Capacity Planning and Allocation for Web‐Based Applications

Motivated by the technology division of a financial services firm, we study the problem of capacity planning and allocation for Web‐based applications. The steady growth in Web traffic has affected the quality of service (QoS) as measured by response time (RT), for numerous e‐businesses. In addition, the lack of understanding of system interactions and availability of proper planning tools has impeded effective capacity management. Managers typically make decisions to add server capacity on an ad hoc basis when systems reach critical response levels. Very often this turns out to be too late and results in extremely long response times and the system crashes. We present an analytical model to understand system interactions with the goal of making better server capacity decisions based on the results. The model studies the relationships and important interactions between the various components of a Web‐based application using a continuous time Markov chain embedded in a queuing network as the basic framework. We use several structured aggregation schemes to appropriately represent a complex system, and demonstrate how the model can be used to quickly predict system performance, which facilitates effective capacity allocation decision making. Using simulation as a benchmark, we show that our model produces results within 5% accuracy at a fraction of the time of simulation, even at high traffic intensities. This knowledge helps managers quickly analyze the performance of the system and better plan server capacity to maintain desirable levels of QoS. We also demonstrate how to utilize a combination of dedicated and shared resources to achieve QoS using fewer servers.     

Cyclic Polygonal Designs with Block Size 3 and Joint Distance α = 2

Polygonal designs are useful in survey sampling in terms of balanced sampling plans excluding contiguous units (BSECs) and balanced sampling plans excluding adjacent units (BSAs). In this article, the method of cyclic shifts has been used for the construction of cyclic polygonal designs (in terms of BSAs) with block size k = 3 and λ = 1, 2, 3, 4, 6, 12 for joint distance α = 2 and 51 new designs for treatments v ≤ 100 are given.     

Multivariate goodness-of-fit tests based on statistically equivalent blocks

Various nonparametric procedures are known for the goodness-of-fit test in the univariate case. The distribution-free nature of these procedures does not extend to the multivariate case. In this paper, we consider an application of the theory of statistically equivalent blocks(SEB)to obtain distribution-free procedures for the multivariate case. The sample values are transformed to random variables which are distributed as sample spacings from a uniform distribution on [0, 1], under the null hypothesis. Various test statistics are known, based on the spacings, which are used for testing uniformity in the univariate case. Any of these statistics can be used in the multivariate situation, based on the spacings generated from the SEB. This paper gives an expository development of the theory of SEB and a review of tests for goodness-of-fit, based on sample spacings. To show an application of the SEB, we consider a test of bivariate normality.     

A Weighted Linear Estimator of Multivariate ARCH Parameters

A weighted linear estimator (WLE) of the parameters of multivariate ARCH models is proposed. The accuracy of WLE in estimating the parameters of multivariate ARCH models is compared with the widely used quasi-maximum likelihood estimator (QMLE) through simulations. Application to real data sets are also presented and forecasts of variance-covariance matrix and value-at-risk (VaR) are obtained. The weighted resampling methods are used to approximate the sampling distribution of the proposed estimator. Our study indicates that the forecasting performance of WLE is not inferior and one-day ahead risk estimates are also found better than the QMLE.