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bestchunk.py
569 lines (423 loc) · 16.9 KB
/
bestchunk.py
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#! /usr/bin/env python
import matplotlib#need to manually install py-matplotlib
matplotlib.use('Agg')
matplotlib.rcParams["font.size"] = 18
matplotlib.rcParams["xtick.labelsize"] = 18
matplotlib.rcParams["ytick.labelsize"] = 18
matplotlib.rcParams["lines.linewidth"] = 3.0
matplotlib.rcParams["pdf.fonttype"] = 42
import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import fsolve
import math
import os, os.path
class PktLoss(object):
def __init__(self, value_from_test=None, m=None):
self.value_from_test = value_from_test
self.m = m
def estimate_according_to_two_indexes(self, index_value, chunk_loss_rate, m=None):
if m == None:
m = self.m
temp = (m+1.0)/(2*m) *(index_value + chunk_loss_rate)
#temp = (index_value+chunk_loss_rate)/2.0
#temp = (m+1)*chunk_loss_rate/(m*2.0)
print "when m=%s index_value=%s chunk_loss_rate=%s, Omega=%s" %(m, index_value, chunk_loss_rate, temp)
if m == 1.0:
print ""
return temp
def estimate_according_to_index_value(self, index_value=None, m=None):
if index_value == None:
index_value = self.value_from_test
if m == None:
m = self.m
temp = 1 - pow(1 - m*index_value, 1.0/m)
print "when m=%s index_value=%s, Omega=%s" %(m, index_value, temp)
return temp
def estimate_accordiing_to_chunk_loss_rate(self, chunk_loss_rate, m=None):
if m == None:
m = self.m
temp = 1 - pow(1 - chunk_loss_rate, 1.0/m)
#print "when chunk_loss_rate=%s, Omega=%s" %(chunk_loss_rate, temp)
return temp
def use_chunk_loss_rate_as_pkt_loss_rate(self, chunk_loss_rate, m=None):
if m == None:
m = self.m
temp = chunk_loss_rate
print "when m=%s chunk_loss_rate=%s, pkt_loss_rate=%s" %(m, chunk_loss_rate, temp)
def get_index_value(self, Omega, m=None):
if m == None:
m = self.m
temp = (1- pow(1-Omega, m))/m
print "when m=%s, Omega=%s, index_value=%s" %(m, Omega, temp)
return temp
def analyze(self):
#0.069, 0.565
index_values = [0.0320, 0.0316]
Omegas = [0.0436, 0.0430]
m = 3.0
for i in range(len(Omegas)):
Omega = Omegas[i]
index_value = index_values[i]
self.estimate_according_to_index_value(index_value, m)
print "expection=%s" %(Omega)
#self.get_index_value(Omega, m)
#print "expection=%s" %(index_value)
pl = PktLoss(value_from_test=0.0, m=3.0)
# pl.analyze()
# pl.estimate_accordiing_to_chunk_loss_rate(chunk_loss_rate=0.03136, m=3.0)
class BestChunk(object):
def __init__(self, Omega, Delta, M, p=None, h=0.5):
self.Omega = Omega
self.Delta = Delta
self.M = M
self.p = p
self.h = h
self.out_dir = "Figure/"
if not os.path.exists(self.out_dir):
os.makedirs(self.out_dir)
def get_payload_size(self, Omega=None, Delta=None):
if Omega==None:
Omega = self.Omega
T = 1 - Omega
if Delta == None:
Delta = self.Delta
M = self.M
#data size per chunk
p = (-1*Delta*math.log(T) -pow((Delta*(math.log(T)))**2-4*M*math.log(T)*Delta, 0.5))/(2*math.log(T))
k = int((Delta+p)/float(M))
r1 = self.get_ratio_lower(k*M)
r2 = self.get_ratio_lower((k+1)*M)
if r1 > r2:
p = k*M - Delta
r = r1
else:
p = (k+1)*M - Delta
r = r2
return p, r
def get_retxN(self, p, Omega):
if Omega == None:
Omega = self.Omega
T = 1 - Omega
