A Markov Chain based method for generating long-range dependence

This paper describes a model for generating time series which exhibit the statistical phenomenon known as long-range dependence (LRD). A Markov Modulated Process based upon an infinite Markov chain is described. The work described is motivated by applications in telecommunications where LRD is a known property of time-series measured on the internet. The process can generate a time series exhibiting LRD with known parameters and is particularly suitable for modelling internet traffic since the time series is in terms of ones and zeros which can be interpreted as data packets and inter-packet gaps. The method is extremely simple computationally and analytically and could prove more tractable than other methods described in the literatureComment: 8 pages, 2 figure

Localization in mobile wireless and sensor networks

[No abstract available

COMPOUND-POISSON SOFTWARE-RELIABILITY MODEL

The probability density estimation of the number of software failures in the event of clustering or clumping of the software failures is the subject of this paper. A discrete compound Poisson (CP) prediction model, as opposed to a Poisson (P) process, is proposed for the random variable (rv) X(rem), which is the remaining number of software failures. The compounding distributions, which are assumed to govern the failure sizes at Poisson arrivals, are respectively taken to be geometric when failures are forgetful and logarithmic-series (LSD) when failures are contagious. The expected value (mu) of X(rem) of CP is calculated as a function of the time-dependent Poisson and compounding distribution based on the failures experienced. Also, the q (variance/mean) parameter for the remaining number of failures, q(rem) is best estimated by q(past) from the failures already experienced. Then, one obtains the pdf of the remaining number of failures estimated by CP(mu,q). The CP model suggests that the CP is superior to Poisson where clumping of failures exists. Its predictive validity is comparable to Musa-Okumoto's (MO) Log-Poisson Model for certain software failure data with q > 1 when software failures clump within the same CPU second or unit time

A STOPPING RULE FOR A COMPOUND POISSON RANDOM VARIABLE

An optimal empirical Bayesian stopping rule for the Poisson compounded with the geometric distribution is developed and applied to the problem of the sequential testing of computer software. For each checkpoint in time, either the software satisfies a desired economic criterion, or else the software testing is continued