Optimising node selection probabilities in multi-hop M/D/1 queuing networks to reduce latency of Tor

The expected cell latency for multi-hop M/D/1 queuing networks, where users choose nodes randomly according to some distribution, is derived. It is shown that the resulting optimisation surface is convex, and thus gradient-based methods can be used to find the optimal node assignment probabilities. This is applied to a typical snapshot of the Tor anonymity network at 50% usage, and leads to a reduction in expected cell latency from 11.7 ms using the original method of assigning node selection probabilities to 1.3 ms. It is also shown that even if the usage is not known exactly, the proposed method still leads to an improvement.