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Fix figure for hops and bandwidth amplification w.r.t. corrected Equation 1 #94

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Fix figure for hops and bandwidth amplification w.r.t. corrected Equation 1 #94

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1687527
Fix plots
alrevuelta Mar 4, 2024
0e2eb3a
Add tikz raws for plots
alrevuelta Mar 4, 2024
37d788e
style fixes for message hops plot
s-tikhomirov Mar 5, 2024
3ae10e3
truncate X axis at 14 instead of 15 in message_hops plot
s-tikhomirov Mar 5, 2024
9177d9b
simplified message propagation figure (via Mathcha)
s-tikhomirov Mar 5, 2024
d14e38d
correct hops formula and figure
s-tikhomirov Mar 13, 2024
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11 changes: 11 additions & 0 deletions rln-delay-simulations/mesh1.svg
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83 changes: 83 additions & 0 deletions rln-delay-simulations/mesh1.txt
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Original file line number Diff line number Diff line change
@@ -0,0 +1,83 @@



\tikzset{every picture/.style={line width=0.75pt}} %set default line width to 0.75pt

\begin{tikzpicture}[x=0.75pt,y=0.75pt,yscale=-1,xscale=1]
%uncomment if require: \path (0,300); %set diagram left start at 0, and has height of 300

%Straight Lines [id:da4934880244897565]
\draw (400,153) -- (393,57) ;
%Straight Lines [id:da723556660409191]
\draw (284,54) -- (393,57) ;
%Straight Lines [id:da5174629846708867]
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\draw [shift={(400,153)}, rotate = 130.05] [color={rgb, 255:red, 208; green, 2; blue, 27 } ,draw opacity=1 ][line width=1.5] (14.21,-4.28) .. controls (9.04,-1.82) and (4.3,-0.39) .. (0,0) .. controls (4.3,0.39) and (9.04,1.82) .. (14.21,4.28) ;
%Straight Lines [id:da10632733185156851]
\draw [color={rgb, 255:red, 208; green, 2; blue, 27 } ,draw opacity=1 ][line width=1.5] (246,109) -- (340.06,219.71) ;
\draw [shift={(342,222)}, rotate = 229.65] [color={rgb, 255:red, 208; green, 2; blue, 27 } ,draw opacity=1 ][line width=1.5] (14.21,-4.28) .. controls (9.04,-1.82) and (4.3,-0.39) .. (0,0) .. controls (4.3,0.39) and (9.04,1.82) .. (14.21,4.28) ;
%Straight Lines [id:da6816754056928209]
\draw (172,69) -- (284,54) ;
%Straight Lines [id:da3114584919767631]
\draw [color={rgb, 255:red, 208; green, 2; blue, 27 } ,draw opacity=1 ][line width=1.5] (162,221) -- (244.2,111.4) ;
\draw [shift={(246,109)}, rotate = 126.87] [color={rgb, 255:red, 208; green, 2; blue, 27 } ,draw opacity=1 ][line width=1.5] (14.21,-4.28) .. controls (9.04,-1.82) and (4.3,-0.39) .. (0,0) .. controls (4.3,0.39) and (9.04,1.82) .. (14.21,4.28) ;
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\draw [color={rgb, 255:red, 208; green, 2; blue, 27 } ,draw opacity=1 ][line width=1.5] (109,121) -- (160.6,218.35) ;
\draw [shift={(162,221)}, rotate = 242.08] [color={rgb, 255:red, 208; green, 2; blue, 27 } ,draw opacity=1 ][line width=1.5] (14.21,-4.28) .. controls (9.04,-1.82) and (4.3,-0.39) .. (0,0) .. controls (4.3,0.39) and (9.04,1.82) .. (14.21,4.28) ;
%Straight Lines [id:da1160123650538184]
\draw (109,121) -- (172,69) ;
%Shape: Circle [id:dp9504268279106153]
\draw [fill={rgb, 255:red, 126; green, 211; blue, 33 } ,fill opacity=1 ] (99,121) .. controls (99,115.48) and (103.48,111) .. (109,111) .. controls (114.52,111) and (119,115.48) .. (119,121) .. controls (119,126.52) and (114.52,131) .. (109,131) .. controls (103.48,131) and (99,126.52) .. (99,121) -- cycle ;
%Shape: Circle [id:dp7615839499489241]
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%Shape: Circle [id:dp2513149049450848]
\draw [fill={rgb, 255:red, 126; green, 211; blue, 33 } ,fill opacity=1 ] (162,69) .. controls (162,63.48) and (166.48,59) .. (172,59) .. controls (177.52,59) and (182,63.48) .. (182,69) .. controls (182,74.52) and (177.52,79) .. (172,79) .. controls (166.48,79) and (162,74.52) .. (162,69) -- cycle ;
%Shape: Circle [id:dp3609119747418006]
\draw [fill={rgb, 255:red, 126; green, 211; blue, 33 } ,fill opacity=1 ] (236,109) .. controls (236,103.48) and (240.48,99) .. (246,99) .. controls (251.52,99) and (256,103.48) .. (256,109) .. controls (256,114.52) and (251.52,119) .. (246,119) .. controls (240.48,119) and (236,114.52) .. (236,109) -- cycle ;
%Shape: Circle [id:dp3150817269332429]
\draw [fill={rgb, 255:red, 126; green, 211; blue, 33 } ,fill opacity=1 ] (332,222) .. controls (332,216.48) and (336.48,212) .. (342,212) .. controls (347.52,212) and (352,216.48) .. (352,222) .. controls (352,227.52) and (347.52,232) .. (342,232) .. controls (336.48,232) and (332,227.52) .. (332,222) -- cycle ;
%Shape: Circle [id:dp17007111937841257]
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%Shape: Circle [id:dp5244384292008021]
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%Shape: Circle [id:dp8612461852143007]
\draw [fill={rgb, 255:red, 126; green, 211; blue, 33 } ,fill opacity=1 ] (390,153) .. controls (390,147.48) and (394.48,143) .. (400,143) .. controls (405.52,143) and (410,147.48) .. (410,153) .. controls (410,158.52) and (405.52,163) .. (400,163) .. controls (394.48,163) and (390,158.52) .. (390,153) -- cycle ;