m = math.ceil((Delta+p)/float(M))
n = pow(float(T), -1*m)
return n
def get_ratio_upper(self, p, Omega=None, Delta=None):
if Omega == None:
Omega = self.Omega
T = 1 - Omega
if Delta == None:
Delta = self.Delta
if type(p) == np.ndarray:
p = p.astype(np.float)
else:
p = float(p)
r = p/(Delta+p)
return r
def get_ratio_reliable(self, p, Omega=None):
if Omega == None:
Omega = self.Omega
T = 1 - Omega
Delta = self.Delta
M = self.M
m = (Delta+p)/float(M)
r = p*T/(Delta+p)
return r
def get_ratio_lower(self, p, Omega=None, Delta=None):
if Omega == None:
Omega = self.Omega
T = 1 - Omega
if Delta == None:
Delta = self.Delta
M = self.M
m = np.ceil((Delta+p)/float(M))
r = p*T**(m)/(Delta+p)
return r
def get_ratio_with_h(self, p, h=None, Omega=None, Delta=None):
if h == None:
h = self.h
if Delta == None:
Delta = self.Delta
r1 = self.get_ratio_lower(p, Omega, Delta=Delta)
r2 = self.get_ratio_upper(p, Omega, Delta=Delta)
# print "h=%s" %(h)
# print "r1", r1
# print "r2", r2
return h*r2 + (1-h)*r1
def f(self, p):
Omega = self.Omega
Delta = self.Delta
M = self.M
h = self.h
assert h!=None, "h==None"
m = (Delta+p)/float(M)
m = math.ceil((Delta+p)/float(M))
return math.pow(1-Omega, m)*( Delta + p*m*math.log(1-Omega) ) + h*Delta/(1-h)
def get_zero_point(self, h=None):
if h != None:
self.h = h
result = fsolve(self.f, [8832.0])
#print result
#print self.f(result)
#print "ratio=%s" %(self.get_ratio_with_h(p=result[0]))
return result
#def __init__(self, Omega, Delta, M, p=None, h=0.5):
class RatioGivenPayload(object):
def __init__(self, Omega):
self.bc = BestChunk(Omega=Omega, Delta=500, M=1472)
def ratio_given_payload_compare(self, data_size1, data_size2):
r1 = self.bc.get_ratio_lower(data_size1)
r2 = self.bc.get_ratio_lower(data_size2)
print "payload=%s, ratio=%s" %(data_size1, r1)
print "payload=%s, ratio=%s" %(data_size2, r2)
rgp = RatioGivenPayload(Omega=0.002)
# rgp.ratio_given_payload_compare(4096, 8350)
class WithH(object):
def __init__(self, h=0.5, Omega=0.01):
self.bc = BestChunk(Omega=Omega, Delta=500, M=1472, p=None, h=h)
def ratio_h(self):
hs = [i*0.01 for i in range(100)]
ps = []
rs = []
crs = []#compare ratios
cps = []#compare payload sizes
for h in hs:
p = self.bc.get_zero_point(h=h)[0]
r = self.bc.get_ratio_with_h(p, h=h)
if h == 0:
base_r = self.bc.get_ratio_lower(p)
base_p = p
ps.append(p)
rs.append(r)
c = r/float(base_r)
#print r, base_r
crs.append(c)
if h<0.9:
cp = p/float(base_p)
cps.append(cp)
#print "h=%s, p=%6s, r=%6s, cr=%s, cp=%s, base_p=%s, p=%s" %(h, p, r, c, cp, base_p, p)
ls = []
plt.cla()
# for ys in [rs, crs]:
# l, = plt.plot(hs, ys)
# ls.append(l)
#
l, = plt.plot(hs, rs)
ls.append(l)
#print ps
plt.ylim(ymin=0.0, ymax=1.2)
plt.ticklabel_format(style='sci', axis='x', scilimits=(3,3))
plt.ticklabel_format(style='sci', axis='y', scilimits=(-2,0))
plt.grid(True)
plt.xlabel("h")
plt.ylabel("Goodput-To-Throughput Ratio")
plt.title("UDP: $\Delta$=%s, M=%s, $\Omega$=%s" %(self.bc.Delta, self.bc.M, self.bc.Omega))
plt.legend([l], ["Max Ratio"], loc="upper left")
plt.twinx()
plt.ylim(ymin=0.0, ymax=3.2)
l, = plt.plot(hs, crs, "g")
ls.append(l)
l, = plt.plot(hs[0:len(cps)], cps, "r")
ls.append(l)
