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Approximate Behavior of Tandem Queues

  • Gordon F. Newell

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 171)

Table of contents

  1. Front Matter
    Pages N2-XI
  2. Gordon F. Newell
    Pages 1-42
  3. Gordon F. Newell
    Pages 43-89
  4. Gordon F. Newell
    Pages 218-230
  5. Gordon F. Newell
    Pages 381-402
  6. Back Matter
    Pages 403-413

About this book

Introduction

The following monograph deals with the approximate stochastic behavior of a system consisting of a sequence of servers in series with finite storage between consecutive servers. The methods employ deterministic queueing and diffusion approximations which are valid under conditions in which the storages and the queue lengths are typically large compared with 1. One can disregard the fact that the customer counts must be integer valued and treat the queue as if it were a (stochastic) continuous fluid. In these approximations, it is not necessary to describe the detailed probability distribution of service times; it suffices simply to specify the rate of service and the variance rate (the variance of the number served per unit time). Specifically, customers are considered to originate from an infinite reservoir. They first pass through a server with service rate ~O' vari­ ance rate ~O' into a storage of finite capacity c . They then pass l through a server with service rate ~l' variance rate ~l' into a storage of capacity c ' etc., until finally, after passing through an nth server, 2 they go into an infinite reservoir (disappear). If any jth storage become , n , the service at the j-lth server is interrupted full j = 1, 2, and, of course, if a jth storage becomes empty the jth server is inter­ rupted; otherwise, services work at their maximum rate.

Keywords

Distribution Image Queues Warteschlange equilibrium evaluation merger probability probability distribution science and technology service value-at-risk

Authors and affiliations

  • Gordon F. Newell
    • 1
  1. 1.Institute of Transportation StudiesUniversity of CaliforniaBerkeleyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-46410-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1979
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-09552-1
  • Online ISBN 978-3-642-46410-2
  • Series Print ISSN 0075-8442
  • Buy this book on publisher's site
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