Single Path Routing with Delay Considerations 1 RAHUL

The importance of optimal routing arises in high traac networks where the average delay across a link is sensitive to the assignment of routes to source-destination pairs. The current single path routing algorithms do not take into account the eeects of routing multiple source-destination pairs over common links and, consequently, may not lead to a minimum delay allocation of routes. In this paper we formulate and study the problem of minimizing queueing delays by explicitly considering the impact of overlapping routes on links. The problem is shown to be NP-Complete. Speciically, we prove that the problem of nding a feasible solution is NP-Complete and thus no polynomial time approximation algorithms exist that provide solutions within a bounded distance from the optimum. Similar complexity results are shown when we consider the special case of a ring network and where it is desirable to minimize packet losses. We provide a polynomial time algorithm for constructing a minimum spanning tree within our routing model for the purpose of broadcasting. A new heuristic to minimize delays, the Sequential Minimum Costs algorithm is proposed for the case of a single source and multiple destinations.