Bounding delays in packet-routing networks
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Dynamic deflection routing on arrays (preliminary version)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Bounds on the greedy routing algorithm for array networks
Journal of Computer and System Sciences
Stability of adaptive and non-adaptive packet routing policies in adversarial queueing networks
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Queueing analysis of oblivious packet-routing networks
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Instability of FIFO in session-oriented networks
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
The effects of temporary sessions on network performance
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Adaptive packet routing for bursty adversarial traffic
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Journal of the ACM (JACM)
Universal-stability results and performance bounds for greedy contention-resolution protocols
Journal of the ACM (JACM)
A general approach to dynamic packet routing with bounded buffers
Journal of the ACM (JACM)
Universal stability of undirected graphs in the adversarial queueing model
Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures
General Dynamic Routing with Per-Packet Delay Guarantees of O(Distance + 1/Session Rate)
SIAM Journal on Computing
From Static to Dynamic Routing: Efficient Transformations of Store-and-Forward Protocols
SIAM Journal on Computing
Stability of Adversarial Queues via Fluid Models
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Source Routing and Scheduling in Packet Networks
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
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A growing amount of work has been invested in recent years in analyzing packet-switching networks under worst-case scenarios rather than under probabilistic assumption. Most of this work makes use of the model of "adversarial queuing theory" proposed by Borodin et al. [J. ACM 48 (1) (2001) 13-38], under which an adversary is allowed to inject into the network any sequence of packets as long as--roughly speaking--it does not overload the network.We show that the protocol Longest In System, when applied to directed acyclic graphs, uses buffers of only linear size (in the length of the longest path in the network). Furthermore, we show that any packet incurs only linear delay as well. These are, to the best of our knowledge, the first deterministic polynomial bounds on queue sizes and packet delays in the framework of adversarial queuing theory (other than on trees and the cycle). Furthermore these results separate Longest In System from other common universally stable protocols for which there exist exponential lower bounds that are obtained on DAGs. Our upper bounds are complemented by matching linear lower bounds on buffer sizes and packet delays.