legends = ["Max Ratio", "Ratio: Max-to-LB", "Payload: Max-to-LB"]
plt.legend(ls[1:], legends[1:], loc="lower right")
plt.ylabel("Payload Size: Max-to-LowerBound")
name = "ratio-h-M%s-Delta%s-Omega%s" %(self.bc.M, self.bc.Delta, self.bc.Omega)
name = name.replace(".", "")
plt.savefig(self.bc.out_dir+"/"+name+".pdf")
print "%s.pdf ends" %(name)
wh = WithH(Omega=0.01)
# wh.ratio_h()
class LossComparsion(object):
def __init__(self):
self.udp = BestChunk(0.01, 500, 1472)
def payload_loss_figure(self):
ps = []
rs = []
rs2 = []
Omegas = [i*0.001 for i in range(1, 201)]
last_p = 0
for Omega in Omegas:
self.udp.Omega = Omega
p, r = self.udp.get_payload_size()
if p != last_p:
print "Omega=%s, p=%s, r=%s" %(Omega, p, r)
last_p = p
ps.append(p)
rs.append(r)
r2 = self.udp.get_ratio_lower(p=4096)
rs2.append(r2/r)
plt.clf()
plt.cla()
l, = plt.plot(Omegas, ps)
plt.legend([l], ["Optimal\nPayload Size"], loc="upper left", prop={'size':18})
#print ps
#plt.ylim(ymin=0.0, ymax=1)
plt.ticklabel_format(style='sci', axis='x', scilimits=(3,3))
plt.ticklabel_format(style='sci', axis='y', scilimits=(-2,0))
plt.grid(True)
plt.xlabel("Packet Loss Rate")
plt.ylabel("Optimal Payload Size per Chunk")
plt.twinx()
# l1, = plt.plot(Omegas, rs, "g")
# l2, = plt.plot(Omegas, rs2, "r")
# plt.ylabel("Max Goodput-to-Throughput Ratio")
# plt.legend([l1, l2], ["Max G2T Ratio", "Ratio of 4096-to-LB"], loc="upper right", prop={'size':18})
#
l1, = plt.plot(Omegas, rs, "g")
#l2, = plt.plot(Omegas, rs2, "r")
plt.ylabel("Max Goodput-to-Throughput Ratio")
plt.legend([l1], ["Max G2T Ratio"], loc="upper right", prop={'size':18})
plt.title("UDP: $\Delta$=%s, M=%s" %(self.udp.Delta, self.udp.M))
name = "payload-loss-M%s-Delta%s" %(self.udp.M, self.udp.Delta)
name.replace(".", "")
plt.savefig(self.udp.out_dir+"/"+name+".pdf")
print "%s.pdf ends" %(name)
def ratio_payload_figure(self):
"""there lines, upper bound, lower bound Omega=0.01, lower bound Omega=0.03
"""
ps = range(1000, 15000, 1)
rss = []
peakx = 0
peaky = 0
for Omega in [0.01, 0.03]:
rs = []
rs2 = []
rs3 = [] #4096
for p in ps:
r = self.udp.get_ratio_lower(p, Omega)
rs.append(r)
if r >=peaky:
peaky = r
peakx = p
if Omega == 0.01:
r = self.udp.get_ratio_upper(p, Omega)
rs2.append(r)
if Omega == 0.01:
rss.append(rs2)
rss.append(rs)
ls = []
plt.cla()
plt.clf()
for rs in rss:
l, = plt.plot(ps, rs)
ls.append(l)
plt.ylim(ymin=0.3, ymax=1)
plt.ticklabel_format(style='sci', axis='x', scilimits=(3,3))
plt.ticklabel_format(style='sci', axis='y', scilimits=(-2,0))
plt.title("UDP: $\Delta$=%s, M=%s, $\Omega$=1%%" %(self.udp.Delta, self.udp.M))
plt.fill_between(ps, rss[0], rss[1], color="red", alpha=0.2)
plt.fill_between(ps, rss[2], rss[1], color="yellow", alpha=0.2)
plt.grid(True)
plt.ylabel("Goodput-To-Throughput Ratio")
plt.xlabel("Payload Size per Chunk")
legends = ["Upper Bound", "Lower Bound: $\Omega$=1%", "Lower Bound: $\Omega$=3%"]
plt.legend(ls, legends, loc="lower right")
plt.plot(peakx, peaky, "yo")
plt.annotate('Peak Point: (%d, %.3f)' %(peakx, peaky), (peakx, peaky),
xytext=(0.6, 0.7), textcoords='axes fraction',
arrowprops=dict(facecolor='black', shrink=0.02),
fontsize=12,
horizontalalignment='left', verticalalignment='bottom')
print peakx, peaky
