ON SOME PROBLEMS IN THE THEORY OF PARTICLE COUNTING AND THE INFINITELY MANY SERVER QUEUE

Abstract

Renewal theory plays a prominent role in the analysis of the behavior of type I and type II particle counters. There is an integral formula (due to R. pyke) for the distribution of the time between successive registrations with a Type I counter under the assumptions that the particles arrive according to a general re current process and that the counter has a random dead time. A resume is given of the renewal theoretic approach to particle counting problems and a shorter proof of Pyke's formula. Takacs' methods were used to solve the problem of where the dead time is allowed to have Erlang-r distribution r > 1, rather than the exponential. The distributions used are 'max-m' distributions, the maximum of m exponential distri butions each with parameter mu. After determin ing the number of impulses present in thetype II counter (the queue size problem), the problem of particle counting is considered. Here is where the 'max-m' distributions make the problem manageable.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1963
Accession Number
AD0407819

Entities

People

  • Joseph L. Gastwirth

Organizations

  • Columbia University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Binomials
  • Dead Time
  • Difference Equations
  • Distribution Functions
  • Equations
  • Government Procurement
  • Integral Equations
  • Integrals
  • Markov Chains
  • New York
  • Particle Counters
  • Probability
  • Random Variables
  • Sequential Analysis
  • Stochastic Processes
  • Time Intervals
  • Two Dimensional

Readers

  • Aerosol Science/Aerosol Physics
  • Statistical inference.
  • Systems Analysis and Design