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If I understand correctly the TCP roundtrip time can be used as a posteriori proxi for the order entry gateway delay. So assuming the roundtrip time is composed of gate delay and independent other delays $RTT_g(t) = dT_g(t) + d_g(t)$ with assumed $Cov(dT_g,d_g)=0$ and $Cov(d_i,d_j)=0$. Minimizing the this combination of gate delay and other delays is ...

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