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Table 1 Iteration system for ECN/RED model with greedy TCP connections

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

\(\phantom {\dot {i}\!}\mu _{\textit {\text {p,i}}}(t+1)=(1-q(\rho _{p}(t)))^{s_{p}(i-1)}\mu _{\textit {\text {p,i}}-1}(t)1_{\{i>1\}}\)
\(+\sum \limits _{j:d(j)=i}\left (1-(1-q(\rho _{p}(t)))^{s_{p}(j)}\right)\mu _{p,j}(t)\quad 1<i<I_{p}\)
\(\mu _{\textit {\text {p,I}}_{p}}(t+1)=(\!1\!-q(\rho _{p}(t)))^{s_{p}(I_{p}-1)}\!\mu _{\textit {\text {p,I}}_{p}-1}(t) +(1-q(\rho _{p}(t)))^{s_{p}(I_{p})}\mu _{\textit {\text {p,I}}_{p}}(t)\)
\(\mu _{\textit {\text {u,i}}}(t+1)=\sum \limits _{j=1}^{I_{u}}\kappa _{(\textit {\text {u,j}}),(\textit {\text {u,i}})}\mu _{\textit {\text {u,j}}}(t)\)
\(\sigma _{p}(t+1)=\sum \limits _{i=1}^{I_{p}}\mu _{\textit {\text {p,i}}}(t+1)s_{p}(i)\quad \quad \sigma _{u}(t+1)=\sum \limits _{i=1}^{I_{u}}\mu _{\textit {\text {u,i}}}(t+1)s_{u}(i)\)
ρ c (t+1)= max (ρ p (t) + σ p (t + 1) + σ u (t + 1) − C, 0) ρ p (t+1)=ρ c (t)