A new solution for a queueing model of a manufacturing cell with negative customers under a rotation rule

In this paper, we consider a queueing model extension for a manufacturing cell composed of a machining center and several parallel downstream production stations under a rotation rule. A queueing model is extended with the arrival processes of negative customers to capture failures of production stations, reorganization of works and disasters in the manufacturing cell. We present an exact solution for the steady-state probabilities of the proposed queueing model. The solution does not require the approximation of the infinite sum. In addition, it provides an alternative way to compute the rate matrix for the matrix-geometric method as well.