Waiting Times for M/G/1 Queues with Service-Time-Dependent Server Vacations

Abstract

This paper shows how to determine the stationary distribution of the virtual wait in M/G/1 queues with either one at-a-time or exhaustive server vacations. Each vacation time may depend on the immediately preceding service time or on whether the server finds the system empty after returning from vacation. In this way, it is possible to model situations such as long service times followed by short vacations, and vice versa. The method of analysis employs level-crossing theory. Detailed examples are given for various cases of service and vacation-time distributions. Keywords: Applied probability; Computational analysis; Computational probability; Markov chains; Numerical methods; Probability; Queues; Stochastic models; Waiting times.

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Document Details

Document Type
Technical Report
Publication Date
Jun 22, 1989
Accession Number
ADA209597

Entities

People

  • Carl M. Harris
  • Percy H. Brill

Organizations

  • George Mason University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Decomposition
  • Differential Equations
  • Distribution Functions
  • Equations
  • Integral Equations
  • Integrals
  • Mathematics
  • Military Research
  • Numbers
  • Operations Research
  • Probability
  • Probability Density Functions
  • Probability Distributions
  • Random Variables
  • Real Numbers
  • Statistics
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Educational Psychology
  • Parallel and Distributed Computing.
  • Statistical inference.