Andrei Z. Broder
Alan M. Frieze
Abstract
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 quasi-static (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 dependices 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 algorithms for routing on a butterfly or two-dimensional mesh 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.
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Index Terms
- A general approach to dynamic packet routing with bounded buffers
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Reviews
Xiangyu Sally Song
This paper deals with dynamic packet routing in networks with bounded buffers at the switching nodes. It accurately models the real network. The analysis of routing algorithm has previously been largely focused on static routing while there are some recent studies on dynamic routing but with unbounded buffer. These approaches simplify the analysis at the cost of a less realistic model. This paper proposes a unique approach to reduce the problem of dynamic routing to the easier and better understood problem of static routing. The major contribution of this paper is the proof of a theorem on stability. This theorem defines a set of relatively simple and sufficient conditions such that if the routing algorithm satisfies them, then the network is stable up to a certain interarrival rate. Furthermore, the expected time a packet spending in the queue and in the network is bounded and formulated as the function of the interarrival distribution. The authors then obtain dynamic routing algorithm by conveniently modifying the prior results on static routing to satisfy the stability criterion. The dynamic versions of the static routing algorithms for 6 comprehensive scenarios are derived. It is shown that the expected time a packet spending in the system deviates from the optimum up to constant factors. At the end, this paper successfully extends this approach to the recently introduced adversarial input model. This paper is concisely written and well organized. Researchers and network designers will benefit from this unique approach. A comprehensive list of reference is included.
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