ONLINE ROUTING OF REAL-TIME MESSAGES

The problem of routing unit-length, real-time messages in a distribute d system is considered. An on-line routing algorithm is one, that rout es messages without any knowledge of future arrivals of messages. An o n-line algorithm is said to be optimal if it produces a feasible route whenever one exists. In this article, we study the issue whether it i s possible to have an optimal on-line algorithm for the following netw orks-unidirectional ring, out-tree, in-tree, bidirectional tree, and b idirectional ring. The problem is considered under various restriction s of the four parameters-origin node, destination node, release time, and deadline. We show that: (1) for a unidirectional ring, no such alg orithm can exist unless one of the four parameters is fixed (i.e., all messages have identical values for that parameter); (2) for an out-tr ee, no such algorithm can exist unless one of the three parameters-ori gin node, destination node, and release time-is fixed; (3) For an in-t ree, no such algorithm can exist unless one of the three parameters-or igin node, destination node, and deadline-is fixed; (4) for a bidirect ional tree, no such algorithm can exist unless the origin node or the destination node is fixed; (5) for a bidirectional ring, no such algor ithm can exist unless the origin node and either the destination node or the release time are fixed. Our results give a sharp boundary delin eating those instances for which an optimal algorithm exists and those for which no such algorithm can exist. (C) 1996 Academic Press, Inc.