Characterizing Coxian Distributions of Algebraic Degree q and Triangular Order p

In this research note we present a procedure to characterize the set of all Coxian distributions of algebraic degree q that have Coxian representations of order p where p > q

Nested Fork-Join Queuing Networks and Their Application to Mobility Airfield Operations Analysis

A single-chain nested fork-join queuing network (FJQN) model of mobility airfield ground processing is proposed. In order to analyze the queuing network model, advances on two fronts are made. First, a general technique for decomposing nested FJQNs with probabilistic forks is proposed, which consists of incorporating feedback loops into the embedded Markov chain of the synchronization station, then using Marie\u27s Method to decompose the network. Numerical studies show this strategy to be effective, with less than two percent relative error in the approximate performance measures in most realistic cases. The second contribution is the identification of a quick, efficient method for solving for the stationary probabilities of the λn/Ck/r/N queue. Unpreconditioned Conjugate Gradient Squared is shown to be the method of choice in the context of decomposition using Marie\u27s Method, thus broadening the class of networks where the method is of practical use. The mobility airfield model is analyzed using the strategies described above, and accurate approximations of airfield performance measures are obtained in a fraction of the time needed for a simulation study. The proposed airfield modeling approach is especially effective for quick-look studies and sensitivity analysis

Aggregate matrix-analytic techniques and their applications

The complexity of computer systems affects the complexity of modeling techniques that can be used for their performance analysis. In this dissertation, we develop a set of techniques that are based on tractable analytic models and enable efficient performance analysis of computer systems. Our approach is three pronged: first, we propose new techniques to parameterize measurement data with Markovian-based stochastic processes that can be further used as input into queueing systems; second, we propose new methods to efficiently solve complex queueing models; and third, we use the proposed methods to evaluate the performance of clustered Web servers and propose new load balancing policies based on this analysis.;We devise two new techniques for fitting measurement data that exhibit high variability into Phase-type (PH) distributions. These techniques apply known fitting algorithms in a divide-and-conquer fashion. We evaluate the accuracy of our methods from both the statistics and the queueing systems perspective. In addition, we propose a new methodology for fitting measurement data that exhibit long-range dependence into Markovian Arrival Processes (MAPs).;We propose a new methodology, ETAQA, for the exact solution of M/G/1-type processes, (GI/M/1-type processes, and their intersection, i.e., quasi birth-death (QBD) processes. ETAQA computes an aggregate steady state probability distribution and a set of measures of interest. E TAQA is numerically stable and computationally superior to alternative solution methods. Apart from ETAQA, we propose a new methodology for the exact solution of a class of GI/G/1-type processes based on aggregation/decomposition.;Finally, we demonstrate the applicability of the proposed techniques by evaluating load balancing policies in clustered Web servers. We address the high variability in the service process of Web servers by dedicating the servers of a cluster to requests of similar sizes and propose new, content-aware load balancing policies. Detailed analysis shows that the proposed policies achieve high user-perceived performance and, by continuously adapting their scheduling parameters to the current workload characteristics, provide good performance under conditions of transient overload

Exit Problems for Lévy and Markov Processes with One-Sided Jumps and Related Topics

Exit problems for one-dimensional Lévy processes are easier when jumps only occur in one direction. In the last few years, this intuition became more precise: we know now that a wide variety of identities for exit problems of spectrally-negative Lévy processes may be ergonomically expressed in terms of two q-harmonic functions (or scale functions or positive martingales) W and Z. The proofs typically require not much more than the strong Markov property, which hold, in principle, for the wider class of spectrally-negative strong Markov processes. This has been established already in particular cases, such as random walks, Markov additive processes, Lévy processes with omega-state-dependent killing, and certain Lévy processes with state dependent drift, and seems to be true for general strong Markov processes, subject to technical conditions. However, computing the functions W and Z is still an open problem outside the Lévy and diffusion classes, even for the simplest risk models with state-dependent parameters (say, Ornstein–Uhlenbeck or Feller branching diffusion with phase-type jumps)

Untangling hotel industry’s inefficiency: An SFA approach applied to a renowned Portuguese hotel chain

The present paper explores the technical efficiency of four hotels from Teixeira Duarte Group - a renowned Portuguese hotel chain. An efficiency ranking is established from these four hotel units located in Portugal using Stochastic Frontier Analysis. This methodology allows to discriminate between measurement error and systematic inefficiencies in the estimation process enabling to investigate the main inefficiency causes. Several suggestions concerning efficiency improvement are undertaken for each hotel studied.info:eu-repo/semantics/publishedVersio

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

Performance of Computer Systems; Proceedings of the 4th International Symposium on Modelling and Performance Evaluation of Computer Systems, Vienna, Austria, February 6-8, 1979

These proceedings are a collection of contributions to computer system performance, selected by the usual refereeing process from papers submitted to the symposium, as well as a few invited papers representing significant novel contributions made during the last year. They represent the thrust and vitality of the subject as well as its capacity to identify important basic problems and major application areas. The main methodological problems appear in the underlying queueing theoretic aspects, in the deterministic analysis of waiting time phenomena, in workload characterization and representation, in the algorithmic aspects of model processing, and in the analysis of measurement data. Major areas for applications are computer architectures, data bases, computer networks, and capacity planning. The international importance of the area of computer system performance was well reflected at the symposium by participants from 19 countries. The mixture of participants was also evident in the institutions which they represented: 35% from universities, 25% from governmental research organizations, but also 30% from industry and 10% from non-research government bodies. This proves that the area is reaching a stage of maturity where it can contribute directly to progress in practical problems