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[doc] Fix Sphinx error; use math for display equations

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This commit is contained in:
Peter D. Barnes, Jr.
2016-07-29 12:36:51 -07:00
parent 65d371e58e
commit ba14b00dc6
1 changed files with 26 additions and 20 deletions
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46
src/internet/doc/tcp.rst
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@@ -475,13 +475,15 @@ congestive and non-congestive states.
The backlog (the number of packets accumulated at the bottleneck queue) is
calculated using Equation (1):
.. math:: N &= Actual \cdot (RTT - BaseRTT) \\
&= Diff \cdot BaseRTT
.. math::
N &= Actual \cdot (RTT - BaseRTT) \\
&= Diff \cdot BaseRTT
where:
.. math:: Diff &= Expected - Actual \\
&= \frac{cWnd}{BaseRTT} - \frac{cWnd}{RTT}
.. math::
Diff &= Expected - Actual \\
&= \frac{cWnd}{BaseRTT} - \frac{cWnd}{RTT}
Veno makes decision on cwnd modification based on the calculated N and its
predefined threshold beta.
@@ -575,26 +577,30 @@ robustness against sudden fluctuations in its delay sampling,
Illinois allows the increment of alpha to alphaMax
only if da stays below d1 for a some (theta) amount of time.
::
/ alphaMax if da <= d1
alpha = (1)
\ k1 / (k2 + da) otherwise
/ betaMin if da <= d2
beta = k3 + k4da if d2 < da < d3 (2)
\ betaMax otherwise
.. math::
alpha &=
\begin{cases}
\quad alphaMax & \quad \text{if } da <= d1 \\
\quad k1 / (k2 + da) & \quad \text{otherwise} \\
\end{cases} \\
\\
beta &=
\begin{cases}
\quad betaMin & \quad \text{if } da <= d2 \\
\quad k3 + k4 \, da & \quad \text{if } d2 < da < d3 \\
\quad betaMax & \quad \text{otherwise}
\end{cases}
where the calculations of k1, k2, k3, and k4 are shown in the following:
.. math::
k1 &= \frac{(dm - d1) \cdot alphaMin \cdot alphaMax}{alphaMax - alphaMin}
k2 &= \frac{(dm - d1) \cdot alphaMin}{alphaMax - alphaMin} - d1
k3 &= \frac{alphaMin \cdot d3 - alphaMax \cdot d2}{d3 - d2}
k1 &= \frac{(dm - d1) \cdot alphaMin \cdot alphaMax}{alphaMax - alphaMin} \\
\\
k2 &= \frac{(dm - d1) \cdot alphaMin}{alphaMax - alphaMin} - d1 \\
\\
k3 &= \frac{alphaMin \cdot d3 - alphaMax \cdot d2}{d3 - d2} \\
\\
k4 &= \frac{alphaMax - alphaMin}{d3 - d2}
Other parameters include da (the current average queueing delay), and