Tuesday, November 23, 2010

Minimum Loss

The paper "Routing Metrics and Protocols for Wireless Mesh Networks" explores the utility of various routing metrics. I was particularly interested in minimum loss (ML). It is interesting because of its simplicity, its performance, and its relationship to probability theory.

It is a simple metric, very much like expected transmission count (ETX). In the paper, the performance of ETX, ML, and two other metrics are compared. Performance was measured in four ways: Number of hops, loss rate, RTT, and throughput. ML consistently led to the highest number of hops, yet the lowest loss.

Throughput was measured from a starting node to each of the other mesh nodes in the network. For all metrics, there was a sharp drop off in throughput for all nodes which were more than one hop away from the starting node. It was interesting to me that this drop was much less pronounced for ML. The drop off curve for ML was much smoother. Throughput using ML for nodes two hops away from the starting node was about twice that of throughput using all other metrics.

The key difference between ETX and ML is multiplication as opposed to addition. When calculating ETX over multiple hops, total ETX is the sum of ETX for each hop. When calculating ML, total loss is the product of losses for each hop. It is interesting to me that the multiplication approach is similar to what is done in probability theory. Total probability of independent events is the product of each of the individual events.

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