Queue reduction in discrete-event systems by relabeling

The customer population of entities potentially requesting to join a queue for service often have identical structure, i.e., the same state set and isomorphic transitions. The state size of the automaton modeling a queue will grow rapidly with increase of the size of this population. However, by relabeling the queue arrival events and service events to the same symbols respectively, the automaton model of a queue will be converted to the structure of a buffer, which is proved to be independent of the total size of the customer population, as long as the queue size is held fixed. We propose the model of a dynamic buffer to embody order and shift of a queue. The result is applied to a manufacturing facility with a dynamic buffer to manage the repair of broken down machines.