Optimality of constant arrival rate for a linear system with a bottleneck entrance

Sadeghi et al. considered a bottleneck system with periodic arrival rate, and proved that a constant-rate arrival maximizes the time-averaged output rate among all periodic arrival 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 arrival rate.