Simple error bounds for the QBD approximation of a special class of two dimensional reflecting random walks

Abstract: This paper considers the QBD approximation of a special class of two-dimensional reflecting random walks (2D-RRWs). A typical example of the 2D-RRWs is a two-node Jackson network with cooperative servers. The main contribution of this paper is to provide simple upper bounds for the relative absolute difference between the time-averaged functionals of the original 2D-RRW and its QBD approximation.