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Top1. Introduction
Polling system is a system of multiple queues attended by a single server in a predetermined cyclic order. Polling systems have been extensively studied during the last six decades because they provide a meaningful mathematical model for performance evaluation of computer, communication, transportation and manufacturing systems that operate under are source sharing mechanism. According to the survey by Vishnevskii, & Semenova (2006), there are over 700 papers on polling systems published by 1996. The standard reference for polling systems is Takagi (1986). Boon, van der Mei & Winands (2011) and Grillo (1990) provides surveys of applications of polling systems. Furthermore, Shiozawa, Takine, Takahashi, & Hasegawa (1990) used polling systems with correlated customer arrival process to analyze a token ring with correlated input process. In response to the evolution of communication technology, some generalizations of polling systems have been considered. These generalizations deal with non-cyclic server allocation to queue policies which includes priority, random, Markovian server allocation policy, or more generally, non-deterministic server allocation policy. With respect to the buffer size at each queue, these generalizations of polling systems can further be classified as finite buffer or infinite buffer systems. Before introducing our model, we group the related literature on polling system deals with non-cyclic server allocation policies under the buffer system classification. For the infinite buffer case, see Kleinrock, & Levy (1988), Lee (1997), Boxma, & Weststrate (1989), Lye, & Seah (1992), Srinivasan (1991), Fayolle, & Lasgouttes (1995) and), Zorine (2014). For the finite buffer case, see Chung, Un, & Jung (1994), Lee (2013), Lee, & Sunjaya (1996) and Takine et al. (1988,1989,1990), Takagi (1985,1991). The finite buffer generalization of a polling system is a loss system. It is usually harder to analyze because provision for overflows have to be taken into consideration. In order to compute the system performance measures, one typically needs to solve a huge system of linear equations. Furthermore, previous studies of the single buffers multiple queues system tend to provide separate analysis depending on whether switchover time is needed when the server moves from one queue to another (i.e., zero or nonzero switchover times).