A Simple Approximation to the Average Queue Size in the Time-Dependent M/M/1 Queue,

Abstract

The time-dependent equations for the M/M/1 queue can be reduced to a single equation for the expected queue size, but the equation is dependent on (P sub O)(t), the probability of no jobs in the system. An exact equation for the behavior of (P sub 0)(t) under special conditions is derived and an approximation relating (P sub 0)(t) to Q(t), the expected queue size at time t, is found for the case when the change in queue size is slow compared to the service rate. It is found that the approximation affords a significant improvement over the use of a steady-state approximation to the time-dependent queue and is simpler to use than the exact equations.

Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1975
Accession Number
ADA020227

Entities

People

  • Kenneth Lloyd Rider

Tags

DTIC Thesaurus Topics

  • Equations
  • Mathematics
  • Probability
  • Steady State

Readers

  • Mathematical Modeling and Probability Theory.
  • Mathematics or Statistics