Weibull and generalised exponential overdispersion models with an application to ozone air pollution

We consider the problem of estimating the mean and variance of the time between occurrences of an event of interest (inter-occurrences times) where some forms of dependence between two consecutive time intervals are allowed. Two basic density functions are taken into account. They are the Weibull and the generalised exponential density functions. In order to capture the dependence between two consecutive inter-occurrences times, we assume that either the shape and/or the scale parameters of the two density functions are given by auto-regressive models. The expressions for the mean and variance of the inter-occurrences times are presented. The models are applied to the ozone data from two regions of Mexico City. The estimation of the parameters is performed using a Bayesian point of view via Markov chain Monte Carlo (MCMC) methods.

Temperature and power-density-dependent inter-shell energy states in InAs/GaAs quantum dots

We have investigated the evolution of exciton state filling in InAs/GaAs quantum dot (QD) structures as a function of the excitation power density by using rnicro-photoluminescence spectroscopy at different temperatures. In addition to the emission bands of exciton recombination corresponding to the atom-like S, P and D, etc. shells of QDs, it was observed that some extra states V between the S and P shells, and D' between the P and D shells appear in the spectra with increasing number of excitons occupying the QDs at a certain temperature. The emergence of these inter-shell excitonic levels is power density and temperature dependent, which is an experimental demonstration of strong exciton-exciton exchange interaction, state hybridization, and coupling of a multi-exciton system in QDs. (c) 2006 Elsevier B.V. All rights reserved.

Temperature and power-density-dependent inter-shell energy states in InAs/GaAs quantum dots

We have investigated the evolution of exciton state filling in InAs/GaAs quantum dot (QD) structures as a function of the excitation power density by using rnicro-photoluminescence spectroscopy at different temperatures. In addition to the emission bands of exciton recombination corresponding to the atom-like S, P and D, etc. shells of QDs, it was observed that some extra states V between the S and P shells, and D' between the P and D shells appear in the spectra with increasing number of excitons occupying the QDs at a certain temperature. The emergence of these inter-shell excitonic levels is power density and temperature dependent, which is an experimental demonstration of strong exciton-exciton exchange interaction, state hybridization, and coupling of a multi-exciton system in QDs. (c) 2006 Elsevier B.V. All rights reserved.

Scheduler-dependent inter-cell interference and its impact on LTE uplink performance at flow level

The Long Term Evolution (LTE) cellular technology is expected to extend the capacity and improve the performance of current 3G cellular networks. Among the key mechanisms in LTE responsible for traffic management is the packet scheduler, which handles the allocation of resources to active flows in both the frequency and time dimension. This paper investigates for various scheduling scheme how they affect the inter-cell interference characteristics and how the interference in turn affects the user’s performance. A special focus in the analysis is on the impact of flow-level dynamics resulting from the random user behaviour. For this we use a hybrid analytical/simulation approach which enables fast evaluation of flow-level performance measures. Most interestingly, our findings show that the scheduling policy significantly affects the inter-cell interference pattern but that the scheduler specific pattern has little impact on the flow-level performance.

Explicit ruin formulas for models with dependence among risks

We show that a simple mixing idea allows one to establish a number of explicit formulas for ruin probabilities and related quantities in collective risk models with dependence among claim sizes and among claim inter-occurrence times. Examples include compound Poisson risk models with completely monotone marginal claim size distributions that are dependent according to Archimedean survival copulas as well as renewal risk models with dependent inter-occurrence times.

Using honeypots to analyse anomalous Internet activities

Monitoring Internet traffic is critical in order to acquire a good understanding of threats to computer and network security and in designing efficient computer security systems. Researchers and network administrators have applied several approaches to monitoring traffic for malicious content. These techniques include monitoring network components, aggregating IDS alerts, and monitoring unused IP address spaces. Another method for monitoring and analyzing malicious traffic, which has been widely tried and accepted, is the use of honeypots. Honeypots are very valuable security resources for gathering artefacts associated with a variety of Internet attack activities. As honeypots run no production services, any contact with them is considered potentially malicious or suspicious by definition. This unique characteristic of the honeypot reduces the amount of collected traffic and makes it a more valuable source of information than other existing techniques. Currently, there is insufficient research in the honeypot data analysis field. To date, most of the work on honeypots has been devoted to the design of new honeypots or optimizing the current ones. Approaches for analyzing data collected from honeypots, especially low-interaction honeypots, are presently immature, while analysis techniques are manual and focus mainly on identifying existing attacks. This research addresses the need for developing more advanced techniques for analyzing Internet traffic data collected from low-interaction honeypots. We believe that characterizing honeypot traffic will improve the security of networks and, if the honeypot data is handled in time, give early signs of new vulnerabilities or breakouts of new automated malicious codes, such as worms. The outcomes of this research include: • Identification of repeated use of attack tools and attack processes through grouping activities that exhibit similar packet inter-arrival time distributions using the cliquing algorithm; • Application of principal component analysis to detect the structure of attackers’ activities present in low-interaction honeypots and to visualize attackers’ behaviors; • Detection of new attacks in low-interaction honeypot traffic through the use of the principal component’s residual space and the square prediction error statistic; • Real-time detection of new attacks using recursive principal component analysis; • A proof of concept implementation for honeypot traffic analysis and real time monitoring.

