The Necessity of Timekeeping in Adversarial Queueing
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.
KeywordsCentral Node Queue Size Transportation Time Priority Function Extra Node
Unable to display preview. Download preview PDF.
- 1.Adler, M., Rosen, A.: Tight Bounds for the Performance of Longest in System on DAGs. In: Proc. of the 19th Symposium on Theoretical Aspects of Computer Science, pp. 88–99 (2002)Google Scholar
- 3.Andrews, M., Fernández, A., Goel, A., Zhang, L.: Source Routing and Scheduling in Packet Networks. In: Proc. of the 42nd Symposium on Foundations of Computer Science, pp. 168–177 (2001)Google Scholar
- 4.Andrews, M., Zhang, L.: The Effects of Temporary Sessions on Network Performance. SIAM Journal of Computation 33(3), 659–673Google Scholar
- 5.Bhattacharjee, R., Goel, A.: Instability of FIFO at arbitrarily low rates in the adversarial queueing model. In: Proc. of the 44th Symposium on Foundations of Computer Science, pp. 160–167 (2003)Google Scholar
- 8.Koukopoulos, D., Mavronicolas, M., Spirakis, P.: FIFO is Unstable at Arbitrarily Low Rates (Even in Planar Networks). Electronic Colloq. on Computational Complexity (2003)Google Scholar
- 9.Rosén, A., Tsirkin, M.S.: On Delivery Times in Packet Networks under Adversarial Traffic. In: Proceedings of the 16th ACM Symposium on Parallelism in Algorithms and Architectures, pp. 1–10 (2004)Google Scholar