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Exponential Ergodicity of the M/G/1 Queue
Marcel F. Neuts and Jozef L. Teugels
SIAM Journal on Applied Mathematics
Vol. 17, No. 5 (Sep., 1969), pp. 921-929
Published by: Society for Industrial and Applied Mathematics
Stable URL: http://www.jstor.org/stable/2099280
Page Count: 9
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If an M/G/1 queue either is transient or is positive and has a service time distribution which is exponentially bounded, then the most important quantities of the queue have distributions which tend exponentially fast to their limits. If we assume somewhat more, i.e., if condition (PE) below is satisfied, then accurate estimates on these distributions are obtained in the positive recurrent case. Some of the studied quantities are: the busy period, the number of customers served during a busy period, the waiting times and the queue length in continuous time. The method of proof is based on the exponential ergodicity theorems for semi-Markov processes and on standard theorems from the theory of Laplace-Stieltjes transforms.
SIAM Journal on Applied Mathematics © 1969 Society for Industrial and Applied Mathematics