Simulation of rare events in communications networks

Computer simulation is an important tool in the analysis and design of communications networks. In spite of the advances in computational power, using simulation to obtain rare event probabilities such as cell/packet loss or delay in networks still requires prohibitively long execution times. We provide an overview of importance sampling techniques and how they can be used to provide orders of magnitude speedup for many network problems     

Quick resource allocation in heterogeneous networks

Wireless Networks - In this paper, an innovative technique is given to reduce the implementation time taken for doing the seamless communication in heterogeneous networks. When a new user arrives...     

Quick fault location in multistage interconnection networks

A new procedure for locating a faulty element in a class of multistage interconnection networks based on 2 × 2 crossbar switches is presented. It allows one kind of fault to be located in a number of steps which does not depend on the network size. With the result so obtained and other recently developed procedures, the networks considered can be diagnosed in a constant number of steps, whatever the type of fault.     

Robust estimation via stochastic approximation

It has been found that robust estimation of parameters may be obtained via recursive Robbins-Monro-type stochastic approximation (SA) algorithms. For the simple problem of estimating location, appropriate choices for the nonlinear transformation and gain constant of the algorithm lead to an asymptotically min-max robust estimator with respect to a familymathcal{F} (y_p,p)of symmetrical distributions having the same masspoutside[-y_p,y_p], 0 < p < 1. This estimator, referred to as thep-point estimator (PPE), has the additional striking property that the asymptotic variance is constant over the familymathcal{F}(Y_p,p). The PPE is also efficiency robust in large samples. Monte Carlo results indicate that small sample robustness may be obtained using both one-stage and two-stage procedures. The good small-sample results are obtained in the one-stage procedure by using an adaptive gain sequence, which is intuitively appealing as well as theoretically justifiable. Some possible extension of the SA approach are given for the problem of estimating a vector parameter. In addition, some aspects of the relationship between SA-type estimators and Huber'sM-estimators are given.     

Modeling rare turn-on events of injection lasers

An efficient numerical method based on photon statistics and rate equations is developed to simulate rare turn-on events of injection lasers. Results indicate that: (1) during the transient stage, with a probability of 10^-9, the side-mode suppression ratio can deteriorate by three orders of magnitude from its steady-state value; (2) there is a turn-on jitter for the main mode, even when the side mode is missing; and (3) the slower the risetime of the laser output the less the transient mode partitioning. The effects of gain compression and driving condition on the transient turn on are discussed     

Limits to estimation in stochastic ill-conditioned inverse problems

Using information-theoretic methods we develop simple results quantifying a lower bound for minimax estimation, a kind of infinite-dimensional Cramer-Rao lower bound, for signal estimation in possibly nonlinear, ill-conditioned, inverse problems. Our results reduce calculation to a geometric computation based on a modulus of continuity and make explicit connections with results in the literature on deterministic ill-conditioned inverse problems. Several applications are discussed     

Ergodic optimization of stochastic differential systems in wireless networks

Multidimensional Systems and Signal Processing - The present work is the second article in a couple of intertwined papers. They form complementary items on the same subject. They both address the...     

Error bounds for stochastic estimation of signal parameters

This paper is concerned with stochastic-approximation algorithms for estimating signal parameters. Emphasis will be on the performance of the algorithm for a finite number of observations as opposed to the asymptotic convergence rate. We use as an upper bound a result due to Dvoretzky. A lower bound on the average mean-square error is derived. This new bound is based on the Cramér-Rao inequality. The conventional Cramér-Rao bound is not directly applicable, because it requires the knowledge of the bias function, which is difficult to find in a recursive estimation scheme. To avoid this difficulty, we introduce the concept of most favorable bias function and use the calculus of variations to derive the lower bound. The new bound also serves as a standard to judge the merits of the stochastic-estimation algorithm, since under some general conditions no estimate can yield smaller error. It is shown that under some conditions the two bounds are nearly equal, and hence the algorithm is near optimal. The asymptotic efficiency of the algorithm is compared with Sakrison's result. A stochastic-estimation algorithm is derived for estimating Doppler frequency, and performance curves in terms of the error bounds are presented.     

Parameter estimation of biological stochastic compartmental models--an application

In this paper linear time invariant biological compartmental models are considered, in which the transfer rate constants are assumed to be stochastic variables.     

