Some Explicit Formulas and Computational Methods for Infinite Server Queues with Phase Type Arrivals.

Abstract

This paper discusses infinite server queues whose input is a Phase Type Renewal Process. The problems of obtaining the transient and steady-state distributions and moments of the queue length are reduced to the solution of certain well-behaved systems of linear differential equations. Sample computations are provided with as many as ten phases. The paper contains some useful explicit formulas and also discusses the interesting special case where the service time is also of phase type. The Phase Type Distributions include a wide variety of models such as generalized Erlang, hyperexponential (mixtures of a finite number of exponentials) as very special cases and possess great versatality in modeling a number of interesting qualitative features such as bimodality.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1978
Accession Number
ADA054882

Entities

People

  • Marcel F. Neuts
  • V. Ramaswami

Organizations

  • University of Delaware

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Computational Science
  • Computations
  • Computer Science
  • Delaware
  • Differential Equations
  • Discrete Distribution
  • Equations
  • Linear Differential Equations
  • Linear Systems
  • Markov Chains
  • Mathematical Analysis
  • Probability
  • Probability Distributions
  • Random Variables
  • Stationary
  • Statistics
  • Steady State

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Statistical inference.