Gates move in finite steps and ignore changes below a deadband, so a gate opening from closed passes at least one quantum per step. For max–min delivery at a canal node through sealing gates that start the day closed, with exact levels and executed commands, it is proved that direct execution excludes users with plans below 1 − 1/(2k) of a quantum, k the deadband in resolution steps. Minimum deliveries cost the max–min level at most the summed quanta over total demand, and whole steps the summed step volumes over the demand of outlets still above quanta. A θ pulse rule serves every positive plan below the daily pulse capacity within −θ to +1 pulse, and carrying the debt forward bounds the cumulative error by one pulse. For ten recorded seasons at the Dustlik node, Kegeyli canal, Uzbekistan, the gates lowered the max–min level of a static constant-level allocation by under 0.001. In closed-loop Saint–Venant simulation with plan-derived demands, direct execution excluded the smallest regulator on exactly the 77 predicted early-April days of assumed demand, pulse rules served it, and carry-over cut its unweighted mean absolute dekadal error from 6.5% (pulse rule) to 1.0% of demand, shifting deliveries between days.

When an irrigation canal is put on restriction, what is fair depends on the water each user receives, not on what was allocated: transport delay and the stabilising low-pass filter re-shape every order on the way to the offtake. We pose the problem as lexicographic max-min optimisation of the fraction of each user’s order delivered inside an agreed window, after the filter. The orders are the decision variables, re-shaped before the filter, leaving the controller and filter untouched. The delivered fractions are affine in the orders, so this is a finite sequence of linear programmes. Relaxing the control law alone yields a certified upper bound; an infeasibility certificate reports whose order cannot be met and what must give. On a published eight-pool test canal the criterion raises the worst-off delivered fraction by 0.074 to 0.180 over leaving orders unchanged; the bound is attained at nine of eleven operable supply levels, where the control layer loses nothing. A 50% larger volume budget leaves the lexicographic answer unchanged. The filter’s order decides whether a feasible schedule exists, its cut-off only what is delivered; neither moves the comparison between criteria much. On this canal filter design precedes the choice of fairness criterion.