Relative location estimation in wireless sensor networks

Self-configuration in wireless sensor networks is a general class of estimation problems that we study via the Cramer-Rao bound (CRB). Specifically, we consider sensor location estimation when sensors measure received signal strength (RSS) or time-of-arrival (TOA) between themselves and neighboring sensors. A small fraction of sensors in the network have a known location, whereas the remaining locations must be estimated. We derive CRBs and maximum-likelihood estimators (MLEs) under Gaussian and log-normal models for the TOA and RSS measurements, respectively. An extensive TOA and RSS measurement campaign in an indoor office area illustrates MLE performance. Finally, relative location estimation algorithms are implemented in a wireless sensor network testbed and deployed in indoor and outdoor environments. The measurements and testbed experiments demonstrate 1-m RMS location errors using TOA, and 1- to 2-m RMS location errors using RSS.     

The estimation of signaling delay in ATM networks

In multimedia applications over ATM networks, more stringent quality of services are required, because these applications are especially sensitive to the time delay. In this letter, a simple estimation of signaling delay is presented using Erlang service models according to ITU-T “Q.2931”. Additionally, the call blocking probability of a realistic network is considered. The simulation results show that the proposed model can be an effective tool to estimate the setup delay. If the connection setup delay can be effectively estimated according to the network load, then the users may decide whether or not to join this congested network, and thus contributes to the load balance of ATM networks     

Centralized and decentralized stochastic routing models in telecommunication networks

With the advent of non-hierarchical routing in circuit-switched telecommunication networks, on-line routing policies have been developed with the objective of optimizing some measure of gain or performance. These policies are decentralized. However, traditional planning models are centralized models. We present a decentralized routing model to be used in network planning. We compare it theoretically and empirically with a centralized multicommodity flow model previously presented. The two models are solved by the same type of algorithm, a convex simplex implementation, adapted differently according to the model. Comparative results between planning models reproducing the two policies are discussed.     

On stochastic complexity estimation: a decision-theoretic approach

The concept of stochastic complexity developed by Rissanen(1989) leads to consistent probability density estimators. These density estimators are defined to achieve the best compromise between likelihood and simplicity, namely, the stochastic complexity based on the observed sample. In this paper, a density estimation-based complexity decision rule is proposed which uses the quality of these estimators to estimate the corresponding unknown element of the true probability density. In the development, we introduce a loss function which includes the total variation of the squared distance of the characteristic functions to evaluate the performance of the density decision rule. The resulting complexity density decision procedure is shown to be admissible, to achieve the minimum expected risk, and to form a minimal complete class     

Robust estimation using the Robbins-Monro stochastic approximation algorithm

The problem of minmax estimation of a location parameter introduced by Huber is considered. It is shown that under general conditions there exists a solution which is a form of the Robbins-Monro stochastic approximation algorithm. This generalizes earlier work by Martin and Masreliez who have given stochastic approximation (SA)-estimate solutions for two particular cases. As with theM-estimate solutions given by Huber, the SA solutions are completely determined by the probability distribution function with least Fisher information in the distribution set used to model the observation errors.     

Orthogonal eigensubspace estimation using neural networks

We present a neural network (NN) approach for simultaneously estimating all or some of the orthogonal eigenvectors of a symmetric nonindefinite matrix corresponding to its repeated minimum (in magnitude) eigenvalue. This problem has its origin in the constrained minimization framework and has extensive applications in signal processing. We recast this problem into the NN framework by constructing an appropriate energy function which the NN minimizes. The NN is of feedback type with the neurons having sigmoidal activation function. The proposed approach is analyzed to characterize the nature of the minimizers:of the energy function. The main result is that “the matrix W* is a minimizer of the energy function if and only if the columns of W* are the orthogonal eigenvectors with a given norm corresponding to the smallest eigenvalue of the given matrix”. Further, all minimizers are global minimizers. Bounds on the integration time-step that is required to numerically solve the system of differential equations (which define the dynamics of the NN) have also been derived. Results of computer simulations are presented to support our analysis     

Topology estimation method for telecommunication networks

In order to resolve the traditional limited lifetime problem, energy harvesting technology has been introduced into wireless sensor network (WSN) in recent years, engendering a new kind of network which is called energy harvesting wireless sensor network (EHWSN). In EHWSNs, besides the traditional issues, such as energy consumption, energy equilibrium, transmission efficiency, etc., there are still new challenges, such as how to utilize harvested energy efficiently and how to make more sensor nodes so as to achieve unlimited lifetime under actual situation. In this paper, inspired by slime mold Physarum polycephalum, a novel bionic routing protocol, abbreviated as EHPRP, is proposed for EHWSNs to address above problems without predicting harvestable energy value. Three distributed routing algorithms with low algorithm complexity are proposed which would prominently reduce the processing delay and conserve energy. Furthermore, the mathematic theoretical analysis is made to prove the stability of EHPRP routing strategy. Finally, simulation results present that, compared with other typical algorithms, EHPRP consumes less energy, always making the whole network obtain an unlimited lifetime, and displaying more uniform network energy distribution under different workload conditions.     

