THE CONTINUITY OF THE SINGLE SERVER QUEUE.

Abstract

In many applications of queueing theory assumptions of either Poisson arrivals or exponential service times are made. The implicit assumption is that if the actual arrival process approximates a Poisson process and the service times are close to exponential, then the quantities of interest in the real queueing system (viz. the virtual waiting time, queue length, idle times, etc.), will approximate those of the idealized model. The paper establishes the continuity of the single server queue acting as functionals of the arrival and service processes. The proof involves an application of the theory of weak convergence of probability measures on metric spaces. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1970
Accession Number
AD0710763

Entities

People

  • Douglas P. Kennedy

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Continuity
  • Convergence
  • Mathematics
  • Probability
  • Queueing Theory
  • Weak Convergence

Readers

  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space