On routing algorithms with end-to-end delay guarantees

We consider the transmission of a message of size r from a source to a destination over a computer network with n nodes and m links. There are three sources of delays: (a) propagation delays along the links, (b) delays due to bandwidth availability on the links, and (c) queuing delays at the intermediate nodes. First, we consider that the delays on various links and nodes are given as functions of the message size. If the delay in (b) is a non-increasing function of the bandwidth, we propose O(m²+mn log n) time algorithm to compute a path with the minimum end-to-end delay for any given message size r. We then consider that the queuing delay in (c) is a random variable correlated with the message size according to an unknown distribution. At each node, the measurements of queuing delays and message sizes are available. We propose two algorithms to compute paths whose delays are close to optimal delays with a high probability, irrespective of the distribution of the delays