Page 184 - Contributed Paper Session (CPS) - Volume 3

CPS1988 Saggou Hafida H. et al.

Unreliable retrial queue with two types
customers, two delays and vacations
Saggou Hafida Hafida, Lach Lachemot Tassadit, Sadeg Ines Ines, Ourbih Tari
Megdouda
Universite Des Sciences Et E La Technologie Houari Boumedienne Alger

1. Introduction
The queueing theory is used in various applications, this classical theory
soon proved ineffective in the face of real system more and more complex.
The limitations of the classical theory of queues that did not allow to explain
the stochastic behavior of telephone systems where subscribers repeated their
calls by redialling the number several times to obtain the communication, this
phenomenon is called retrial queues.
Queueing systems with retrials are characterized by the next customer who
finds the server busy is obliged to leave and joins the retrial group
(called”Orbit”) and repeat this demand for service after some random time.
The retrial queue have been widely used in the telephone switching systems,
computer networks and computer systems, maintenance and repair problems.
For more details on these models, see (Yand and Templeton, 1987; Falin, 1990;
Kulkani and Liang, 1997) and monographs by (Falin and Templeton 1997;
Artalejo and Gomez-Corral, 2008).
(Fayolle, 1986) considered an M/M/1 retrial queue, in which a customer
who finds the server busy joins the tail of a retrial queue. Only the customer
at the head of the orbit is allowed to attempt to receive service after an
exponentially distributed retrial time in competition with a new primary
customer. (Farhamand, 1996) called this discipline a retrial queue with FCFS
orbit. (Choi and al, 1992) generalized this retrial policy by considering an
M/M/1 retrial queue with general retrial times.
In this paper, we consider an [] //1 retrial queue with general retrial
time with two classes of customers, transit and recurrent customers, service
subject to random actives breakdowns and repairs. The customer whose
service is interrupted stays in the service, waiting for the first delay of
verification, repair and second delay of verification. After the second delay of
verification, this customer completes his service. We assume that after every
service completion, the server has the option to leave for a vacation of random
length with probability (1 − ) or to can serve the next customer with
probability r. The batch arrival who finds the server busy or failed or under the
1 or 2 delay of verification or repair or vacation are allowed to balk with
st
nd
probability 1 − or to stay in the system with probability in according with
F.C.F.S.

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