A Birth and Death Process Approximation for the Slotted ALOHA Algorithm.

Abstract

Many authors have concerned themselves with the bistable behavior of the finite-user slotted ALOHA protocol under heaving loading. Recently Nelson used a catastrophe-theoretic approach to demonstrate that under a fluctuating load the protocol suffers hysteresis as well as bistability. He uses results from catastrophe theory to give a possible improved control algorithm. Central to Nelson's approach is a diffusion approximation of the queue of backlogged users. This approximation has the advantage of yielding a continuing probability density for the process, thus allowing the use of (stochastic) catastrophe theory. Unfortunately, as will be seen later, the approximation requires difficult numerical integration and yields no closed form solution. It is being proposed here that the process should remain discrete, and that it can be approximated reasonably well as a birth-death process. This allows rapid computation of the approximate stationary distribution.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1985
Accession Number
ADA162153

Entities

People

  • W. Rising
  • W. Rosenkrantz

Organizations

  • University of Massachusetts Amherst

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Computations
  • Control Systems
  • Diffusion
  • Markov Chains
  • Mathematical Analysis
  • Mathematics
  • New York
  • Numerical Integration
  • Probability
  • Random Variables
  • Stationary
  • Stochastic Processes
  • Transitions
  • Universities

Readers

  • Calculus or Mathematical Analysis
  • Computer Networking
  • Control Systems Engineering.