Asymptotic Behavior of the Stationary Distributions in the GI/PH/c Queue with Heterogeneous Servers.

Abstract

This paper deals with the stable c-server queue with renewal input. The service time distributions may be different for the various servers. They are however all probability distributions of phase type. It is shown that the stationary distribution of the queue length at arrivals has an exact geometric tail of rate n, o < n < 1. It is further shown that the stationary waiting time distribution at arrivals has an exact exponential tail of decay parameter xi > 0. The quantities n and xi may be evaluated together by an elementary algorithm. For both distributions, the multiplicative constants which arise in the asymptotic forms may be fully characterized. These constants are however difficult to compute in general. (Author)

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1980
Accession Number
ADA091036

Entities

People

  • Marcel F. Neuts
  • Yukio Takahashi

Organizations

  • University of Delaware

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Air Force
  • Applied Mathematics
  • Computations
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Markov Chains
  • Markov Processes
  • Mathematics
  • Probability
  • Probability Distributions
  • Random Variables
  • Scientific Research
  • Stationary
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Statistical inference.