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

  • Book
  • © 1984

Overview

Authors:
  1. G. F. Newell

    1. Transportation Engineering and Operations Reserach, University of California, Berkeley, USA

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

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Table of contents (9 chapters)

  1. Front Matter

    Pages N2-XI
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  2. Introduction

    • G. F. Newell
    Pages 1-6

  3. Limit properties for a » 1

    • G. F. Newell
    Pages 6-12

  4. Descriptive properties of the evolution

    • G. F. Newell
    Pages 12-19

  5. The overflow distribution

    • G. F. Newell
    Pages 19-67

  6. Joint distributions

    • G. F. Newell
    Pages 67-89

  7. A diffusion equation

    • G. F. Newell
    Pages 89-96

  8. Transient properties

    • G. F. Newell
    Pages 96-109

  9. Equilibrium properties of the diffusion equation

    • G. F. Newell
    Pages 109-115

  10. Equivalent random method

    • G. F. Newell
    Pages 115-122

  11. Back Matter

    Pages 123-129
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Keywords

About this book

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.

Authors and Affiliations

  • Transportation Engineering and Operations Reserach, University of California, Berkeley, USA

    G. F. Newell

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