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On extreme values of orbit lengths in M/G/1 queues with constant retrial rate


Gómez-Corral, Antonio (2001) On extreme values of orbit lengths in M/G/1 queues with constant retrial rate. Or Spektrum, 23 (3). pp. 395-409. ISSN 0171-6468

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In the design of waiting facilities for the units in a retrial queue, it is of interest to know probability distributions of extreme values of the orbit length. The purpose of this paper is to investigate the asymptotic behavior of the maximum orbit length in the M/G/1 queue with constant retrial rate. as the time interval increases. From the classical extreme value theory, we observe that, under standard linear normalizations, the maximum orbit length up to the nth time the positive recurrent queue becomes empty does not have a limit distribution. However, by allowing the parameters to vary with n, we prove the convergence of maximum orbit lengths to three possible limit distributions when the traffic intensity rho (n) approaches I from below and it approaches infinity.

Tipo de documento:Artículo
Palabras clave:Extreme values; queueing theory; limit theorems; repeated attempts
Materias:Ciencias > Matemáticas > Procesos estocásticos
Código ID:15851

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