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.     

Modelling and estimation of social interaction effects in new product diffusion

We present a new product choice model in which individual agents are assumed to interact with each other across spatial hierarchies under random Gaussian laws. A restricted form that allows estimation of the model and inference on the random interaction structure on available data is then derived. This is essentially a random coefficients model which we estimate on repeated cross-sectional data for the adoption of video cassette recorders in Britain. It is argued that the random coefficient approach, based on economic and social-theoretic arguments allows for more accurate inference on the structure of social interactions, and thus may provide a useful way to help alleviate the inferential problem caused by the identification issues stated in the literature. This very same problem has for long been at the core of the debate between alternative economic and marketing theories of new product diffusion.     

Analysis of the dynamics of Cournot team-game with heterogeneous players

In this paper, we study a dynamical system of a two-team Cournot game played by a team consisting of two firms with bounded rationality and a team consisting of one firm with naive expectation. The equilibrium solutions and the conditions of their locally asymptotic stability are studied. It is demonstrated that, as some parameters in the model are varied, the stability of the equilibrium will get lost and many such complex behaviors as the period bifurcation, chaotic phenomenon, periodic windows, strange attractor and unpredictable trajectories will occur. The great influence of the model parameters on the speed of convergence to the equilibrium is also shown with numerical analysis.     

A quality of service negotiation-based vertical handoff decision scheme in heterogeneous wireless systems

This paper introduces a novel vertical handoff decision scheme. The objective is to provide users with enhanced quality of service (QoS) and maximize the network revenue. This scheme balances both-side interests via a suitably defined network merit function and a user–operator negotiation model. The merit function evaluates network performance based on user preferences and decides the most appropriate network for users. The negotiation model is defined as a semi-Markov decision process (SMDP). An optimal policy that maximizes the network revenue without violating QoS constraints is found by resolving the SMDP problem using Q-learning. Furthermore, a time-adaptive QoS monitoring mechanism is combined with the merit function in order to decrease the power consumption on terminal interface activation. The simulation results demonstrate that the proposed vertical handoff decision scheme enhances the performance in terms of power consumption, handoff call-dropping probability (HCDP) and network revenue.     

Models of unidirectional propagation in heterogeneous excitable media

Two differential equation models of excitable media (threshold and recovery kinetics) with solutions that exhibit unidirectional propagation are presented. It is shown that unidirectional propagation in heterogeneous excitable media with non-oscillatory kinetics can be initiated from homogeneous initial data. Simulations on a reaction-diffusion model with FitzHugh-Nagumo kinetics and spatially heterogeneous parameters yields a rotating wave on a one-dimensional circular spatial domain. An ordinary differential equation model with four semi-coupled excitable cells and heterogeneous parameters is analyzed to determine a critical parameter region over which unidirectional propagation may occur.     

Controlling predator-prey discrete dynamics utilizing a threshold policy with hysteresis

This paper introduces a threshold policy with hysteresis (TPH) for the control of the logistic one-species model, the Lotka-Volterra and Rosenzweig-MacArthur two species density-dependent predator-prey models. A nonstandard scheme is used for the discretization of the models since it results in preservation of the qualitative characteristics of the continuous-time models. Two theorems that establish the global stability of the discrete logistic model subject to the threshold policy (TP) and the TPH are proved. The proposed policy (TPH) is more realistic than a pure threshold policy (TP) proposed earlier in the literature and changes the dynamics of the system in such a way that a low amplitude bounded oscillation, far from the extinction region, is achieved. Furthermore, it can be designed by a suitable choice of so called virtual equilibrium points in a simple and intuitive manner.     

Diffusion with a Discontinuous Potential: a Non-Linear Semigroup Approach

This paper studies existence of mild solution to a sharp cut off model for contact driven tumor growth. Analysis is based on application of the Crandall-Liggett theorem for ω-quasi-contractive semigroups on the Banach space L~1(?). Furthermore,numerical computations are provided which compare the sharp cut off model with the tumor growth model of Perthame, Quirós, and Vázquez [13].     

Continuous and discontinuous opinion dynamics with bounded confidence

In this paper, we study a continuous-time version of the Hegselmann-Krause opinion dynamics, which models bounded confidence by a discontinuous interaction. Intending solutions in the sense of Krasovskii, we provide results of existence, completeness and convergence to clusters of agents sharing a common opinion. For a deeper understanding of the role of the mentioned discontinuity, we study a class of continuous approximating systems, and their convergence to the original one. Our results indicate that their qualitative behavior is similar, and we argue that discontinuity is not an essential feature in bounded confidence opinion dynamics.     

Partial mean field limits in heterogeneous networks

We investigate systems of interacting stochastic differential equations with two kinds of heterogeneity: one originating from different weights of the linkages, and one concerning their asymptotic relevance when the system becomes large. To capture these effects, we define a partial mean field system, and prove a law of large numbers with explicit bounds on the mean squared error. Furthermore, a large deviation result is established under reasonable assumptions. The theory will be illustrated by several examples: on the one hand, we recover the classical results of chaos propagation for homogeneous systems, and on the other hand, we demonstrate the validity of our assumptions for quite general heterogeneous networks including those arising from preferential attachment random graph models.     

Diffusion approximations for open queueing networks with service interruptions

This paper establishes functional central limit theorems describing the heavy-traffic behavior of open single-class queueing networks with service interruptions. In particular, each station has a single server which is alternatively up and down. There are two treatments of the up and down times. The first treatment corresponds to fixed up and down times and leads to a reflected Brownian motion, just as when there are no service interruptions, but with different parameters. To represent long rare interruptions, the second treatment has growing up and down times with the up and down times being of ordern andn ^1/2, respectively, when the traffic intensities are of order 1-n^–1/2. In this case we establish convergence in the SkorohodM ₁ topology to a multidimensional reflection of multidimensional Brownian motion plus a multidimensional jump process.     

