Stable Priority Disciplines for Multiclass Networks

It is well known that a multiclass network may not be stable under the usual traffic condition that the arrived nominal workload is less than one. That this instability may happen in many “favorite” disciplines (such as first-in-first-out, shorted expected service times, and shorted expected remaining service times) has been the focus of many recent studies. In this paper, we address the stability issue from a different angle by asking: whether given any network satisfying the traffic condition, a simple priority discipline can be identified under which the network is guaranteed to be stable. We show this can be done under the condition of acyclic class transfer. This covers a wide class of networks, including all networks with a deterministic routing mechanism, such as re-entrant lines and Kelly networks.

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