In recent years, there has been an increasing interest in the investigation of the retrial phenomenon in communication systems. Retrial queues are characterized by the feature that any arriving customer who finds the server busy on arrival joins a group of blocked customers called orbit and reapplies for getting served after random time intervals. Such situations arise in many practical problems such as computer and communication networks, including wireless networks, wavelength-routed optical networks, call centers, computer network streaming services at hot spots, e-mail systems, etc. For a detailed overview, we refer the readers to Falin and Templeton (1997) and Artalejo (1999).
In the retrial queues, the most usual retrial policy is the classical retrial policy, in which each source in orbit repeats its call after an exponentially distributed time with parameter a. So, the probability of a new arrival in the next interval (t, t + dt) is
nadt + o(dt), when the orbit size is n ³ 0. This type of retrial policy is used in modeling subscriber’s behavior in telephone networks. In the past years, another type of retrial policy, in which the time between two successive repeated attempts is independent of the number of customers in the orbit, is used. This type of retrial policy is called constant retrial policy, i.e., the retrial rate is n. This kind of retrial control policy is well known for the ALOHA protocol in communication systems. Other applications include local area networks, communication protocols, mobile systems (Fayolle, 1986; Choi
et al., 1992; and Shikata et al., 1999), etc. Recently, Artalejo and Gomez-Corall (1997) unified both models by defining a versatile retrial policy called linear retrial policy with rate (1 – dn0)n + na. This type of retrial policy has wide applications in computer and telecommunication networks (Artalejo and Gomez-Corall, 2008).
In retrial queueing system with feedback, when the service of a customer is not fulfilled, it may retry again and again until a successful service is completed. Retrial queueing systems with feedback have many practical applications in designing service systems and telecommunication systems. For example, in data transmission, a packet transmitted from the source to the destination may be returned and it may go on like that until the packet is finally transmitted. It was first studied by Takacs (1963). Later on, Choi and Kulkarni (1992) studied an M/G/1 retrial queue with feedback. An
M/M/c retrial queue with geometric loss and feedback was investigated by Choi et al. (1998). Krishna et al. (2002) discussed an M/G/1 retrial queue with feedback and starting failures using supplementary variable technique. Atencia and Moreno (2003) analyzed a single server feedback retrial queue with infinite buffer and linear retrial policy. Under the steady-state condition, the probability generating function of system size and decomposition law were discussed. Lee (2005) discussed an M/G/1 feedback retrial queue with two types of customers. Krishna and Raja (2006) studied the multiserver retrial queue with feedback and balking of customers. A multiserver feedback retrial queue with finite buffer was analyzed by Krishna et al. (2009). Recently, Do (2010) investigated a multiserver feedback retrial queue with large queueing capacity.
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