The two-machine one-buffer continuous time model with restart policy

This paper deals with the performance evaluation of production lines in which well defined machine start/stop control policies are applied.
A modeling approach has been developed in order to reduce the complexity of a two-machine one-buffer line where a specific control policy, called “restart policy”, is adopted. The restart policy exercises control over the start/stop condition of the first machine: when the buffer gets full and, as a consequence, the first machine is forced to stop production (i.e., it is blocked), the control policy keeps the first machine in an idle state until the buffer becomes empty again. The rationale behind this policy is to reduce the blocking frequency of the first machine, i.e. the probability that a blockage occurs on the first machine due to the buffer filling up. Such a control policy is adopted in practice when outage costs (e.g., waste production) are related to each restart of the machine.
The two-machine one-buffer line with restart policy (RP line) is here modeled as a continuous time Markov process so as to consider machines having different capacities and working in an asynchronous manner. The mathematical RP model is described along with its analytical solution. Then, the most critical line performance measures are derived and, finally, some numerical examples are reported to show the effects of such a policy on the blocking frequency of the first machine.