This analysis has been done using the result of the Session 3 experiments.

The session 3 parameters are based on the session 1 parameters, but the peering degrees ($C$) are determined probabilistically as defined in the session 3 of the dissemination time experiment. The main difference between the two sessions is that, in session 3, there are hotspot nodes that are connected to much more peers than others.

We use the same parameter $N$ (the number of mixes) defined in the session 1 to compare results accurately. Since the $N$ of the session 1 is 32 at the maximum, which is much smaller than the one in the session 3 of the dissemination time experiment ($10^5$), the peering degree parameter was redefined as below. Also, the $N$ is fixed to 32 to reduce the experiment time.

$N=32$

$C = \{ 2:87\%; 12: 12.3\%; 24:0.7\% \}$

Later, this experiment can be rerun with the larger $N=10^5$ as defined in the session 3 of the dissemination time experiment to simulate the network similar as the real network example (Monero).

Raw Statistical Results

Latency Comparison

This section compares the latency results between the session 1 and 3 to see the impact of hotspots in the network for each queue type.

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In all mix queue types, the average latency in the session 3 is 2~3x longer than the session 1, even though the average hops for messages to arrive in the receiver is shorter in the session 3. It is because of a large number of data messages staying in the queues in the session 3. The following table shows the number of data messages staying in the queue at each time frame. Although the table doesn’t show the statistics of only hotspot nodes, the average number of data messages in queues is higher in the session 3.

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Ordering Coefficient Comparison

This section compares the ordering coefficients between the session 1 and 3 to see the impact of hotspots in the network for each queue type.

According to the results below, NonMix and PureCoinFlipping show higher average ordering coefficients in the session 3 compared to the session 1. But, PureRandomSampling and PermutedCoinFlipping have almost the same ordering coefficients in both sessions. On the other hand, NoisyCoinFlipping has lower ordering coefficients in the session 3.

It's not easy to understand the correlation between the coefficients and the hotspots in the network from these results alone, but we can see that PureRandomSampling and PermutedCoinFlipping, which performed well in the session 1, are still performing well in this session.

Strong Ordering Coefficients

Casual Ordering Coefficients

Weak Ordering Coefficients