The M/M/1 Queue
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The M/M/1 queueing system is discussed. Key properties are stated, many with proofs. Steady state and transient probabilities are presented along with many other well-known properties. A variety of analytical techniques are used in the presentation. Graphs are used to illustrate several aspects of this system.
Keywords:
queueing;
Poisson process;
limiting probability;
transient probability;
PASTA;
level crossing;
laplace transform;
busy period;
birth and death process
[1] Ronald W. Wolff,et al. Poisson Arrivals See Time Averages , 1982, Oper. Res..
[2] J. Little. A Proof for the Queuing Formula: L = λW , 1961 .
[3] Carl M. Harris,et al. Fundamentals of Queueing Theory: Gross/Fundamentals of Queueing Theory , 2008 .