Page 188 - Contributed Paper Session (CPS) - Volume 3

CPS1988 Saggou Hafida H. et al.
4. Performance Measures
In this section, we deduce some performance measures of the system
under the study state condition.
1. Distribution of the system size in terms of generating function is given by

Distribution of the orbit size interms of generating function is given by

2. Distribution of the number of transit customers in the orbit in terms of
generating function is given by

Distribution of the number of transit customers in the system interms of
generating function is given by

For p = 1 , we obtain Φ() = × Ψ() where, () = () × ()
K
Given that

then the results are obtained by using the Hospital’s rule.
For the mean waiting time of customers in the retrial queue and in the
system, they can be obtained respectively by the following formulas

and
Corrolary
1. The probability that the server is busy is given by

2. The probability that the server is under first verification delay is given by

3. The probability that the server is under repair is given by

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