Deployment Policies to Reliably Maintain and Maximize Expected Coverage in a Wireless Sensor Network

The long-term operation of a wireless sensor network (WSN) requires the deployment of new sensors over time to restore any loss in network coverage and communication ability resulting from sensor failures. Over the course of several deployment actions it is important to consider the cost of maintaining the WSN in addition to any desired performance measures such as coverage, connectivity, or reliability. The resulting problem formulation is approached first through a time-based deployment model in which the network is restored to a fixed size at periodic time intervals. The network destruction spectrum (D-spectrum) has been introduced to estimate reliability and is more commonly applied to a static network, rather than a dynamic network where new sensors are deployed over time. We discuss how the D-spectrum can be incorporated to estimate reliability of a time-based deployment policy and the features that allow a wide range of deployment policies to be evaluated in an efficient manner. We next focus on a myopic condition-based deployment model where the network is observed at periodic time intervals and a fixed budget is available to deploy new sensors with each observation. With a limited budget available the model must address the complexity present in a dynamic network size in addition to a dynamic network topology, and the dependence of network reliability on the deployment action. We discuss how the D-spectrum can be applied to the myopic condition-based deployment problem, illustrating the value of the D-spectrum in a variety of maintenance settings beyond the traditional static network reliability problem. From the insight of the time-based and myopic condition-based deployment models, we present a Markov decision process (MDP) model for the condition-based deployment problem that captures the benefit of an action beyond the current time period. Methodology related to approximate dynamic programming (ADP) and approximate value iteration algorithms is presented to search for high quality deployment policies. In addition to the time-based and myopic condition-based deployment models, the MDP model is one of the few addressing the repeated deployment of new sensors as well as an emphasis on network reliability. For each model we discuss the relevant problem formulation, methodology to estimate network reliability, and demonstrate the performance in a range of test instances, comparing to alternative policies or models as appropriate. We conclude with a stochastic optimization model focused on a slightly different objective to maximize expected coverage with uncertainty in where a sensor lands in the network. We discuss a heuristic solution method that seeks to determine an optimal deployment of sensors, present results for a wide range of network sizes and explore the impact of sensor failures on both the model formulation and resulting deployment policy

Inference in Additively Separable Models With a High-Dimensional Set of Conditioning Variables

This paper studies nonparametric series estimation and inference for the effect of a single variable of interest x on an outcome y in the presence of potentially high-dimensional conditioning variables z. The context is an additively separable model E[y|x, z] = g0(x) + h0(z). The model is high-dimensional in the sense that the series of approximating functions for h0(z) can have more terms than the sample size, thereby allowing z to have potentially very many measured characteristics. The model is required to be approximately sparse: h0(z) can be approximated using only a small subset of series terms whose identities are unknown. This paper proposes an estimation and inference method for g0(x) called Post-Nonparametric Double Selection which is a generalization of Post-Double Selection. Standard rates of convergence and asymptotic normality for the estimator are shown to hold uniformly over a large class of sparse data generating processes. A simulation study illustrates finite sample estimation properties of the proposed estimator and coverage properties of the corresponding confidence intervals. Finally, an empirical application to college admissions policy demonstrates the practical implementation of the proposed method

Performance of sequential batching-based methods of output data analysis in distributed steady-state stochastic simulation

