Local-count independence with through-flow dependence (source code)

= Local-count independence with through-flow dependence

In the <stationary law of a two-resource linear flow network>, the local counts are independent geometric variables with parameters $q_i=\rho_i/(1-\rho_0)$. Conditional on local counts $a,b$, the through count has a <negative binomial distribution> with mean $\rho_0(a+b+1)/(1-\rho_0)$. With positive loads, it is correlated with each local count, even though those two local counts are independent. Degenerate zero-load cases must be distinguished from the positive-load assertion.