Reliable estimation via simulation

Let a and s denote the inter arrival times and service times in a GI/GI/1 queue. Let a (n), s (n) be the r.v.s, with distributions as the estimated distributions of a and s from iid samples of a and s of sizes n. Let w be a r.v. with the stationary distribution lr of the waiting times of the queue with input (a, s). We consider the problem of estimating E [w~], tx > 0 and 7r via simulations when (a (n), s (n)) are used as input. Conditions for the accuracy of the asymptotic estimate, continuity of the asymptotic variance and uniformity in the rate of convergence to the estimate are obtained. We also obtain rates of convergence for sample moments, the empirical process and the quantile process for the regenerative processes. Robust estimates are also obtained when an outlier contaminated sample of a and s is provided. In the process we obtain consistency, continuity and asymptotic normality of M-estimators for stationary sequences. Some robustness results for Markov processes are included.

Bayesian Analysis of a Superimposed Renewal Process

Stochastic behavior of an aero-engine failure/repair process has been analyzed from a Bayesian perspective. Number of failures/repairs in the component-sockets of this multi-component system are assumed to follow independent renewal processes with Weibull inter-arrival times. Based on the field failure/repair data of a large number of such engines and independent Gamma priors on the scale parameters and log-concave priors on the shape parameters, an exact method of sampling from the resulting posterior distributions of the parameters has been proposed. These generated parameter values are next utilised in obtaining the posteriors of the expected number of system repairs, system failure rate, and the conditional intensity function, which are computed using a recursive formula.

Optimal control of arrivals to queues with delayed queue length information

We consider discrete-time versions of two classical problems in the optimal control of admission to a queueing system: i) optimal routing of arrivals to two parallel queues and ii) optimal acceptance/rejection of arrivals to a single queue. We extend the formulation of these problems to permit a k step delay in the observation of the queue lengths by the controller. For geometric inter-arrival times and geometric service times the problems are formulated as controlled Markov chains with expected total discounted cost as the minimization objective. For problem i) we show that when k = 1, the optimal policy is to allocate an arrival to the queue with the smaller expected queue length (JSEQ: Join the Shortest Expected Queue). We also show that for this problem, for k greater than or equal to 2, JSEQ is not optimal. For problem ii) we show that when k = 1, the optimal policy is a threshold policy. There are, however, two thresholds m(0) greater than or equal to m(1) > 0, such that mo is used when the previous action was to reject, and mi is used when the previous action was to accept.

DNA Assisted Self-Assembly of PAMAM Dendrimers

We report DNA assisted self-assembly of polyamidoamine (PAMAM) dendrimers using all atom Molecular Dynamics (MD) simulations and present a molecular level picture of a DNA-linked PAMAM dendrimer nanocluster, which was first experimentally reported by Choi et al. (Nano Lett., 2004, 4, 391-397). We have used single stranded DNA (ssDNA) to direct the self-assembly process. To explore the effect of pH on this mechanism, we have used both the protonated (low pH) and nonprotonated (high pH) dendrimers. In all cases studied here, we observe that the DNA strand on one dendrimer unit drives self-assembly as it binds to the complementary DNA strand present on the other dendrimer unit, leading to the formation of a DNA-linked dendrimer dimeric complex. However, this binding process strongly depends on the charge of the dendrimer and length of the ssDNA. We observe that the complex with a nonprotonated dendrimer can maintain a DNA length dependent inter-dendrimer distance. In contrast, for complexes with a protonated dendrimer, the inter-dendrimer distance is independent of the DNA length. We attribute this observation to the electrostatic complexation of a negatively charged DNA strand with the positively charged protonated dendrimer.

How does TCP generate Pseudo-self-similarity?

Long-range dependence has been observed in many recent Internet traffic measurements. In addition, some recent studies have shown that under certain network conditions, TCP itself can produce traffic that exhibits dependence over limited timescales, even in the absence of higher-level variability. In this paper, we use a simple Markovian model to argue that when the loss rate is relatively high, TCP's adaptive congestion control mechanism indeed generates traffic with OFF periods exhibiting power-law shape over several timescales and thus introduces pseudo-long-range dependence into the overall traffic. Moreover, we observe that more variable initial retransmission timeout values for different packets introduces more variable packet inter-arrival times, which increases the burstiness of the overall traffic. We can thus explain why a single TCP connection can produce a time-series that can be misidentified as self-similar using standard tests.

