Randomization Procedures in the Computation of Cumulative-Time Distributions Over Discrete Stare Markov Process

Article Abstract:

A computational methodology for obtaining bounds on cumulative-time distributions is given. This problem arises in queueing theory where delay time statistics on individual transactions are needed. A randomization procedure to compute results for transient Markov processes is used. This transient distribution is equivalent to the requisite cumulative-time distribution. An application is presented. Graphs show sojourn times and the number of steps to absorption. Tables contain numerical results.

Queuing theory, Poisson distribution, Markov Process, Queuing Networks

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Two Probability Models of Pyramid or Chain Letter Schemes Demonstrating That Their Promotional Claims Are Reliable

Article Abstract:

Variations of chain letters and pyramid schemes continue to be offered to the public illegally. Two probability models of these schemes are reviewed. Fraud is indicated where a limit is placed on the maximum number of participants and where a participant can sell but two letters for each purchased letter. A small number of participants will make money but most will lose.

Network analyzers, LAN Monitor, Applications, Models, Legal Issues, Stochastic Model

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Reconciliation of Probability Distributions

Article Abstract:

Distributions are characterized by their mean and standard deviations. Several individual probability distributions need to be reconciled. The usual procedure is to use least squares. However, t-distributions can be used with greater effectiveness particularly if even a minor deviation from normality exists.

Curve fitting, Statistical Analysis, Approximation, Bayesian Theory, Least Squares Approximation

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