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 take into account 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, we provide an alternative way to compute the rate matrix for the matrixgeometric method as well.