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The M/M/∞Service System with Ranked Servers in Heavy Traffic

  • G. F. Newell

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 231)

Table of contents

  1. Front Matter
    Pages N2-XI
  2. G. F. Newell
    Pages 1-6
  3. G. F. Newell
    Pages 6-12
  4. G. F. Newell
    Pages 12-19
  5. G. F. Newell
    Pages 19-67
  6. G. F. Newell
    Pages 67-89
  7. G. F. Newell
    Pages 89-96
  8. G. F. Newell
    Pages 96-109
  9. G. F. Newell
    Pages 115-122
  10. Back Matter
    Pages 123-129

About this book

Introduction

We are concerned here with a service facility consisting of a large (- finite) number of servers in parallel. The service times for all servers are identical, but there is a preferential ordering of the servers. Each newly arriving customer enters the lowest ranked available server and remains there until his service is completed. It is assumed that customers arrive according to a Poisson process of rate A , that all servers have exponentially distributed service times with rate ~ and that a = A/~ is large compared with 1. Generally, we are concerned with the stochastic properties of the random function N(s ,t) describing the number of busy servers among the first s ordered servers at time t. Most of the analysis is motivated by special applications of this model to telephone traffic. If one has a brunk line with s primary channels, but a large number (00) of secondary (overflow) channels, each newly arriving customer is assigned to one of the primary channels if any are free; otherwise, he is assigned to a secondary channel. The primary and secondary channels themselves could have a preferential ordering. For some purposes, it is convenient to imagine that they did even if an ordering is irrelevant.

Keywords

System boundary element method equilibrium poisson process research

Authors and affiliations

  • G. F. Newell
    • 1
  1. 1.Transportation Engineering and Operations ReserachUniversity of CaliforniaBerkeleyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-45576-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 1984
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-13377-3
  • Online ISBN 978-3-642-45576-6
  • Series Print ISSN 0075-8442
  • Buy this book on publisher's site
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