Tests for exponentiality against NBUE alternatives: a Monte Carlo comparison

Testing of various classes of life distributions has been addressed in the literature for more than 45 years. In this paper, we consider the problem of testing exponentiality (which essentially implies no ageing) against positive ageing which is captured by the fairly large class of new better than used in expectation (NBUE) distributions. These tests of exponentiality against NBUE alternatives are discussed and compared. The empirical size of the tests is obtained by simulations. Power comparisons for different popular alternatives are done using Monte Carlo simulations. These comparisons are made for both small and large sample sizes. The paper concludes with a discussion in which suggestions are made regarding the choices of the test when a particular alternative is suspected

On some generalized ageing orderings

Some partial orderings which compare probability distributions with the expo- nential distribution, are found to be very useful to understand the phenomenon of ageing. Here, we introduce some new generalized partial orderings which de- scribe the same kind of characterization of some generalized ageing classes. We give some equivalent conditions for each of the orderings. Inter-relations among the generalized orderings have also been discussed

Optimization and Evaluation of Service Speed and Reliability in Modern Caching Applications

The performance of caching systems in general, and Internet caches in particular, is evaluated by means of the user-perceived service speed, reliability of downloaded content, and system scalability. In this dissertation, we focus on optimizing the speed of service, as well as on evaluating the reliability and quality of data sent to users. In order to optimize the service speed, we seek optimal replacement policies in the first part of the dissertation, as it is well known that download delays are a direct product of document availability at the cache; in demand-driven caches, the cache content is completely determined by the cache replacement policy. In the literature, many ad-hoc policies that utilize document sizes, retrieval latency, probability of references, and temporal locality of requests, have been proposed. However, the problem of finding optimal policies under these factors has not been pursued in any systematic manner. Here, we take a step in that direction: Still under the Independent Reference Model, we show that a simple Markov stationary policy minimizes the long-run average metric induced by non-uniform documents under optional cache replacement. We then use this result to propose a framework for operating caches under multiple performance metrics, by solving a constrained caching problem with a single constraint. The second part of the dissertation is devoted to studying data reliability and cache consistency issues: A cache object is termed consistent if it is identical to the master document at the origin server, at the time it is served to users. Cached objects become stale after the master is modified, and stale copies remain served to users until the cache is refreshed, subject to network transmit delays. However, the performance of Internet consistency algorithms is evaluated through the cache hit rate and network traffic load that do not inform on data staleness. To remedy this, we formalize a framework and the novel hit* rate measure, which captures consistent downloads from the cache. To demonstrate this new methodology, we calculate the hit and hit* rates produced by two TTL algorithms, under zero and non-zero delays, and evaluate the hit and hit* rates in applications

Divergence Measure in Information Theory and Reliability Analysis

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On Some Generalized Orderings: In the Spirit of Relative Ageing

We introduce some new generalized stochastic orderings (in the spirit of relative ageing) which compare probability distributions with the exponential distribution. These orderings are useful to understand the phenomenon of positive ageing classes and also helpful to guide the practitioners when there are crossing hazard rates and/or crossing mean residual lives. We study some characterizations of these orderings. Inter-relations among these orderings have also been discussed.Comment: arXiv admin note: substantial text overlap with arXiv:1410.198