On the characterization of departure rules for discrete-time queueing networks with batch movements and its applications

This paper supplements and generalizes the results of nOsawa in this special issue from the viewpoint of discrete-time networks of queues with batch arrivals and batch departures, due to Henderson and Taylor. It first notes that the D-rule of nOsawa is equivalent to the specific form for the release rate function, introduced by Henderson and Taylor. Such forms have widely appeared in the literature, too. nOsawa found that the D-rule can be characterized in terms of the reversed-time process of a certain vector-valued process. nOsawa obtained this characterization for a single node model. The paper generalizes this result for networks of queues with batch arrivals and batch departures. This reveals why the specific form of the release rate function is common in the literature. Furthermore, the characterization is useful to consider traffic flows in a discrete-time queueing network.