Generalizations of Palm's Theorem and Dyna-METRIC's Demand and Pipeline Variability

Abstract

Palm's theorem is a useful tool in modeling inventory problems in logistics models such as METRIC and Mod-METRIC. However, to fit its limited domain of applicability, time-dependent customer arrival rates have been approximated by the required constant rates, which results in a possible loss of accuracy. This report reviews the extension of Palm's theorem for time-dependent arrival rates and service distributions under Poisson input, and it provides further extensions to compound Poisson input. The extensions make it possible to model processes in which the number either of demands or of customers in service has variance-to-mean ratios greater than or equal to unity. The report introduces the nonhomogeneous Poisson queue with infinite servers, and develops a generalization of Palm's Theorem to nonhomogeneous Poisson input. The author shows that comparable results hold for compound Poisson input. He then relates these results to two-echelon repair systems. Finally, he covers various initial conditions of the queueing system. Keywords: Logistics; Inventory; Models; Poisson density functions; Distribution functions; Poisson equation; Repair; Queueing theory. (JHD)

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1989
Accession Number
ADA213283

Entities

People

  • Manuel J. Carrillo

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accuracy
  • Air Force
  • Aircrafts
  • Corporations
  • Distribution Functions
  • Equations
  • Logistics
  • New York
  • Operations Research
  • Poisson Density Functions
  • Poisson Equation
  • Probability
  • Probability Distributions
  • Queueing Theory
  • Random Variables
  • Steady State
  • United States

Readers

  • Calculus or Mathematical Analysis
  • Computational Modeling and Simulation
  • Logistics and Supply Chain Management.