William G. Bulgren

A Monte Carlo Investigation of the Robustness of T 2

Abstract The robustness of T2 for samples of size 5, 10 and 20 from several bivariate distributions is investigated. Samples are presented from bivariate normal, uniform, exponential, gamma, lognormal and double exponential distributions. Related observations on the one sample t and paired t are also given. Highly skewed distributions resulted in too many extreme values of T2 Other distributions gave conservative results. The use of the t-test and non-simultaneous techniques gave large overall levels of significance.

On Representations of the Doubly Non- Central F Distribution

Abstract The cumulative doubly non-central F-distribution associated with the random variable F″ = mS1/nS2 is considered where S1 and S2 are two independent non-central chi-square varites with degrees of freedom n and m and non-centrality parameters λ1 and λ2, respectively. Representations in terms of series are presented together with efficient computational procedures for the special functions used in numerical evaluation.

Inequalities for Some Multivariate f-Distributions with Applications

The inequality Pr (a ≤ Wi ≤ b; i = 1, 2, …, n) ≥ II n c=i Pr (a ≤ Wi ≤ b) is shown to hold when the random variables W 1, …, Wn , have a particular multivariate f-distribution which is defined. It is used in this paper to construct conservative simultaneous prediction intervals for failure times in certain life test experiments. An additional inequality is shown to hold for all bivariate distributions belonging to a class of bivariate f-distributions which is defined. An indication of the use of this latter inequality is given. Some tables are included which indicate the sharpness of each of the inequalities.

A Bivariate t-Distribution with Applications

Abstract A particular bivariate t-distribution is defined and investigated. Included is a discussion of how to compute probabilities for this distribution. Applications involve the construction of double sample tests for hypotheses pertaining to the mean of a normal distribution with unknown variance. Some bounds are given for the error incurred when the two component variables are provisionally assumed to be independent.

A Note on Product-Form Solution for Queuing Networks with Poisson Arrivals and General Service-Time Distributions with Finite Means

Product form was first introduced by Jackson [Operations Research, 1957; Management Science, 1963] who considered only negative exponential service distributions with queue length dependent service rates. Posner and Bernholtz [Operations Research, 1968] showed that one has product form in the case where there are many classes of customers, service times are exponential with class queue length dependent service rates, and lag times (the time for a customer to travel between two servers is a random variable with continuously differentiable distribution function). Baskett, Chandy, Muntz and Palacios [JACM, 1975] extended these results to networks with multiple classes of customers and service time distributions which have rational Laplace transforms vanishing at ∞. Chandy, Howard and Towsley [JACM, 1977] extended this further to the case where the service time distribution functions are continuously differentiable. They also introduced the concept of station balance and established some important relationships between station balance, local balance and product form. In particular, for the closed queueing network they showed that if each queue in the network satisfies local balance in isolation with Poisson arrivals then one has product form

Double Sample Tests for Hypotheses about the Mean of an Exponential Distribution

In this note it is shown how the methodology of the Zeigler and Tietjen double sample test for testing a hypothesis about the variance of a normal distribution can be used to construct double sample tests for testing hypotheses about the mean of an exponential distribution.

Studies in Markov models of computer systems

A new general model of I/O - CPU interation is described. The model is a discrete Markov process, and takes into account mean CPU time between physical I/O requests, mean I/O service times for each device, single or double buffering, and CPU queue discipline. A simple method of finding the steady state probability vector is shown. The utilization results are calculated and compared to, for three CPU queue disciplines, and for various service times, the results of earlier analytical models, with some interesting outcomes. The new model is limited presently to small systems (i.e., five or less tasks, and six or less I/O queues) due to the number of states necessary to model a large system.

A Note on a Double Sample Test

Abstract A double sample test for a hypothesis concerning the mean μ of a normal random variable with unknown variance σ2 is presented in this note. This test is an alternative to the usual single sample t test and is made by taking samples at two stages. After the first sample has been observed the hypothesis is rejected, accepted or a second sample is taken. This double sample test is a modification of a double sample test suggested by D. Owen. However, for the test being suggested here if the second sample is taken the information from the first sample is used in making the final decision. A table is included which is a tabulation of the rejection and acceptance points for various sample sizes and α = .05 and α = .01. Additional tables are included which give some power values and expected sample sizes for the new test and Owens test. These power values are compared with power values of various single sample t tests. Conclusions about desirable sample sizes are presented for both the new test and Owen...

An introductory algorithm teacher

A non-machine specific design of an algorithm teacher is proposed. It is a programmed environment to help students in a beginning computer science course learn problem solving skills. This paper provides an overview of the problem, a motivation and justification, followed by a brief description of what the program should provide the student.

A performance model of space-division ATM switches with input and output queueing

An analytic model for the performance evaluation of space-division asynchronous transfer mode (ATM) switches is presented. This model assumes that the switch has a fixed capacity of m, where 1/spl les/m/spl les/N (N is the number of trunks). Other important parameters include arrival rate and buffer sizes. Numerical solutions for the maximum throughput, cell delay, and cell loss probability are given with simulation being utilized in order to validate the analytic model. For independent and identical Bernoulli arrivals, the study shows that the contention processes can be modeled as discrete M/D/m (FIFO or Random) queues, while input queues can be modeled by Geom/G/1 queues, and the output queues are G/sup [X]//D/1 queues. A closed-form approximation for cell delay when m>2 is given. The result shows that the performance of switches with a small capacity can approach that of output queueing. The model and result can be used for switch design analysis and higher layer performance models.