name = "ratio-payload-M%s-Delta%s-Omega001003" %(self.udp.M, self.udp.Delta)
name.replace(".", "")
plt.savefig(os.path.join(self.udp.out_dir,name+".pdf"))
print "%s.pdf ends" %(name)
def ratio_to_4096(self):
rs = []
rs2 = []
rs4 = []
Omegas = [i*0.001 for i in range(1, 31)]
last_p = 0
for Omega in Omegas:
self.udp.Omega = Omega
self.Delta = 438
p, r = self.udp.get_payload_size(Omega=Omega, Delta=438)
r2 = self.udp.get_ratio_upper(p=p, Omega=Omega, Delta=438)
r3 = self.udp.get_ratio_lower(p=4096, Omega=Omega, Delta=438) #4096
r4 = (0.3*r + 0.7*r2)/r3
rs.append(r/r3)
rs2.append(r2/r3)
rs4.append(r4)
plt.cla()
ls = []
l, = plt.plot(Omegas, rs)
ls.append(l)
l, = plt.plot(Omegas, rs2)
ls.append(l)
l, = plt.plot(Omegas, rs4)
ls.append(l)
plt.legend(ls, ["LB to Base", "UP to Base", "h=0.7 to Base"], loc="upper left", prop={'size':18})
#print ps
plt.ylim(ymin=0.0, ymax=2)
plt.ticklabel_format(style='sci', axis='x', scilimits=(3,3))
plt.ticklabel_format(style='sci', axis='y', scilimits=(-2,0))
plt.grid(True)
plt.xlabel("Packet Loss Rate")
plt.ylabel("Ratio Comparision")
plt.title("UDP: $\Delta$=%s, M=%s" %(self.udp.Delta, self.udp.M))
name = "ratio-to-4096-loss-M%s-Delta%s" %(self.udp.M, self.udp.Delta)
name.replace(".", "")
plt.savefig(self.udp.out_dir+"/"+name+".pdf")
print "%s.pdf ends" %(name)
lc = LossComparsion()
lc.payload_loss_figure()
lc.ratio_payload_figure()
lc.ratio_to_4096()
class ChannelComparision(object):
def __init__(self):
self.udp = BestChunk(0.01, 500, 1472)
#bc2 = BestChunk(0.03, 500, 1472)
self.ideal = BestChunk(0, 500, 1500)
self.tcp = BestChunk(0.01, 500, 1460)
#
# self.udp.Omega = 0.03
# self.tcp.Omega = 0.03
def ratio_payload_compare_figure(self):
"""three lines
"""
ps = range(1000, 15000, 1)
rss = []
peakx = 0
peaky = 0
rs = []
rs1 = []
rs2 = []
for p in ps:
r = self.ideal.get_ratio_lower(p)#ideal
rs.append(r)
r = self.tcp.get_ratio_reliable(p)#tcp
rs1.append(r)
r = self.udp.get_ratio_lower(p)#udp
rs2.append(r)
rss = [rs, rs1, rs2]
ls = []
plt.cla()
for rs in rss:
l, = plt.plot(ps, rs)
ls.append(l)
plt.ylim(ymin=0.5, ymax=1)
plt.ticklabel_format(style='sci', axis='x', scilimits=(3,3))
plt.ticklabel_format(style='sci', axis='y', scilimits=(-2,0))
plt.fill_between(ps, rss[0], rss[1], color="red", alpha=0.2)
plt.fill_between(ps, rss[2], rss[1], color="yellow", alpha=0.2)
plt.grid(True)
plt.ylabel("Goodput-To-Throughput Ratio")
plt.xlabel("Payload Size per Chunk")
legends = ["Error-Free Channel: M=1.5K", "Reliable Service: TCP", "Best-Efforts Service: UDP"]
plt.legend(ls, legends, loc="lower right")
plt.title("$\Delta$=%s, $\Omega$=%s" %(self.udp.Delta, self.udp.Omega))
plt.plot(peakx, peaky, "yo")
plt.annotate('Peak Point: (%d, %.3f)' %(peakx, peaky), (peakx, peaky),
xytext=(0.6, 0.7), textcoords='axes fraction',
arrowprops=dict(facecolor='black', shrink=0.02),
fontsize=12,
horizontalalignment='left', verticalalignment='bottom')
print peakx, peaky
name = "ratio-payload-compare-Delta%s-Omega%s" %(self.udp.Delta, self.udp.Omega)
name = name.replace(".", "")
plt.savefig(self.udp.out_dir+"/"+name+".pdf")
print "%s.pdf ends" %(name)
cc = ChannelComparision()
cc.ratio_payload_compare_figure()
print "end"