The performance of simple routing algorithms that drop packets
Proceedings of the ninth annual ACM symposium on Parallel algorithms and architectures
Scheduling time-constrained communication in linear networks
Proceedings of the tenth annual ACM symposium on Parallel algorithms and architectures
From static to dynamic routing: efficient transformations of store-and-forward protocols
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Locally efficient on-line strategies for routing packets along fixed paths
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Journal of the ACM (JACM)
Universal-stability results and performance bounds for greedy contention-resolution protocols
Journal of the ACM (JACM)
Dynamic routing on networks with fixed-size buffers
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Tight Bounds for the Performance of Longest-in-System on DAGs
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Design and Analysis of Dynamic Processes: A Stocastic Approach
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Asynchronous throughput-optimal routing in malicious networks
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
The network as a storage device: dynamic routing with bounded buffers
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
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We prove a sufficient condition for the stability of dynamic packet routing algorithms. Our approach reduces the problem of steady state analysis to the easier and better understood question of static routing. We show that certain high probability and worst case bounds on the quasistatic (finite past) performance of a routing algorithm imply bounds on the performance of the dynamic version of that algorithm. Our technique is particularly useful in analyzing routing on networks with bounded buffers where complicated dependencies make standard queuing techniques inapplicable. We present several applications of our approach. In all cases we start from a known static algorithm, and modify it to fit our framework. In particular we give the first dynamic algorithm for routing on a butterfly with bounded buffers. Both the injection rate for which the algorithm is stable, and the expected time a packet spends in the system are optimal up to constant factors. Our approach is also applicable to the recently introduced adversarial input model.