Regenerative Simulation for Extreme Values.

Abstract

Let (X sub t : t > or = 0) denote the regenerative process being simulated and assume that X sub t converges weakly (in distribution) to a limit random variable X. Our concern here is in estimating the extreme values of the process (X sub t : > or = 0). Suppose we are interested in the largest value attained in the interval (0, t): (X sub t)* = sup (X sub s : 0 < or = s < or = t). Examples of this are the maximum queue lengths or waiting times in a queueing system. As t increases so will (X sub t)*, without bound if the state space of (X sub t : > or = 0) is unbounded. This report developes two methods for estimating the distribution of (X sub t)*. When the regenerative process is either the GI/G/1 queue or a birth-death process theoretical results are available for the distribution of (X sub t)*. The waiting time, queue length, and virtual waiting time for an M/M/1 queue were simulated. The two methods for estimating the distribution of (X sub t)* were employed and the simulation results compared with the theoretical results. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1977
Accession Number
ADA047945

Entities

People

  • Donald Iglehart

Organizations

  • Stanford University

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Convergence
  • Data Science
  • Estimators
  • Information Science
  • Markov Chains
  • Markov Processes
  • Military Research
  • Operations Research
  • Probability
  • Random Variables
  • Simulations
  • Simulators
  • Statistical Analysis
  • Statistical Estimation
  • Statistical Inference
  • Statistics
  • Weak Convergence

Readers

  • Computational Modeling and Simulation
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space