The Asymptotic Mathematical Expectation for the Time at Which the Number of Customers in the M/G/1 Queue Reaches a finite Number for the First Time

Document Type : Original Article

Author

Dep. of Pure Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt

Abstract

In this paper the mathematical expectation and its asymptotic value for the time ζₙ at which the number of customers in the queue reaches n for the first time are derived for a M/G/1 bulk service queue. Moreover the fundamental lemmas and a limit theorem are obtained.

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