The survival of the weakest in networks

We study here dynamic antagonism in a fixed network, represented as a graph G of n vertices. In particular, we consider the case of k≤n particles walking randomly independently around the network. Each particle belongs to exactly one of two antagonistic species, none of which can give birth to children. When two particles meet, they are engaged in a (sometimes mortal) local fight. The outcome of the fight depends on the species to which the particles belong. Our problem is to predict (i.e. to compute) the eventual chances of species survival. We prove here that this can indeed be done in expected polynomial time on the size of the network, provided that the network is undirected.

Diffusion dynamics near critical bifurcations in a nonlinearly damped pendulum system

We numerically study the diffusion dynamics near critical bifurcations such as sudden widening of the size of a chaotic attractor, intermittency and band-merging of a chaotic attractor in a nonlinearly damped and periodically driven pendulum system. The system is found to show only normal diffusion. Near sudden widening and intermittency crisis power-law variation of diffusion constant with the control parameter ω of the external periodic force f sin ωt is found while linear variation of it is observed near band-merging crisis. The value of the exponent in the power-law relation varies with the damping coefficient and the strength of the added Gaussian white noise.     

Convergence dynamics of stochastic reaction–diffusion recurrent neural networks with continuously distributed delays

Convergence dynamics of reaction–diffusion recurrent neural networks (RNNs) with continuously distributed delays and stochastic influence are considered. Some sufficient conditions to guarantee the almost sure exponential stability, mean value exponential stability and mean square exponential stability of an equilibrium solution are obtained, respectively. Lyapunov functional method, M-matrix properties, some inequality technique and nonnegative semimartingale convergence theorem are used in our approach. These criteria ensuring the different exponential stability show that diffusion and delays are harmless, but random fluctuations are important, in the stochastic continuously distributed delayed reaction–diffusion RNNs with the structure satisfying the criteria. Two examples are also given to demonstrate our results.     

Approximation of an Analog Diffusion Network with Applications to Image Estimation

This work is concerned with a numerical procedure for approximating an analog diffusion network. The key idea is to take advantage of the separable feature of the noise for the diffusion machine and use a parallel processing method to develop recursive algorithms. The asymptotic properties are studied. The main result of this paper is to establish the convergence of a continuous-time interpolation of the discrete-time algorithm to that of the analog diffusion network via weak convergence methods. The parallel processing feature of the network makes it attractive for solving large-scale optimization problems. Applications to image estimation are considered. Not only is this algorithm useful for the image estimation problems, but it is widely applicable to many related optimization problems.     

On fuzzy cliques in fuzzy networks

A definition of fuzzy clique in social networks is suggested which overcomes five limitations of current definitions. This definition is based on the networks in which the 0–1 strengths, the weighted strengths, and fuzzy strengths are all allowed. The fuzzy distance in such a network is defined. The node‐clique and clique‐clique coefficients are suggested. The core and the periphery of fuzzy cliques are discussed formally. A “cone like” property of the cores is discovered. The network structures are discussed using the new definition. A “no circle” property of networks is found. Basic fuzzy tools and the related algorithms are also discussed. Some examples are analyzed to demonstrate the theory.     

A preferential attachment model with Poisson growth for scale-free networks

We propose a scale-free network model with a tunable power-law exponent. The Poisson growth model, as we call it, is an offshoot of the celebrated model of Barabási and Albert where a network is generated iteratively from a small seed network; at each step a node is added together with a number of incident edges preferentially attached to nodes already in the network. A key feature of our model is that the number of edges added at each step is a random variable with Poisson distribution, and, unlike the Barabási–Albert model where this quantity is fixed, it can generate any network. Our model is motivated by an application in Bayesian inference implemented as Markov chain Monte Carlo to estimate a network; for this purpose, we also give a formula for the probability of a network under our model.     

Bayesian networks with a logistic regression model for the conditional probabilities

Logistic regression techniques can be used to restrict the conditional probabilities of a Bayesian network for discrete variables. More specifically, each variable of the network can be modeled through a logistic regression model, in which the parents of the variable define the covariates. When all main effects and interactions between the parent variables are incorporated as covariates, the conditional probabilities are estimated without restrictions, as in a traditional Bayesian network. By incorporating interaction terms up to a specific order only, the number of parameters can be drastically reduced. Furthermore, ordered logistic regression can be used when the categories of a variable are ordered, resulting in even more parsimonious models. Parameters are estimated by a modified junction tree algorithm. The approach is illustrated with the Alarm network.     

Risk neutral and risk averse power optimization in electricity networks with dispersed generation

Models and algorithms for risk neutral and risk averse power optimization under uncertainty are presented. The approach differs from previous ones by incorporating the transmission network explicitly.     

Perturbation analysis of communication networks with feedback control using stochastic hybrid models

Communication networks may be abstracted through Stochastic Fluid Models (SFM) with the node dynamics described by switched flow equations as various events take place, thus giving rise to hybrid automaton models with stochastic transitions. The inclusion of feedback mechanisms complicates these dynamics. In a tandem setting, a typical feedback mechanism is the control of a node processing rate as a threshold-based function of the downstream node’s buffer level. We consider the problem of controlling the threshold parameters so as to optimize performance metrics involving average workload and packet loss and show how Infinitesimal Perturbation Analysis (IPA) can be used to analyze congestion propagation through a network and develop gradient estimators of such metrics.