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

TL;DR

This paper proves that for a linear system with a bottleneck, a constant inflow maximizes output rate, extending previous periodic results to general non-periodic inflow scenarios using a simple proof.

Contribution

It provides a straightforward proof that constant inflow is optimal for maximizing output, extending prior periodic results to non-periodic inflow cases.

Findings

Constant inflow maximizes output rate in bottleneck systems.

The proof is elementary and does not rely on optimal control theory.

Extension to non-periodic inflow rates is established.

Abstract

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.