Research for Queuing Theory

A survey of nonparametric methods (methods which make no distributional assumptions about the data) for survival curve estimation is presented. This is provided as background to the discussion of the Cox regression model, which can be applied to cross-sectional data. The Cox model is then compared to probit analysis on the 1973 recruit cohort of four-year obligors. Evidence is presented to show that the Cox model can be useful for estimating recruit survival from cross-sectional data.

Computer programs for calculating sample size requirements are presented and illustrated. Given the desired significance level and the desired probability that the sample will achieve that level, sample size requirements are calculated for determining that a unit rating: exceeds a criterion on level (with replacement); is less than a criterion level (with replacement); is between two criterion levels (with replacement); exceeds a criterion level (without replacement). The last calculation is done exactly (with the hypergeometric distribution) and also with a normal approximation. In all cases, the required sample size is calculated as a function of the true unit rating.

Some apparent contradictions in the operations research literature of search theory and information theory are reviewed, and the source of the conflict is isolated. The information processes connected with a search operation are examined by studying the geometric properties of information surfaces in search-allocation space. Some new theorems are developed which show that the connection between search and information theory is much stronger than previously believed. It is demonstrated that the amount of search effort, C is a critical parameter in the relation between search and information gain. For very small values of C, there is no unique relation between detection probability and information gain; for very large values of C, the optimal whereabouts search policy produces the greatest information gain; for a broad intermediate range of C (including many cases of practical interest) the optimal detection search policy produces the greatest information gain.

A method for modeling elements of the Navy's CLAMP resupply system is described and examples presented.