Generating Control Policies for Timed Discrete-Event Systems through Efficient State Space Exploration
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Production systems are event driven and require knowledge of timing of events across all elements of the system particularly when developing policies for production control. A suite of time-dependent models are derived for a class of discrete systems, in particular, an N-Server, N+1-Buffer sequential line. First, time-dependent models for buffers and servers are derived. From the time-dependent server and buffer arrival and departure models the maximum number of entities any buffer in the serial line will experience across all times is derived. One assumption is then relaxed, thereby reducing the capacity of a queue. The transition and block times for all queues and servers are derived and time-dependent models for server and queue arrivals and departures are developed. Lastly, a buffer cluster concept is proposed and a time based parametric model is derived that determines the sizing of the buffer cluster. A reduced time space for which to search for the buffer cluster sizing is derived and a model that determines an optimal buffer clustering policy is presented. Real world production examples are used to illustrate where the models are utilized and discuss several additional applications and benefits of the models.