Stability Preserving Transformations: Packet Routing Networks with Edge Capacities and Speeds

Abstract

In the context of an adversarial input model, we consider the effect on "universal" stability results when edges in packet routing networks can have capacities and speeds/slowdowns. A packet routing scheduling rule is universally stable if it is stable for any network and a network is universally stable if every "greedy" scheduling rule is stable on this network. In traditional packet routing networks, every edge is considered to have the same unit capacity and unit speed. We consider both static modifications (i.e. where the capacity or speed of an edge is fixed) and dynamic modifications where either the capacity or the speed of an edge can be dynamically changing over time. Amongst our results, we show that the universal stability of LIS (i.e. Longest in System packet gets highest priority) is not preserved when either the capacity or the speed is changing dynamically whereas many other common scheduling protocols do maintain their universal stability. The situation for static modifications is not as clear but we are able to show that (in contrast to the dynamic case) that any "well defined" universally stable scheduling rule maintains its universality under static capacities, and common scheduling rules also maintain their universal stability under static speeds. In terms of universal stability of networks, stability is preserved for dynamically changing capacities and speeds.