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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1981
- Accession Number
- ADA117089
Entities
People
- Gordon B. Crawford
Organizations
- RAND Corporation