# Accession Number:

## ADA070158

# Title:

## The Distribution of the Minimum Distance between a Random Target and Units Patrolling along a Line.

# Descriptive Note:

## Master's thesis,

# Corporate Author:

## NAVAL POSTGRADUATE SCHOOL MONTEREY CA

# Personal Author(s):

# Report Date:

## 1979-03-01

# Pagination or Media Count:

## 66.0

# Abstract:

The probability distribution of the minimum of the distances from a randomly occurring trouble spot to n carriers patrolling along a line of length L is analyzed. Two approximations, a Poisson process and a fixed lattice of equally spaced points, which bound the analytic model are developed and their usefulness and limitations are discussed. It is hypothesized that a two dimensional Poisson field and a two dimensional lattice of fixed points will form upper and lower bounds for the more algebraically tedious two-dimensional area patrol model. The hypothetical bounding distributions are developed for n units patrolling an area. Finally a one dimensional radius of influence model is developed which quantifies the contribution that the effective operational radius of a carrier airwing makes to the initial minimum distance analytic model. Author

# Descriptors:

- *PATROLLING
- MATHEMATICAL MODELS
- SPATIAL DISTRIBUTION
- DEPLOYMENT
- COASTAL REGIONS
- PROBABILITY DISTRIBUTION FUNCTIONS
- RANDOM VARIABLES
- ONE DIMENSIONAL
- THESES
- TARGETS
- APPROXIMATION(MATHEMATICS)
- COMMAND AND CONTROL SYSTEMS
- AIRCRAFT CARRIERS
- NAVAL OPERATIONS
- PACIFIC OCEAN
- RANGE(DISTANCE)
- AREA COVERAGE
- INDIAN OCEAN

# Subject Categories:

- Statistics and Probability
- Naval Surface Warfare