Mostrando recursos 1 - 15 de 15

  1. On Discrete Time Markovian N-policy Queues involving Batches

    Böhm, Walter; Mohanty, Sri Gopal
    Consider two Markovian N-policy queueing models in discrete time, one with batch arrival, the other with batch service. In this paper the transient behaviour of both models is studied and the analogous continuous time results are achieved by a limiting process. The steady state solution for the model with batch arrival is derived. (author's abstract)

  2. Über die Busy Period von Er/M/1 Systemen. Ein kombinatorischer Beweis

    Böhm, Walter
    Die analytische Herleitung der Wahrscheinlichkeitsdichte der Busy Period in Warteschlangenmodellen mit exponentiellen Service- und Erlang verteilten Zwischenankunftszeiten ist mit beträchtlichem Aufwand verbunden. Eine vergleichsweise elementare Lösung wird möglich durch Anwendung von Methoden der Gitterpfadkombinatorik. (Autorenref.)

  3. A Note on M/M/1 Queues with Gamma-Distributed Vacations

    Böhm, Walter
    In this note we derive a simple formula for the density of Sn = i=1n Ti, where Ti is the duration of the i-th busy cycle in an M/M/1 queueing model with gamma distributed server vacations. Using this result we find the distribution of the queue length by standard renewal arguments. (author's abstract)

  4. On Random Walks with Barriers and their Application to Queues

    Böhm, Walter; Mohanty, Sri Gopal
    The n-step transition probabilities of a random walk with two barriers, each being either reflecting or absorbing are considered on the basis of a simple renewal argument. The relation of these walks to queueing problems is pointed out and the distributions of the queue length in the finite capacity case, the same during a busy period and of the maximum queue length are derived for discrete time models. By taking the limit the solutions of continuous time models are derived, verifying some known results. (author's abstract)

  5. A transient Analysis of M/G/1 Queues with N-policy

    Böhm, Walter
    We consider an M/G/1 queueing model with N-policy operating. This means, that the server will start up only if a queue of a prescribed length has built up. For this model the time dependent distribution of the queue lenght is given by simple renewal arguments without resorting to integral transform techniques. (author's abstract)

  6. Das Unbeobachtbare erfassen - Dynamische stochastische Modelle in den Umweltwissenschaften

    Frühwirth-Schnatter, Sylvia
    Ziel dieses Beitrags ist es, an hand ausgewählter Aufgabenstellungen auf Aussagemöglichkeiten hinzuweisen, die sich durch Anwendung dynamischer stochastischer Modelle (ZustandsraummodeIle) ergeben. In Abschnitt 2 wird nach einem kurzen Überblick über die dynarnische stochastische Modellierung an den beiden Aufgabenstellungen illustriert, wie zu einer gegebenen Zeitreihe ein dynamisches stochastisches Model1 tatsächlich formuliert werden kann. In Abschnitt 3 werden mögliche statistische Aussagen über unbeobachtbare Größen und zukünftige Prozeßverläufe diskutiert und an den beiden Modellen erläutert. Abschnitt 4 schließlich enthält zwei Fallstudien zu den beiden Aufgabenstellungen. (Autorenref.)

  7. Monitoring von ökologischen und biometrischen Prozessen mit statistischen Filtern

    Frühwirth-Schnatter, Sylvia
    Diese Arbeit ist ein Überblick über die Ideen und Methoden der dynamischen stochastischen Modellierung von normalverteilten und nicht-normalverteilten Prozessen. Nach einer Einführung der allgemeinen Modellform werden Aussagemöglichkeiten wie Filtern, Glätten und Vorhersagen diskutiert und das Problem der Identifikation unbekannter Hyperparameter behandelt. Die allgemeinen Ausführungen werden an zwei Fallstudien, einer Zeitreihe des mittleren jährlichen Grundwasserspiegels und einer Zeitreihe von Tagesmittelwerten von SO2-Emissionen illustriert. (Autorenref.)

  8. Optimal and Practicable Designs for Measuring Plaque pH-Profiles

    Fedorov, Valery V.; Hackl, Peter; Müller, Werner
    In this paper we will show that the theory of optimal experimental design leads to quite different patterns of measurement. These patterns take into account (a) the structure of the ongoing process and (b) what parameters or characteristics are object of inference. We will demonstrate that the use of optimal designs or of designs that are close to optimal ones allows to reduce the sample size without decreasing the accuracy of the results. In Section 2 we present a model that is suitable to describe the pH-profile and we give some justification on an empirical basis. Section 3 discusses optimal...

