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

From: Formal modelling of TCP congestion control mechanisms ECN/RED and SAP-LAW in the presence of UDP traffic

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