Analysis of Some Stochastic Inventory Models with Pooling Retrial of Customers

The thesis deals with analysis of some Stochastic Inventory Models with Pooling/Retrial of Customers.. In the first model we analyze an (s,S) production Inventory system with retrial of customers. Arrival of customers from outside the system form a Poisson process. The inter production times are exponentially distributed with parameter µ. When inventory level reaches zero further arriving demands are sent to the orbit which has capacity M(<∞). Customers, who find the orbit full and inventory level at zero are lost to the system. Demands arising from the orbital customers are exponentially distributed with parameter γ. In the model-II we extend these results to perishable inventory system assuming that the life-time of each item follows exponential with parameter θ. The study deals with an (s,S) production inventory with service times and retrial of unsatisfied customers. Primary demands occur according to a Markovian Arrival Process(MAP). Consider an (s,S)-retrial inventory with service time in which primary demands occur according to a Batch Markovian Arrival Process (BMAP). The inventory is controlled by the (s,S) policy and (s,S) inventory system with service time. Primary demands occur according to Poissson process with parameter λ. The study concentrates two models. In the first model we analyze an (s,S) Inventory system with postponed demands where arrivals of demands form a Poisson process. In the second model, we extend our results to perishable inventory system assuming that the life-time of each item follows exponential distribution with parameter θ. Also it is assumed that when inventory level is zero the arriving demands choose to enter the pool with probability β and with complementary probability (1- β) it is lost for ever. Finally it analyze an (s,S) production inventory system with switching time. A lot of work is reported under the assumption that the switching time is negligible but this is not the case for several real life situation.

Analysis of Some Single and Two Commodity Inventory Problems

This thesis is devoted to the study of some stochastic models in inventories. An inventory system is a facility at which items of materials are stocked. In order to promote smooth and efficient running of business, and to provide adequate service to the customers, an inventory materials is essential for any enterprise. When uncertainty is present, inventories are used as a protection against risk of stock out. It is advantageous to procure the item before it is needed at a lower marginal cost. Again, by bulk purchasing, the advantage of price discounts can be availed. All these contribute to the formation of inventory. Maintaining inventories is a major expenditure for any organization. For each inventory, the fundamental question is how much new stock should be ordered and when should the orders are replaced. In the present study, considered several models for single and two commodity stochastic inventory problems. The thesis discusses two models. In the first model, examined the case in which the time elapsed between two consecutive demand points are independent and identically distributed with common distribution function F(.) with mean  (assumed finite) and in which demand magnitude depends only on the time elapsed since the previous demand epoch. The time between disasters has an exponential distribution with parameter . In Model II, the inter arrival time of disasters have general distribution (F.) with mean  ( ) and the quantity destructed depends on the time elapsed between disasters. Demands form compound poison processes with inter arrival times of demands having mean 1/. It deals with linearly correlated bulk demand two Commodity inventory problem, where each arrival demands a random number of items of each commodity C1 and C2, the maximum quantity demanded being a (< S1) and b(

Métodos de solução para um problema de sequenciamento da produção com sincronismo de execução de tarefas

Pós-graduação em Engenharia Mecânica - FEG

Statistical problems related to excitation threshold and reset value of membrane potentials

Die vorliegende Arbeit ist motiviert durch biologische Fragestellungen bezüglich des Verhaltens von Membranpotentialen in Neuronen. Ein vielfach betrachtetes Modell für spikende Neuronen ist das Folgende. Zwischen den Spikes verhält sich das Membranpotential wie ein Diffusionsprozess X der durch die SDGL dX_t= beta(X_t) dt+ sigma(X_t) dB_t gegeben ist, wobei (B_t) eine Standard-Brown'sche Bewegung bezeichnet. Spikes erklärt man wie folgt. Sobald das Potential X eine gewisse Exzitationsschwelle S überschreitet entsteht ein Spike. Danach wird das Potential wieder auf einen bestimmten Wert x_0 zurückgesetzt. In Anwendungen ist es manchmal möglich, einen Diffusionsprozess X zwischen den Spikes zu beobachten und die Koeffizienten der SDGL beta() und sigma() zu schätzen. Dennoch ist es nötig, die Schwellen x_0 und S zu bestimmen um das Modell festzulegen. Eine Möglichkeit, dieses Problem anzugehen, ist x_0 und S als Parameter eines statistischen Modells aufzufassen und diese zu schätzen. In der vorliegenden Arbeit werden vier verschiedene Fälle diskutiert, in denen wir jeweils annehmen, dass das Membranpotential X zwischen den Spikes eine Brown'sche Bewegung mit Drift, eine geometrische Brown'sche Bewegung, ein Ornstein-Uhlenbeck Prozess oder ein Cox-Ingersoll-Ross Prozess ist. Darüber hinaus beobachten wir die Zeiten zwischen aufeinander folgenden Spikes, die wir als iid Treffzeiten der Schwelle S von X gestartet in x_0 auffassen. Die ersten beiden Fälle ähneln sich sehr und man kann jeweils den Maximum-Likelihood-Schätzer explizit angeben. Darüber hinaus wird, unter Verwendung der LAN-Theorie, die Optimalität dieser Schätzer gezeigt. In den Fällen OU- und CIR-Prozess wählen wir eine Minimum-Distanz-Methode, die auf dem Vergleich von empirischer und wahrer Laplace-Transformation bezüglich einer Hilbertraumnorm beruht. Wir werden beweisen, dass alle Schätzer stark konsistent und asymptotisch normalverteilt sind. Im letzten Kapitel werden wir die Effizienz der Minimum-Distanz-Schätzer anhand simulierter Daten überprüfen. Ferner, werden Anwendungen auf reale Datensätze und deren Resultate ausführlich diskutiert.