Algorithm 2 An iterative algorithm for solving timeout setting problem with multiple parallel paths.

Input: One physical path set, $P(P_1,P_2,\dots ,P_i,\dots P_M)(2\le i\le M$); One logic path set that contains physical path in P, ${\mathbb{P}}_k(k=1or2)$; The bandwidth of physical path $P_i$, $C_i$; The bandwidth of ${\mathbb{P}}_k$, ${\mathbb{C}}_k(k=1or2)$; The total flow number, N; The number of flows mapping to ${\mathbb{P}}_1$ when ideal load balancing effect is achieved, $\mu$; The probabilities of ${\mathbb{P}}_1$ and ${\mathbb{P}}_2$ is chosen as the routing path for newly triggered flowlet, p and q; The m-th minimum value which must be less then $\delta$, ${\delta }_m(1\le m\le M-1)$; Output:    The maximum value of ${\delta }_m$, ${\delta }_{min}$; 1:for m from 1 to M-1 do 2:   $P_p$ ← pick the first physical path in P; 3:   ${\mathbb{P}}_1$ ← ($P_p$) and ${\mathbb{P}}_2$← P - ${\mathbb{P}}_1$; 4:   ${\mathbb{C}}_1\leftarrow {\sum }_{P_i\in {\mathbb{P}}_1}{C}_i$ and ${\mathbb{C}}_2\leftarrow {\sum }_{P_i\in {\mathbb{P}}_2}{C}_i$; 5:   $\mu \leftarrow ⌊\frac{{\mathbb{C}}_1}{{\mathbb{C}}_1+{\mathbb{C}}_2}\times N⌋$; 6:   $p\leftarrow \frac{1}{M+1-m}andq\leftarrow \frac{M-m}{M+1-m}$; 7:   According to (7), we get the ${\delta }_m$; 8:   N ← N-μ; 9:   Remove $P_p$ from physical path set P; 10:end for 11:${\delta }_{min}$ ← max$\left({\delta }_m\right)(1\le m\le M-1);$ 12:return ${\delta }_{min}$;