William T. Zaumen

Loop-free multipath routing using generalized diffusing computations

A new distributed algorithm for the dynamic computation of multiple loop-free paths from source to destination in a computer network or Internet are presented, validated, and analyzed. According to this algorithm, which is called DASM (diffusing algorithm for shortest multipath), each router maintains a set of entries for each destination in its routing table, and each such entry consists of a set of tuples specifying the next router and distance in a loop-free path to the destination. DASM guarantees instantaneous loop freedom of multipath routing tables by means of a generalization of Dijkstra and Scholtens diffusing computations. With generalized diffusing computations, a node in a directed acyclic graph (DAG) defined for a given destination has multiple next nodes in the DAG and is able to modify the DAG without creating a directed loop. DASM is shown to be loop-free at every instant, and its average performance is analyzed by simulation and compared against an ideal link-state algorithm and the diffusing update algorithm (DUAL).

Load-balanced anycast routing in computer networks

We present a practical approach to routing and anycasting with near-optimum delays taking into account the processing loads at routers and processing elements of a computer network. To accomplish this, the minimum-delay routing problem formulated by Gallager (1977) is generalized into the problem of minimum-delay routing with load-balancing to account for processing delays in network nodes (servers and routers). Gallagers theorem for necessary and sufficient conditions for minimum-delay routing is modified to include processing delays and changes of traffic levels at network nodes. The first distributed algorithm for load-balanced anycasting and routing in computer networks is presented. This algorithm, named MIDAS, provides approximate solutions to the modified necessary and sufficient conditions for minimum-delay routing. Simulations are use to compare the performance of the new algorithm with the performance of a traditional approach to sever load balancing.

Area-based, loop-free internet routing

The diffusing update algorithms (DUAL) constitute a family of distributed routing algorithms that has been shown to be loop-free at every instant, to converge after an arbitrary sequence of link-cost or topological changes, and to outperform all other loop-free routing algorithms previously proposed from the standpoint of the combined temporal, message, and storage complexities. Two hierarchical routing schemes based on DUAL are presented to make it more applicable to very large internets. A scheme based on McQuillans (1974, 1980) hierarchical routing scheme and a backbone-oriented scheme, similar to the one used in OSPF, are introduced to reduce the amount of routing information maintained at each router. The performance of these schemes is compared by simulation to the performance of the basic DUAL, an ideal routing algorithm based on topology broadcast, and OSPF. The simulation results suggest that DUAL with areas outperforms OSPF, and provide additional insight on the performance of OSPF, EIGRP, and area-based routing algorithms in general.<<ETX>>

Steady-state response of shortest-path routing algorithms

The steady-state response of link-state and loop-free distance-vector routing algorithms to multiple changes in the costs of links is investigated. A quantitative comparison of an ideal link-state algorithm similar to the one used in the open shortest path first (OSPF) and in the OSI intradomain routing protocol, and a new loop-free distance-vector algorithm, is made for several computer network topologies. A variety of quantities, including the length of messages and the average number of paths affected by routing loops, are computed as a function of time after a link or node change. Probabilities of various conditions, including the existence of loops, are also obtained as a function of time. The results show that in steady state, a loop-free distance-vector algorithm operates with essentially the same communication overhead as the ideal link state algorithm, and requires substantially fewer CPU cycles. The results also suggest that it may be possible to correlate the performance of the routing algorithms with various parameters that can be used to characterize networks.<<ETX>>