The Randomization Technique as a Modeling tool and Solution Procedure for Transient Markov Processes.

Abstract

The randomization procedure for computing transient solutions to Markov processes (discrete state space, continuous time) is presented. This procedure computes transient state probabilities. It is based on a construction relating a continuous time Markov process to a discrete time Markov chain. Modifications and extensions of the randomization method allow for computation of distributions of first passage and sojourn times in Markov processes, and also computation of expected cumulative occupancy times and expected number of events occurring during a time interval. Several implementations of the randomization procedure are discussed. The implementation for a general class of Markov processes which can be described in terms of state space (S), event set (E), rate vectors (R), and target vectors (T) --abbreviated as SERT-- is presented. This general approach can handle systems whose state spaces are quite large and have sparse generators. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Aug 10, 1982
Accession Number
ADA121730

Entities

People

  • Donald Gross
  • Douglas R. Miller

Organizations

  • George Washington University

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies
  • Ground and Sea Platforms
  • Weapons Technologies

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Computational Science
  • Differential Equations
  • Engineering
  • Equations
  • Logistics Management
  • Markov Chains
  • Markov Processes
  • National Security
  • Numerical Analysis
  • Operations Research
  • Probability
  • Random Variables
  • Reliability
  • Stochastic Processes
  • Time Intervals

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space