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This work investigates the machine interference problems in robot-served manufacturing systems using a stochastic approach for modelling the system. Two new parameters are introduced: the robot availability parameter and the machine stoppage. The problem is modelled for both priority and no-priority situations. The models are analysed to obtain an evaluation for the system's performance of machine efficiencies and robot utilizations that reflect the behaviour of the system under given conditions. Also, the models are evaluated to determine the optimum number of machines that can be located within a manufacturing cell.