Page 190 - Contributed Paper Session (CPS) - Volume 3

CPS1988 Saggou Hafida H. et al.
5. Stochastic decomposition
We note the probability generating function of the system size distribution
for = 1 is given by

Let χ() be the probability generating function of the number of
customers in the orbit, given that the server is idle or busy serving a recurrent
customers or under first and second delay of verification or under repair.
Under this definition, it can easily seen that

.

Φ() = Φ () × ()
0
We obtain,

6. Conclusion

In this paper we have studied an [] //1 retrial queue with recurrent
customers, geometric loss and Bernoulli vacation, where the server is
unreliable, which consists of breakdowns period, repairs, and two delays of
verifications. We have obtained the probability generating function of various
states in the steady state solution with performance measures of the system.
Some numerical examples were given to show the effect of breakdowns,
repairs, two delays of verifications and size of batch arrivals in the system on
the main performance measures.

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