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Top1. Introduction
Retrial queues (or queues with repeated attempts) are characterized by the feature that a customer that finds, upon arrival, the server busy, is obliged to leave the service area and repeat his demand for service after some time called “retrial time.” Between trials, the blocked customer joins a pool of unsatisfied customers called “orbit.” Queues in which customers are allowed to conduct retrials have been widely used to model many practical problems in telephone switching systems, telecommunication networks and computers competing to gain service from a central processing unit. Moreover, retrial queues are also used as mathematical models for several computer systems such as packet switching networks, shared bus local area networks operating under the carrier-sense multiple access protocol and collision avoidance star local area networks etc. For a review of the main results and methods, the reader is referred to the survey papers of Yang and Templeton (1987), Falin (1990), Kulkarni and Liang (1997) and the book by Falin and Templeton (1997). For more recent references, see the bibliographical overviews in (Artalejo 2010; Artalejo, 1999; Artalejo, 1999). Further, a comprehensive comparison between retrial queues and their standard counterparts with classical waiting lines can be found in Artalejo and Falin (2002).
Many of the queueing systems with repeated attempts operate under the classical retrial policy, where each block of customers generates a stream of repeated attempts independently of the rest of the customers in the orbit, i.e., the intervals between successive repeated attempts are exponentially distributed with rate 
(say), when the number of customers in the orbit is n. However, there is a second kind of policy, called constant retrial policy, which arises naturally in problems where the server is required to search for customers (Sengupta 1990) and in communication protocols of type carrier sense multiple access (CSMA). The latter discipline was introduced by Fayolle (1986), who investigated an M/M/1 retrial queue in which the repeat customers form a queue and only the head customers of the orbit queue can request a service after an exponentially distributed retrial time with some parameter γ (say), i.e., the retrial rate is 
, where 
denotes the Kronecker’s delta, when the number of units in the orbit is n. Farahmand 1990) called this discipline a retrial queue with FCFS orbit retrial policy. Choi et al. (1992) generalized this retrial policy by considering an M/M/1 retrial queue with general retrial times. Artalejo and Gomez-Corral (1997) introduced a more general kind of retrial incorporating both possibilities by assuming that when there are n customers in the system, the time intervals between successive repeated attempts are exponentially distributed random variables with parameter 
, where θ can be considered as the retrial per customer and γ the rate at which the server seeks service for customers whenever it is idle. Such a type of retrial policy is known as a linear retrial policy. Recently, Choudhury (2008) investigated such a queueing model for two phases of service under Bernoulli vacation schedule.