Optimality of constant inflow for a linear system with a bottleneck entrance

Sadeghi et al. considered a bottleneck system with periodic inflow rate, and proved that a constant-rate input maximizes the time-averaged output rate among all periodic inflow rates. Here we provide a short and elementary proof of this result, without use of optimal control theory. The new approach developed here allows us to prove an extension of the result to the case of a general non-periodic inflow rate.