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Table 2 Iteration system for SAP-LAW model with greedy TCP connections

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

\(\mu _{\textit {\text {p,i,j}}}(t+1)=\sum _{i^{\prime }=1}^{I_{p}} \sum _{j^{\prime }=0}^{i-1}\mu _{\textit {\text {p,i}}^{\prime },j^{\prime }}(t)1_{f(i^{\prime },j^{\prime },h(\vec \rho _{u}(t)))=(\textit {\text {i,j}})}\)
\(\mu _{\textit {\text {u,i}}}(t+1)=\sum _{j=1}^{I_{u}}\kappa _{(\textit {\text {u,j}}),(\textit {\text {u,i}})}\mu _{\textit {\text {u,j}}}(t)\)
\(\sigma _{p}(t+1)=\sum _{i=1}^{I_{p}}\sum _{j=1}^{i-1}\mu _{\textit {\text {p,i,j}}}(t+1)\min (s_{p}(i),s_{p}(h(\vec \rho _{u}(t))))\)
\(\quad \quad \quad \quad \quad \times \sigma _{u}(t+1)=\sum _{i=1}^{I_{u}}\mu _{\textit {\text {u,i}}}(t+1)s_{u}(i)\)
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 ui (t+1)=ρ u(i−1)(t),1≤iY ρ u0(t+1)=σ u (t+1)