Universal stability results for greedy contention-resolution protocols

In this paper we analyze the behavior of communication networks in which packets are generated dynamically at the nodes and routed in discrete time steps across the edges. We focus on a basic adversarial model of packet generation and path determination for which the time-averaged injection rate of packets requiring the use of any edge is limited to be less than 1. A crucial issue that arises in such a setting is that of stability-will the number of packets in the system remain bounded, as the system runs for an arbitrarily long period of time? Among other things, we show: (i) There exist simple greedy protocols that are stable for all networks. (ii) There exist other commonly-used protocols (such as FIFO) and networks (such as arrays and hypercubes) that are not stable. (iii) The n-node ring is stable for all greedy routing protocols (with maximum queue-size and packet delay that is linear in n). (iv) There exists a simple distributed randomized greedy protocol that is stable for all networks and requires only polynomial queue size. Our results resolve several questions posed by Borodin et al. and provide the first examples of (i) a protocol that is stable for all networks, and (ii) a protocol that is not stable for all networks