Peter A. W. Lewis

Statistical analysis of non-stationary series of events in a data base system

Central problems in the performance evaluation of computer systems are the description of the behavior of the system and characterization of the workload. One approach to these problems comprises the interactive combination of data-analytic procedures with probability modeling. This paper describes methods, both old and new, for the statistical analysis of non-stationary univariate stochastic point processes and sequences of positive random variables. Such processes arefr equently encountered in computer systems. As an illustration of the methodology an analysis is given of the stochastic point process of transactions initiated in a running data base system. On theb asis of the statistical analysis, a non-homogeneous Poissonp rocess model for the transaction initiation process is postulated for periods of high system activity and found to be an adequate characterization of the data. For periods of lower system activity, the transaction initiation process has a complex structure, with more clustering evident. Overall models of this type have application to the validation of proposed data base subsystem models.

Regenerative Simulation with Internal Controls

Abstract : A new variance reduction technique is introduced called internal control variables, to be used in the context of regeneration simulations. The idea is to identify a sequence of control random variables, each one defined within a regenerative cycle, whose mean can be calculated analytically. These controls should be highly correlated with the usual quantities observed in a regenerative simulation. This correlation reduces the variance of the estimate for the parameter of interest. Numerical examples are included for the waiting time process of an M/M/1 queue and for several Markov chains. (Author)

Regression-adjusted estimates for regenerative simulations, with graphics

Abstract : The independent block structure of regenerative processes and the known convergence rates of the means of ratio estimators are exploited to produce bias-free regression-adjusted estimates (rares) for regenerative simulations. Direct assessments of the variances of the estimates are obtained, as well as indications--both formal and graphical--of their normality or non-normality. (Author)

Two-parameter lifetime distributions for reliability studies of renewal processes

Probability functions are defined for use in reliability studies of equipments which are maintained over a long period of time through replacement of components. These are: lifetime distribution function, lifetime density function, probability of survival, hazard, expected number of replacements, and renewal rate. Theoretical results of renewal theory are adapted to reliability studies of complex systems. n nThe exponential law is equivalent to the assumption that survival probability for any given time interval is independent of the age oaf component at the beginning of the interval. It seems more realistic, however, to assume that this survival probability is a monotonically decreasing function of initial age, or, equivalently, that the hazard is a monotonically increasing function of the age of the component. Consequently, three two-parameter models of distribution functions, with the properties: (1) initial lifetime density greater than zero, and (2) monotonically increasing hazard, are proposed and discussed. The lifetime behavior associated with these models ranges from complete determinacy to complete randomness. An entropic measure of this randomness is introduced. n nThe expected number of replacements is numerically calculated and plotted as a function of time for several different parameter values in each model.

An experimental 50-megacycle arithmetic unit

An experimental 50-megacycle arithmetic unit has been built which performs a repetitive multiplication program and checks the results for errors. The unit uses pulse circuitry which has been developed to perform digital operations at a 50-megacycle pulse-repetition rate. This paper describes the arithmetic system and the circuits which perform the required functions. These circuits include a full binary adder, a phase-locked frequency divider which provides a 3.125-megacycle secondary timing source, a reshaping and retiming circuit using germanium diodes and capacitive storage, a high-speed shift register, a high-speed indicator register, and a binary word generator. n nVarious novel features of a digital system operating at these high speeds are described. These include the use of coaxial delay lines Cor the distribution of signals and as storage elements, and the use of secondary emission tubes in amplifier and multivibrator circuits. n nIn a 50-megacycle system the interdependence of the space and time dimensions is marked, and although this introduces problems which are not ordinarily encountered in computing systems, it may be used advantageously to provide features such as the variable-phase clock system used in the arithmetic unit. n nThe performance and reliability of the arithmetic unit are discussed as well as the reliability of the components and circuits which make up the system. Although the techniques and circuitry discussed here have been applied only to a relatively simple arithmetic unit, it is felt that they could be useful in a variety of high-speed computing and measurements applications.