Fully Distributed Algorithms for Minimum Delay Routing Under Heavy Traffic

We study a minimum delay routing problem in the context of distributed networks with and without partial load information. Even though a general minimum delay routing problem is NP hard, assuming uniformly distributed \(K\) source-destination (SD) pairs at random, we provide a lower bound on the average delay and demonstrate by simulation that it is tight for a certain classes of regularly deployed networks. We also show that some routing in a distributed manner is enough to achieve asymptotically optimal load balancing with high probability as \(K\) tends to infinity. In order to set such routing, however, each SD pair should know global load information, which is unrealistic for most networks. We propose novel predetermined path routing algorithms in which each SD pair chooses its routing path only among a set of predetermined paths. We then propose an efficient way of distributed construction for predetermined paths that are able to distribute traffic over a network. Our predetermined path routing algorithms work in a fully distributed manner with very limited load information or without any load information. In various network models, we demonstrate by simulation that the delay of the predetermined path routing algorithms quickly converges to that of the distributed routing with global load information.