  9. A Combination of Nonparametric Tests for Trend in Location

    Hatzinger, Reinhold; Katzenbeisser, Walter
    A combination of some well known nonparametric tests to detect trend in location is considered. Simulation results show that the power of this combination is remarkably increased. (author's abstract)

  10. CUSUM Chart for Correlated Control Variables

    Böhm, Walter; Hackl, Peter
    The cumulative sum (CUSUM) technique is well-established in theory and practice of process control. A comprehensive exposition of the method is given, e.g., by Wetherill and Brown (1991). A question that is seldom treated in the literature is that on the effect of serial correlation of the control variable. Johnson and Bagshaw (1974) investigate the effect of correlation on the run length distribution when the control variable follows a first order autoregressive or moving average process. They also give an approximate expression for the average run length of the CUSUM- technique for correlated control variables. In this paper we derive...

  11. Quasi-Likelihood Methoden zur Analyse von unabhängigen und abhängigen Beobachtungen

    Hatzinger, Reinhold
    Ausgehend vom klassischen linearen Modell werden Regressionsmethoden für Datenstrukturen dargestellt, bei denen die Standardannahmen (Unabhängigkeit, normalverteilte Fehler und konstante Varianz) nicht erfüllt sind. Läßt man die Responsevariable aus einer Exponentialfamilie zu, so erhält man die Klasse generalisierter linearer Modelle (GLM) . Dies erlaubt, den Erwartungswert von verschiedensten stetigen und diskreten Responsevariablen (z .B. Anteile, Häufigkeiten, etc.) über eine fixe Kovariatenstruktur zu modellieren. Hebt man zusatzlich die Notwendigkeit auf, eine Verteilung aus Exponentialfamilien spezifizieren zu müssen, erhält man Quasi-Likelihood Modelle, bei denen nur mehr eine Beziehung zwischen Erwartungswert und Varianz festgelegt werden muß. Die Berücksichtigung einer Korrelationsstruktur führt zu verallgemeinerten Schätzgleichungen,...

  12. On the Fisher Information of Discretized Data

    Pötzelberger, Klaus; Felsenstein, Klaus
    In this paper we study the loss of Fisher information in approximating a continous distribution by a multinominal distribution coming from a partition of the sample space into a finite number of intervals. We describe and characterize the Fisher information as a function of the partition chosen especially for location parameters. For a small number of intervals the consequences of the choice is demonstrated by instructive examples. For increasing number of individuals we give the asymptotically optimal partition. (author's abstract)

  13. An asymptotic Result on Principal Points for univariate Distributions

    Pötzelberger, Klaus; Felsenstein, Klaus
    In various situations it is desirable to fit a set of points to a continuous variable giving rise to groups. In 'cluster analysis' such points are referred to as 'cluster means'. See Cox(1957) and Hartigan(1978) for details. Following the terminology used by Flury(1990) we study so called principal points for univariate distributions. (author's abstract)

  14. On the Approximation of finite Markov-exchangeable processes by mixtures of Markov Processes

    Pötzelberger, Klaus
    We give an upper bound for the norm distance of (0,1) -valued Markov-exchangeable random variables to mixtures of distributions of Markov processes. A Markov-exchangeable random variable has a distribution that depends only on the starting value and the number of transitions 0-0, 0-1, 1-0 and 1-1. We show that if, for increasing length of variables, the norm distance to mixtures of Markov processes goes to 0, the rate of this convergence may be arbitrarily slow. (author's abstract)

  15. Integration-based Kalman-filtering for a Dynamic Generalized Linear Trend Model

    Schnatter, Sylvia
    The topic of the paper is filtering for non-Gaussian dynamic (state space) models by approximate computation of posterior moments using numerical integration. A Gauss-Hermite procedure is implemented based on the approximate posterior mode estimator and curvature recently proposed in 121. This integration-based filtering method will be illustrated by a dynamic trend model for non-Gaussian time series. Comparision of the proposed method with other approximations ([15], [2]) is carried out by simulation experiments for time series from Poisson, exponential and Gamma distributions. (author's abstract)

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