## Comparison Between Two Averaging Schemes

### Arithmetic Avering Size VS Exponential Moving Averaging alpha=0.5

#### Arithmetic Mean

Original pruned stream:
sendgap1 sendgap2 sendgap3 ...
recvgap1 recvgap2 recvgap3 ...
size1    size2    size3 ...
Normalized stream:
sendgap1' sendgap2' sendgap3' ...
recvgap1' recvgap2' recvgap3' ...
2segments 2segments 2segments ...
New pruned stream: avg_size=k
new_sendgap1=sendgap1+...+sendgapk new_sendgap2=sendgap2+...+sendgap(k+1) new_sendgap3=sendgap3+...+sendgap(k+2) ...
new_recvgap1=recvgap1+...+recvgapk new_recvgap2=recvgap2+...+recvgap(k+1) new_recvgap3=recvgap3+...+recvgap(k+2) ...
new_size1=2segments                new_size2=2segments		          new_size3=2segments ...

#### Exponential Moving Averaging

Original Pruned stream:
sendgap1 sendgap2 sendgap3 ...
recvgap1 recvgap2 recvgap3 ...
size1    size2    size3 ...
Normalized stream:
sendgap1' sendgap2' sendgap3' ...
recvgap1' recvgap2' recvgap3' ...
2segments 2segments 2segments ...
new pruned steam:
new_sendgap1=sendgap1 new_sendgap2=alpha*new_sendgap1+(1-alpha)*sendgap2 ...
new_recvgap1=recvgap1 new_recvgap2=alpha*new_recvgap1+(1-alpha)*recvgap2 ...
new_size1=2segments   new_size2=2segments ...

#### 1. AB_est

When abest is computed with "averaged/smoothed" rate:

When abest is computed with original probing rate:
for alrithmatic sliding window averaging:
for elements in the excursion, abest_per_probe=the probing rate of the previous elements of the excursion in the original pruned stream
eg. avg_size= a
excursion starts from i
if i!= 0, abest assigned to the excursion is the probing rate of i-1 th elements in the original pruned stream
if i==0, abest assigned to the excursion is the probing rate of the i(0) th elements in the original pruned stream
for exponential averaging:
find excursions with averaged streams, but assign abest_per_probe with the probing rate for the original pruned stream