Owner: @Youngjoon Lee
Introduction
These analyses were done by the results of:
All the following analyses are for the PermutedCoinFlipping queue that was chosen by the Ordering Experiments: The Primary Queuing Mechanism.
In this document, we will first see the impact of each parameter on the latency and the quality of mixing, in order to find a few reasonable candidate values. And then, we will try to find several combinations of parameters that meet our requirement for latency and bandwidth, using those candidate values.
Understanding the Impact of Parameters
The impact of $\Rho$
- $\Rho$: How often the sender generates a new data message, each time sending a message to each connection.
- $\Rho$ affects latency when $M$ is low. If $M$ is high, the impact of $\Rho$ is low.
- $\Rho$ and the ordering coefficients are proportionally.
- However, $\Rho$ is like a constant which depends on the consensus protocol and is likely to be low (under 1%).
| $G$ |
$C$ |
$\Rho$ |
$M$ |
latency_mean |
strong_coeff_mean |
casual_coeff_mean |
weak_coeff_mean |
| 32 |
4 |
0.01 |
0.015625 |
8 |
0.0 |
0.0 |
0.9 |
| 32 |
4 |
0.1 |
0.015625 |
8 |
2.7 |
4.2 |
40.2 |
| 32 |
4 |
0.5 |
0.015625 |
19 |
35.2 |
34.4 |
72.0 |
| 32 |
4 |
0.01 |
0.03125 |
31 |
0.0 |
0.0 |
0.4 |
| 32 |
4 |
0.1 |
0.03125 |
141 |
0.2 |
0.2 |
1.9 |
| 32 |
4 |
0.5 |
0.03125 |
776 |
1.6 |
1.6 |
3.3 |
| 32 |
4 |
0.01 |
0.0625 |
1606 |
0.0 |
0.0 |
0.0 |
| 32 |
4 |
0.1 |
0.0625 |
1771 |
0.0 |
0.0 |
0.2 |
| 32 |
4 |
0.5 |
0.0625 |
2829 |
0.4 |
0.4 |
1.1 |
The impact of $M$
- $M$: How often a mix node generates a new cover traffic (a fake data message), each time sending a message to each connection.
- $M$ affect latency significantly. It seems that latency increases exponentially as $M$ increases. Also, it depends on $C$. If $C$ is high, the increment is also high because the queues grow faster, even though $C$ and latency are inversely proportional.
- The impact of $M$ on ordering coefficients is not so high because PermutedCoinFlipping already has a good quality of mixing.
- If $M≥3\%$, strong/casual/weak coefficients are already under 1, regardless of $\Rho$.
- If $M=1\%$, strong/casual/weak coefficients are under 1, if $\Rho=1\%$.
- If $\Rho=10\%$, coefficients are 2~40, which are quite high. But, $\Rho$ is going to be very low, as mentioned above.
- Thus, it seems that it is reasonable to set $M$ to $1\%$ for now, which gives a low latency and low ordering coefficients, with an assumption that $\Rho=1\%$.
- Actually, $\Rho=1\%$ is still too high, as mentioned above. But, we will move forward with this value because that is what we have used in the experiments. Later, we can re-run the experiments with a more realistic value (or by devising a more realistic parameter).