Page 186 - Contributed Paper Session (CPS) - Volume 3

CPS1988 Saggou Hafida H. et al.
another transit customer with probability . We assume that the vacation
times are i.i.d random variables with a probability distribution function
th
(), a density function (), an LST () and n moments .

6. The server is subject to active breakdowns, i. e. the server fails if and only
if it is rending service. It fails after an exponential amount of time with rate
> 0. The customer receiving service during a breakdown has to wait
until the service is recovered. Once the system breaks down, its repairs is
not supported immediately, there is a first delay time verification which
has a general distribution with a distribution function (), a density
1
th
function (), an LST ()and n moments ∅ 1, .
1
1

7. After a first verification delay, the repair process starts immediately. The
repair times are i.i.d random variables according to a general distribution
function (), a density function (), an LST () and n moments .
th

8. As soon as the repair time is over, the server will have a second verification
delay, the delay times are independent with a commonprobability
distribution function (), a density function (), an LST ()and n th
2
2
2
moments ∅ 2, .

The customer whose service is interrupted remains in service. Once the
second verification delay completed, the server takes over the service of this
customer. The server is not authorized to accept another customer until the
customer in service leaves the system. The customer at the head of the orbit
enter in competition with a new transit customer for an attempt to receive
service.
The state of the system at time t can be described by the following Markov
process

where () takes its values in the {0,1,2,3,4,5,6} according to the server
being idle, busy with a transit customer, busy with a recurrent customer, under
first delay of verification, under repair, under vacation, or under second delay
of verification. If () = 3, 4 6, we define ∗ () as a type of customers in
service ( ∗ () = 1 2 according to the occupancy of the server by a transit
or a recurrent customer). If () = 0 and () > , then () represents the
0
elapsed retrial time of the transit customer. If () = 1, we define () as the
1
elapsed service time of the transit customer. If () = 2, we define () as
2
the elapsed service time of the recurrent customer. If () = 3, we define
() as the elapsed first verification delay time. If () = 4, we define ()
4
3
as the elapsed repair time; If () = 5, we define () as the elapsed
5
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