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

Abstract

This paper supplements and generalizes the results of Ōsawa [11] in this special issue from the viewpoint of discrete-time networks of queues with batch arrivals and batch departures, due to Henderson and Taylor [7]. We first note that the D-rule of Ōsawa [11] is equivalent to the specific form for the release rate function, introduced in [7]. Such forms have widely appeared in the literature, too. Ōsawa [11] found that the D-rule can be characterized in terms of the reversed-time process of a certain vector-valued process. He obtained this characterization for a single node model. We generalize 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.