Collect the Roadside Box on a Schedule or When It Is Full? A Fill-Trigger Rule and Its Overflow Risk

Posting boxes are emptied on timetables written for the average box, though boxes fill at wildly different rates. This paper compares a fixed collection schedule with a fill trigger — empty the box when it holds a stated number of items, reported by sensor or by the deliverer's count. At a stated arrival rate of 26 items a day, trip cost USD 7.50 and delay priced at USD 0.03 per item-day, the best fixed schedule collects every 4.39 days at USD 3.421 a day, while the best overflow-safe trigger, 98 items, costs USD 3.445 a day — marginally more than the schedule, the premium for holding the threshold far enough below capacity — with a mean wait of 1.87 days. The trigger's real advantage is not this margin but its self-adjustment: it collects oftener as the box's use grows and seldomer as it fades, without a timetable review. Its risk is priced too: with a half-day response lag, the probability of the 120-item box overflowing after the trigger fires is 0.7622 percent. SIMULATED, NOT MEASURED.