Table 4 Iteration system for ECN/RED model with temporary TCP connections

\(\tilde {\mu }_{p,1,1}(t+1)=\sum _{i^{\prime }=1}^{I_{p}}\sum _{j^{\prime }=1}^{i} \tilde {\mu }_{\textit {\text {p,i}}^{\prime },j^{\prime }}(t)\left (1-(1-w)^{\min (s_{p}(i^{\prime }),s_{p}(h(\vec \rho _{u}(t))))}\right) \)

\(\tilde {\mu }_{\textit {\text {p,i,j}}}(t+1)= \sum _{i^{\prime }=1}^{I_{p}}\sum _{j^{\prime }=1}^{i}\tilde {\mu }_{\textit {\text {p,i}}^{\prime },j^{\prime }}(t)1_{f(i^{\prime },j^{\prime },h(\vec \rho _{u}(t)))=(\textit {\text {i,j}})} (1-w)^{\min (s_{p}(i^{\prime }),s_{p}(h(\vec \rho _{u}(t))))} \)

\(\sigma _{p}(t+1)=\sum _{i=1}^{I_{p}} \tilde {\mu }_{\textit {\text {p,i,j}}}(t+1) \frac {1-(1-w)^{\min (s_{p}(i),s_{p}(h(\vec \rho _{u}(t))))}}{w} ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(20) \)

\(\quad \qquad \times \sigma _{u}(t+1)=\sum _{i=1}^{I_{u}}\mu _{\textit {\text {u,i}}}(t+1)s_{u}(i) \)

ρ _c (t+1)= max(ρ _c (t)+σ _p (t+1)+σ _u (t+1)−C,0)

ρ _p (t+1)=ρ _c (t) ρ _up (t+1)=ρ _uc (t),i>0 ρ _uc (t+1)=σ _u (t+1)