Evaluate multipath balia congestion control on ns3

 The dumbbell topology in [1] is used for to evaluate balia performance on ns3.

n0--L0--n2--L1--n3--L2--n4
n1--L3--n2--L1--n3--L4--n5

 The control rule in balia [2] is:
$$w_r\leftarrow \{\begin{array}{ll}{w}_r+\frac{x_r}{{\tau }_r(\sum x_k{)}^2}\cdot \frac{1+{\alpha }_r}{2}\cdot \frac{4+{\alpha }_r}{5}& \text{When an ack is received}\\ w_r-\frac{w_r}{2}\min (1.5,{\alpha }_r)& \text{When packet loss happens}\end{array}\text{\hspace{1em}(1)}$$
  Here,$\alpha =\frac{\max x_k}{x_r}$. $x_r=\frac{w_r}{{\tau }_r}$
 But the code implementaion in linux [3]for ai is:

	/*			(sum_rate)^2 * 10 * w_r
	 * ai = ------------------------------------
	 *			(x_r + max_rate) * (4x_r + max_rate)
	 */

  That gets me confused, since ai is not in consitent with (1).
  According to (1) and ${\tau }_r=\frac{w_r}{x_r}$:
$$ai=\frac{10\cdot (\sum x_k{)}^2\cdot {\tau }_r}{(x_r+max\_rate)\cdot (4x_r+max\_rate)}$$
 What I got is:

	/*			         (sum_rate)^2 * 10 * w_r
	 * ai_correct= ------------------------------------
	 *			    x_r*(x_r + max_rate) * (4x_r + max_rate)
	 */

  I dont know the reason behind the formular (1) to control the increase process of cwnd.
But at least, the ai_correct is indeed has the same unit with w_r.
  So, in implemementation, I use ai_correct to control the increase process of cwnd.

Test1

 The bandiwidth of L1 is 5Mbps.
 flow1 and flow4 are two subflows of a multipath session. flow2 and flow3 take Reno for rate control. flow1 and flow2 take route(n0->n4). flow3 and flow4 take route(n1->n5).
 The sending rate of each flow:

 Packets received rate, here mp denotes the total throughput of the multipath session:

Test2

 The bandiwidth of L1 is 8Mbps.
 The sending rate of each flow:

 Packets received rate:

[1] Evaluation multipath weswood congestion control on ns3
[2] Multipath TCP: Analysis, Design, and Implementation
[3] balia implementation in mptcp