Diffusion Approximations for Complex Repair Systems

Abstract

A wide variety of complex repair systems can be modeled as continuous time Markov chains. These systems are closed networks of queues with a total of n jobs circulating in the network. The process of interest is the number of jobs, X sub n (t), at the various repair centers at time t. After appropriate translation and scaling, we show that the processes (X sub n (t) : t > or = 0) converge weakly to a limiting multivariate Ornstein-Uhlenbeck process. This limit process is then used to obtain computable approximations for X sub n (t). Numerical results are presented for three specific repairman models and the approximations are compared with exact results obtained through product form formulae. In most cases the approximation is quite accurate.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1991
Accession Number
ADA238100

Entities

People

  • Atam Lalchandani
  • Donald Iglehart

Organizations

  • Stanford University

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Convergence
  • Differential Equations
  • Diffusion
  • Equations
  • Markov Chains
  • Markov Processes
  • Military Research
  • Operations Research
  • Partial Differential Equations
  • Probability
  • Queueing Theory
  • Random Variables
  • Theorems
  • Universities
  • Weak Convergence

Readers

  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.