Measurement, Modelling and Evaluation of Computing Systems by Holger Hermanns

Author:Holger Hermanns
Language: eng
Format: epub
ISBN: 9783030430245
Publisher: Springer International Publishing

In a similar way we can compute costs for the provider when a user is lost due to all channels busy and his selected program is not among the programs online.

Remark. Combining our two approaches from Propositions 1 and 2 to the same system we have an interesting conclusion. We consider the simplest system with one channel and one customer class and note that in Corollary 1 of Proposition 1 the state space is . Then the stationary probability for an empty system is

(30)

by standard insensitivity arguments and using the exponential system with mean of the relevant busy period distribution. The point is: We need not to know the value of , because (30) holds for any service time distribution in the Engset model and carries over to the exponential system by insensitivity.

Considering now the detailed system from Proposition 2. Here we do not need to know the value of to obtain the stationary probability for the system to be empty. This probability is by (13) and (12)

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