On Approximating and Bounding GI/M/c Queues -- A Summary,

Abstract

Bounds and approximations for steady-state measures of effectiveness and state probabilities for GI/M/c queues are developed, requiring the ability to approximate and bound the single root, in (0,1), of the generating function equation associated with the GI/M/c queue. A method for obtaining this root for any GI, and the special cases GI = gamma and hyperexponential (H2) are discussed. The relation between the root and the coefficient of variation of the interarrival time distribution is investigated. Approximations to the root using GI = gamma (or H2), where the first two moments of GI are matched to those of gamma (or H2), are shown empirically to be good when the traffic intensity if at least moderate (greater than 0.5). Also included is an appendix containing an annotated bibliography of pertinent references.

Document Details

Document Type
Technical Report
Publication Date
Sep 30, 1976
Accession Number
ADA032106

Entities

People

  • Donald Gross
  • Faiz A. Al-khayyal

Organizations

  • George Washington University

Tags

DTIC Thesaurus Topics

  • Bibliographies
  • Coefficients
  • Equations
  • Intensity
  • Measures Of Effectiveness
  • Steady State

Readers

  • Approximation Theory.
  • Gulf War Illness and Chronic Multisymptom Illness in Veterans.
  • Mathematical Modeling and Probability Theory.