Wir haben die Anpassung von Sequentiellen Analysemethoden von Stochastik Simulationen an einem Szenario von mehreren Unabhängigen Replikationen in Parallel (MRIP) untersucht. Die Hauptidee ist, die statistische Kontrole bzw. die Beschleunigung eines Simulationexperiment zu automatisieren. Die vorgeschlagenen Methoden der Literatur sind auf einzelne Prozessorszenarien orientiert. Wenig ist bekannt hinsichtlich der Anwendungen von Verfahen, die auf Methoden unter MRIP basieren. Auf den ersten Blick sind beide Ziele entgegengesetzt, denn man braucht eine grosse Menge von Beobachtungen, um eine hohe Qualität der Resultate zu erreichen. Dafür benötig man viel Zeit. Man kann jedoch durch einen ausfürlichen Entwurf zusammen mit einem robusten Werkzeug, das auf unabhängige Replikationen basiert ist, ein effizientes Mittel bezüglich Analyse der Resultate produzieren. Diese Recherche wurde mit einer sequentiellen Version des klassischen Verfahren von Nonoverlaping Batch Means (NOBM) angefangen. Obwohl NOBM sehr intuitiv und populär ist, bietet es keine gute Lösung für das Problem starker Autokorrelation zwischen den Beobachtungen an, die normalerweise bei hohen Auslastungen entstehen. Es lohnt sich nicht, grösserer Rechnerleistung zu benutzen, um diese negative Merkmale zu vermindern. Das haben wir mittles einer vollständigen Untersuchung einer Gruppe von Warteschlangsystemen bestätig. Deswegen haben wir den Entwurf von sequentiellen Versionen von ein paar Varianten von Batch Means vorgeschlagen und sie genauso untersucht. Unter den implementierten Verfahren gibt es ein sehr attraktives: Overlapping Batch Means (OBM). OBM ermöglicht eine bessere Nutzung der Daten, da jede Beobachtungen ein neues Batch anfängt, d.h., die Anzahl von Batches ist viel grösser, und das ergibt eine kleinere Varianz. In diesem Fall ist die Anwendung von MRIP empfehlenswert, da diese Kombination weniger Beobachtungen benötigt und somit eine höhere Beschleunigung. Im Laufe der Recherche haben wir eine Klasse von Methoden (Standardized Time Series - STS) untersucht, die teoretisch bessere asymptotische Resultate als NOBM produziert. Die negative Auswirkung von STS ist, dass sie mehr Beobachtungen als die Batch-Means-Verfahren benoetigt. Aber das ist kein Hindernis, wenn wir STS zusammen mit MRIP anwenden. Die experimentelle Untersuchungen bestätigte, dass die Hypothese richtig ist. Die nächste Phase war es, OBM und STS einzustellen, um beide Verfahren unter den grösstmöglichen Anzahl von Prozessoren arbeiten lassen zu können. Fallstudien zeigten uns, dass sich beide sequentiellen Verfahren für die parallele Simulation sowie MRIP einigen.We investigated the feasibility of sequential methods of analysis of stochastic simulation under an environment of Multiple Replications in Parallel (MRIP). The main idea is twofold, the automation of the statistical control and speedup of simulation experiments. The methods of analysis found suggested in the literature were conceived for a single processor environment. Very few is known concerning the application of procedures based in such methods under MRIP. At first glance, sind both goals in opposition, since one needs a large amount of observations in order to achieve good quality of the results, i.e., the simulation takes frequently long time. However, by means of a careful design, together with a robust simulation tool based on independent replications, one can produce an efficient instrument of analysis of the simulation results. This research began with a sequential version of the classical method of Nonoverlapping Batch Means (NOBM). Although intuitiv and popular, under hight traffic intensity NOBM offers no good solution to the problem of strong correlation among the observations. It is not worthwhile to apply more computing power aiming to diminish this negative effect. We have confirmed this claim by means of a detailed and exhaustive analysis of four queuing systems. Therefore, we proposed the design of sequential versions of some Batch Means variants, and we investigated their statistical properties under MRIP. Among the implemented procedures there is one very attractive : Overlapping Batch Means (OBM). OBM makes a better use of collected data, since each observation initiates a new (overlapped) batch, that is, die number of batches is much larger, and this yields smaller variance. In this case, MRIP is highly recommended, since this combination requires less observations and, therefore, speedup. During the research, we investigated also a class of methods based on Standardized Time Series -- STS, that produces theoretically better asymptotical results than NOBM. The undesired negative effect of STS is the large number of observations it requires, when compared to NOBM. But that is no obstacle when we apply STS together with MRIP. The experimental investigation confirmed this hypothesis. The next phase was to tun OBM and STS, in order to put them working with the possible largest number of processors. A case study showed us that both procedures are suitable to the environment of MRIP

A Fast Algorithm for Robust Regression with Penalised Trimmed Squares

The presence of groups containing high leverage outliers makes linear regression a difficult problem due to the masking effect. The available high breakdown estimators based on Least Trimmed Squares often do not succeed in detecting masked high leverage outliers in finite samples. An alternative to the LTS estimator, called Penalised Trimmed Squares (PTS) estimator, was introduced by the authors in \cite{ZiouAv:05,ZiAvPi:07} and it appears to be less sensitive to the masking problem. This estimator is defined by a Quadratic Mixed Integer Programming (QMIP) problem, where in the objective function a penalty cost for each observation is included which serves as an upper bound on the residual error for any feasible regression line. Since the PTS does not require presetting the number of outliers to delete from the data set, it has better efficiency with respect to other estimators. However, due to the high computational complexity of the resulting QMIP problem, exact solutions for moderately large regression problems is infeasible. In this paper we further establish the theoretical properties of the PTS estimator, such as high breakdown and efficiency, and propose an approximate algorithm called Fast-PTS to compute the PTS estimator for large data sets efficiently. Extensive computational experiments on sets of benchmark instances with varying degrees of outlier contamination, indicate that the proposed algorithm performs well in identifying groups of high leverage outliers in reasonable computational time.Comment: 27 page