On rate-constrained distributed estimation in unreliable sensor networks

We study the problem of estimating a physical process at a central processing unit (CPU) based on noisy measurements collected from a distributed, bandwidth-constrained, unreliable, network of sensors, modeled as an erasure network of unreliable "bit-pipes" between each sensor and the CPU. The CPU is guaranteed to receive data from a minimum fraction of the sensors and is tasked with optimally estimating the physical process under a specified distortion criterion. We study the noncollaborative (i.e., fully distributed) sensor network regime, and derive an information-theoretic achievable rate-distortion region for this network based on distributed source-coding insights. Specializing these results to the Gaussian setting and the mean-squared-error (MSE) distortion criterion reveals interesting robust-optimality properties of the solution. We also study the regime of clusters of collaborative sensors, where we address the important question: given a communication rate constraint between the sensor clusters and the CPU, should these clusters transmit their "raw data" or some low-dimensional "local estimates"? For a broad set of distortion criteria and sensor correlation statistics, we derive conditions under which rate-distortion-optimal compression of correlated cluster-observations separates into the tasks of dimension-reducing local estimation followed by optimal distributed compression of the local estimates.     

Modelling buffer admission mechanisms using stochastic automata networks

The stochastic automata networks formalism is an attractive technique to model complex systems with interacting components. Each component of the system is modelled by a single automaton; interactions between components are modelled by labels on the arcs which may represent synchronization and state-dependent transitions. Every automaton is associated with some matrices which allow to build the transition matrix of the underlying Markov chain, using tensor algebra. To illustrate this methodology, we introduce two buffer policies which could be used inAtm switching node. Every policy manages two priority levels which have distinct cell loss requirements. The first buffer policy is based on the push-out mechanism : a high priority cell replaces a low priority cell when the buffer is full. The second policy causes the discarding of all the low priority cells when the user transmits a request to send a burst of cells. In both studies, we compute the loss probabilities of each type of cells under various assumptions.     

Power scheduling of universal decentralized estimation in sensor networks

We consider the optimal power scheduling problem for the decentralized estimation of a noise-corrupted deterministic signal in an inhomogeneous sensor network. Sensor observations are first quantized into discrete messages, then transmitted to a fusion center where a final estimate is generated. Supposing that the sensors use a universal decentralized quantization/estimation scheme and an uncoded quadrature amplitude modulated (QAM) transmission strategy, we determine the optimal quantization and transmit power levels at local sensors so as to minimize the total transmit power, while ensuring a given mean squared error (mse) performance. The proposed power scheduling scheme suggests that the sensors with bad channels or poor observation qualities should decrease their quantization resolutions or simply become inactive in order to save power. For the remaining active sensors, their optimal quantization and transmit power levels are determined jointly by individual channel path losses, local observation noise variance, and the targeted mse performance. Numerical examples show that in inhomogeneous sensing environment, significant energy savings is possible when compared to the uniform quantization strategy.     

Dynamic estimation of local mean power in GSM-R networks

The dynamic estimation algorithm for Rician fading channels in GSM-R networks is proposed, which is an expansion of local mean power estimation of Rayleigh fading channels. The proper length of statistical interval and required number of averaging samples are determined which are adaptive to different propagation environments. It takes advantage of signal samples and Rician fading parameters of last estimation to reduce measurement overhead. The performance of this method was evaluated by measurement experiments along Beijing–Shanghai high-speed railway. When it is NLOS propagation, the required sampling intervals can be increased from $1.1{\lambda}$ in Lee’s method to $3.7{\lambda}$ of the dynamic algorithm. The sampling intervals can be set up to $12{\lambda}$ although the length of statistical intervals decrease when there is LOS signal, which can reduce the measurement overhead significantly. The algorithm can be applied in coverage assessment with lower measurement overhead, and in dynamic and adaptive allocation of wireless resource.