Exact analysis of asymmetric random polling systems with single buffers and correlated input process

We introduce a simple approach for modeling and analyzing asymmetric random polling systems with single buffers and correlated input process. We consider two variations of single buffers system: the conventional system and the buffer relaxation system. In the conventional system, at most one customer may be resided in any queue at any time. In the buffer relaxation system, a buffer becomes available to new customers as soon as the current customer is being served. Previous studies concentrate on conventional single buffer system with independent Poisson process input. It has been shown that the asymmetric system requires the solution of m(2^m − 1) linear equations; and the symmetric system requires the solution of 2^m−1 − 1 linear equations, where m is the number of stations in the system. For both the conventional system and the buffer relaxation system, we give the exact solution to the more general case and show that our analysis requires the solution of 2^m − 1 linear equations. For the symmetric case, we obtain explicit expressions for several performance measures of the system. These performance measures include the mean and second moment of the cycle time, loss probability, throughput, and the expected delay observed by a customer.