several features that significantly improve the efficiency of the basic approach. Computational results attest to the efficacy of the proposed algorithm, which can solve medium- to large-scale problems to optimality.     

Viral conductance: Quantifying the robustness of networks with respect to spread of epidemics

In this paper, we propose a novel measure, viral conductance (VC), to assess the robustness of complex networks with respect to the spread of SIS epidemics. In contrast to classical measures that assess the robustness of networks based on the epidemic threshold above which an epidemic takes place, the new measure incorporates the fraction of infected nodes at steady state for all possible effective infection strengths. Through examples, we show that VC provides more insight about the robustness of networks than does the epidemic threshold. We also address the paradoxical robustness of Barabási–Albert preferential attachment networks. Even though this class of networks is characterized by a vanishing epidemic threshold, the epidemic requires high effective infection strength to cause a major outbreak. On the contrary, in homogeneous networks the effective infection strength does not need to be very much beyond the epidemic threshold to cause a major outbreak. To overcome computational complexities, we propose a heuristic to compute the VC for large networks with high accuracy. Simulations show that the heuristic gives an accurate approximation of the exact value of the VC. Moreover, we derive upper and lower bounds of the new measure. We also apply the new measure to assess the robustness of different types of network structures, i.e. Watts–Strogatz small world, Barabási–Albert, correlated preferential attachment, Internet AS-level, and social networks. The extensive simulations show that in Watts–Strogatz small world networks, the increase in probability of rewiring decreases the robustness of networks. Additionally, VC confirms that the irregularity in node degrees decreases the robustness of the network. Furthermore, the new measure reveals insights about design and mitigation strategies of infrastructure and social networks.     

Fast, Efficient Equipment Placement Heuristics for Broadband Switched or Internet Router Networks

Planning and designing the next generation of IP router or switched broadband networks seems a daunting challenge considering the many complex, interacting factors affecting the performance and cost of such networks. Generally, this complexity implies that it may not even be clear what constitutes a “good” network design for a particular specification. Different network owners or operators may view the same solution differently, depending on their unique needs and perspectives. Nevertheless, we have observed a core common issue arising in the early stages of network design efforts involving leading-edge broadband switched technologies such as ATM, Frame Relay, and SMDS; or even Internet IP router networks. This core issue can be stated as follows: Given a set of service demands for the various network nodes, where should switching or routing equipment be placed to minimize the Installed First Cost of the network? Note that the specified service demands are usually projections for a future scenario and generally entail significant uncertainty. Despite this uncertainty, we have found that network owners and operators generally feel it is worthwhile to obtain high-level advice on equipment placement with a goal of minimizing Installed First Cost. This paper reports on a heuristic approach we have implemented for this problem that has evolved out of real network design projects. A tool with both a Solution Engine and an intuitive Graphical User Interface has been developed. The approach is highly efficient; for example, the tool can often handle LATA-sized networks in seconds or less on a workstation processor. By using only nodal demands rather than the more complex point-to-point demands usually required in tools of this sort, we have created an approach that is not only highly efficient, but is also a better match to real design projects in which demand data is generally scant and highly uncertain.     

Graphical Explanation in Belief Networks

Abstract

Belief networks provide an important bridge between statistical modeling and expert systems. This article presents methods for visualizing probabilistic “evidence flows” in belief networks, thereby enabling belief networks to explain their behavior. Building on earlier research on explanation in expert systems, we present a hierarchy of explanations, ranging from simple colorings to detailed displays. Our approach complements parallel work on textual explanations in belief networks. Graphical-Belief, Mathsoft Inc.'s belief network software, implements the methods.     

A cross entropy approach to design of reliable networks

One of the most important parameters determining the performance of communication networks is network reliability. The network reliability strongly depends on not only topological layout of the communication networks but also reliability and availability of the communication facilities. The selection of optimal network topology is an NP-hard problem so that computation time of enumeration-based methods grows exponentially with network size. This paper presents a new solution approach based on cross-entropy method, called NCE, to design of communication networks. The design problem is to find a network topology with minimum cost such that all-terminal reliability is not less than a given level of reliability. To investigate the effectiveness of the proposed NCE, comparisons with other heuristic approaches given in the literature for the design problem are carried out in a three-stage experimental study. Computational results show that NCE is an effective heuristic approach to design of reliable networks.     

A cooperative differential game model based on transmission rate in wireless networks

Network throughput and energy efficiency are paramount for network performance in an energy-constrained wireless network. However, it is difficult to achieve optimal objectives simultaneously. Therefore, it is necessary to find a rate control solution based on tradeoff between network throughput and energy efficiency. In this paper, we propose a cooperative differential game model and find an optimal rate control of each player to get the total minimal cost with tradeoff between network throughput and energy efficiency of the networks.     

Quality of service statistics over heterogeneous networks: Analysis and applications

Heterogeneous wireless/wired networks and ubiquitous environments are gaining ever more attention by research community. To properly control and manage such puzzles a deep knowledge of quality of service parameters is needed and, therefore, a complete and robust performance assessment is necessary. This paper deals with a performance evaluation and measurement of a number of heterogeneous end-to-end paths taking into account a wide range of statistics. To study the behavior of QoS parameters, an active measurement approach has been introduced for the analysis of properties we called (i) concise statistics (mean, standard deviation, inter quantile range, minimum, maximum, and median) and (ii) detailed statistics (Probability Density Function, Auto-correlation Function, Entropy, Complementary Cumulative Distribution Function, and Bivariate Probability Density Function). We show how, thanks to this view on QoS statistics, a more complete understanding of QoS parameters behavior is possible. In addition, we show how the measured statistics can be fruitfully used in the context of network control and management. More precisely, we present two proof of concepts regarding frameworks for QoS-based anomaly detection and for QoS-based identification of network elements.