% Text Node
\draw (94,84) node [anchor=north west][inner sep=0.75pt] {$P_{1}$};
% Text Node
\draw (158,31) node [anchor=north west][inner sep=0.75pt] {$P_{2}$};
% Text Node
\draw (150,230.4) node [anchor=north west][inner sep=0.75pt] {$P_{3}$};
% Text Node
\draw (233,69) node [anchor=north west][inner sep=0.75pt] {$P_{4}$};
% Text Node
\draw (330.4,230.8) node [anchor=north west][inner sep=0.75pt] {$P_{5}$};
% Text Node
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% Text Node
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% Text Node
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% Text Node
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% Text Node
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% Text Node
\draw (273.2,164) node [anchor=north west][inner sep=0.75pt] [color={rgb, 255:red, 208; green, 2; blue, 27 } ,opacity=1 ] {$_{5}^{4} L_{t}$};
% Text Node
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% Text Node
\draw (153,176.6) node [anchor=north west][inner sep=0.75pt] [color={rgb, 255:red, 208; green, 2; blue, 27 } ,opacity=1 ] {$L_{v}^{3}$};
% Text Node
\draw (236,126) node [anchor=north west][inner sep=0.75pt] [color={rgb, 255:red, 208; green, 2; blue, 27 } ,opacity=1 ] {$L_{v}^{4}$};
% Text Node
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% Text Node
\draw (399,112) node [anchor=north west][inner sep=0.75pt] [color={rgb, 255:red, 208; green, 2; blue, 27 } ,opacity=1 ] {$L_{v}^{8}$};
% Text Node
\draw (120,110) node [anchor=north west][inner sep=0.75pt] [color={rgb, 255:red, 208; green, 2; blue, 27 } ,opacity=1 ] {$L_{g}$};


\end{tikzpicture}

40 changes: 23 additions & 17 deletions rln-delay-simulations/message_hops.py
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Original file line number Diff line number Diff line change
Expand Up @@ -12,9 +12,12 @@

def delay_last_hop(n, d, l):
# multiply by l for latencies
return ceil(log(n)/log(d))
numerator = log(((n - 1) * (d - 2) / d) + 1)
denominator = log(d - 1)
return ceil(numerator / denominator)

ds = np.arange(2,15)

ds = np.arange(3,15)
ls = np.ones(len(ds))*L

# astype(int) is ok since ceil() returns integers
Expand All @@ -26,22 +29,25 @@ def delay_last_hop(n, d, l):
fig, ax1 = plt.subplots()
ax2 = ax1.twinx()

ax1.plot(ds, delays_1, color='r', label=r"$N_1=$"+str(N1))
ax1.plot(ds, delays_2, color='g', label=r"$N_2=$"+str(N2))
ax1.plot(ds, delays_3, color='b', label=r"$N_3=$"+str(N3))
ax2.plot(ds, ds, color='y', label="Bandwidth ampl.")
print(delays_1)
print(ds)
ax1.plot(ds, delays_1, color='r', label=str(N1)+" nodes")
ax1.plot(ds, delays_2, color='g', label=str(N2)+" nodes")
ax1.plot(ds, delays_3, color='b', label=str(N3)+" nodes")
ax2.plot(ds, ds, color='y', label="Bandwidth\namplification")
ax1.autoscale(tight=True)
ax2.autoscale(tight=True)
ax1.legend(loc=0)
ax2.legend(loc=0)
ax1.set(title='Worst case maximum hops vs bandwidth')
ax1.set(**dict(xlabel='Outbound degree (D)', ylabel='Amount of hops'))
ax2.set(**dict(ylabel='Bandwidth amplification'))
#ax2.set_xlim([2, 14])
fig.savefig('message_hops.svg', dpi=300)

ax1.legend(loc=(0.08, 0.7))
ax2.legend(loc=(0.5, 0.76))
ax1.set(title='$h_{max}$ and bandwidth amplification depending on node degree $D$\n')
ax1.set(**dict(xlabel='Node degree (D)', ylabel='Maximum number of hops ($h_{max}$)\n'))
ax2.set(**dict(ylabel='\nBandwidth amplification'))

# Set the limits of the x-axis and y-axis
ax1.set_xlim(3, 14)
ax1.set_ylim(3, ax1.get_ylim()[1]) # Ensure that the lower limit is 2

# Set the limits of the second y-axis to match the first y-axis
ax2.set_ylim(ax1.get_ylim())

fig.savefig('message_hops.svg', dpi=600)
plt.close()


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