Palm's Theorem for Nonstationary Processes

Abstract

This report provides both an introduction for the layman and a statement and technical proof of the dynamic form of Palm's Theorem. It is intended to help the layman develop a feeling for what is, and what is not, an appropriate application. A general statement of the theorem is given along with less general forms that are easy to use and exact in many applications. Section 2 explains the importance of the theorem to stock calculations and presents an intuitive proof of the classical form of Palm's Theorem for steady-state arrivals and discrete time. Section 3 gives several different steady-state examples to provide an understanding of what is, and what is not, a Poisson arrival process and when the dynamic form of Palm's Theorem applies. Several different statements of Palm's Theorem are developed in Section 4 to facilitate its application. These forms are used to prove what has been known as the worst- case approximation theorem. Section 4 ends with a discussion of the application of the dynamic form to the calculation of war readiness spares requirements for aircraft.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1981
Accession Number
ADA117089

Entities

People

  • Gordon B. Crawford

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • Air Platforms
  • Human Systems
  • Materials and Manufacturing Processes
  • Space

DTIC Thesaurus Topics

  • Aerospace Industry
  • Air Force
  • Aircrafts
  • Differential Equations
  • Equations
  • Integrals
  • Mathematical Models
  • Measure Theory
  • Models
  • New York
  • O Rings
  • Probability
  • Probability Distributions
  • Random Variables
  • Steady State
  • Stochastic Processes
  • Time Intervals

Readers

  • Graph Algorithms and Convex Optimization.
  • Plasma Physics / Magnetohydrodynamics
  • Systems Analysis and Design