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The M/G/1 Queue

  • Randolph Nelson
Chapter

Abstract

In this chapter we analyze a simple single server queue that is frequently used to model components of computer systems. This queue is termed the M/G/1 queue. This is standard “queueing notation,” first introduced by Kendall. Typically a queue is described by four variables
$$ A/S/k/c, $$
which have the following interpretation:

A,S — The arrival (A) or service (S) process where M means Poisson arrivals and exponential service times, G means the process is generally distributed, E denotes an -stage Erlang distribution, and D denotes a deterministic distribution.

k — The number of servers.

c — The buffer size of the system. This is the total number of customers the system can hold. Arrivals to the system already containing c customers are assumed to be lost. If not specified, c is assumed to be infinite.

Keywords

Service Time Queue Length Busy Period Probability Generate Function Poisson Arrival 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliographic Notes

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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Randolph Nelson
    • 1
    • 2
  1. 1.OTA Limited PartnershipPurchaseUSA
  2. 2.Modeling MethodologyIBM T.J. Watson Research CenterYorktown HeightsUSA

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