Unified analysis of BMAP/G/1 cyclic polling models

In this paper we present a unified analysis of the BMAP/G/1 cyclic polling model and its application to the gated and exhaustive service disciplines as examples. The applied methodology is based on the separation of the analysis into service discipline independent and dependent parts. New expressions are derived for the vector-generating function of the stationary number of customers and for its mean in terms of vector quantities depending on the service discipline. They are valid for a broad class of service disciplines and both for zero- and nonzero-switchover-times polling models. We present the service discipline specific solution for the nonzero-switchover-times model with gated and exhaustive service disciplines. We set up the governing equations of the system by using Kronecker product notation. They can be numerically solved by means of a system of linear equations. The resulting vectors are used to compute the service discipline specific vector quantities.