- English (3) (remove)
- The necessity of timekeeping in adversarial queueing (2005)
- We study queueing strategies in the adversarial queueing model. Rather than discussing individual prominent queueing strategies we tackle the issue on a general level and analyze classes of queueing strategies. We introduce the class of queueing strategies that base their preferences on knowledge of the entire graph, the path of the packet and its progress. This restriction only rules out time keeping information like a packet's age or its current waiting time. We show that all strategies without time stamping have exponential queue sizes, suggesting that time keeping is necessary to obtain subexponential performance bounds. We further introduce a new method to prove stability for strategies without time stamping and show how it can be used to completely characterize a large class of strategies as to their 1-stability and universal stability.
- The effects of local randomness in the adversarial queueing model (2008)
- We study the effect of randomness in the adversarial queueing model. All proofs of instability for deterministic queueing strategies exploit a finespun strategy of insertions by an adversary. If the local queueing decisions in the network are subject to randomness, it is far from obvious, that an adversary can still trick the network into instability. We show that uniform queueing is unstable even against an oblivious adversary. Consequently, randomizing the queueing decisions made to operate a network is not in itself a suitable fix for poor network performances due to packet pileups.
- Deciding the FIFO stability of networks in polynomial time (2005)
- FIFO is the most prominent queueing strategy due to its simplicity and the fact that it only works with local information. Its analysis within the adversarial queueing theory however has shown, that there are networks that are not stable under the FIFO protocol, even at arbitrarily low rate. On the other hand there are networks that are universally stable, i.e., they are stable under every greedy protocol at any rate r < 1. The question as to which networks are stable under the FIFO protocol arises naturally. We offer the first polynomial time algorithm for deciding FIFO stability and simple-path FIFO stability of a directed network, answering an open question posed in [1, 4]. It turns out, that there are networks, that are FIFO stable but not universally stable, hence FIFO is not a worst case protocol in this sense. Our characterization of FIFO stability is constructive and disproves an open characterization in .