This paper describes an unreliable server batch arrival retrial queue with two types of
repair and second optional service. The server provides preliminary first essential
service (FES) to the primary arriving customers or customers from retrial group. On
successful completion of FES, the customer may opt for second optional service (SOS) with
probability α. The server is subject to active break downs. The customer
under FES (or SOS) during the failure decides, with probability q, to
join the orbit(impatientcustomer) and, with complementary probability
p, to remain in the server for repair in order to conclude his
remaining service (patientcustomer). Both service and repair times are
assumed to have general distribution. It is considered that the repair time of server
during the presence of patient customer and the repair time of the server while the
customer (impatientcustomer) joining the orbit due to failure, are
different. For this queueing system, the orbit and system size distributions are obtained.
Reliability of the proposed model is analysed. Some particular cases are also discussed.
Other performance measures are also obtained. The effects of several parameters on the
system are analysed numerically.