Sizing a Village Parcel Locker Bank: How Many Compartments Keep Turned-Away Parcels Under Two Percent

A parcel locker bank fails quietly: it does not queue, it turns parcels away when every compartment is occupied. This paper sizes the bank as an Erlang loss system. Parcels arrive at 15 per day and stay a mean of 2.0 days awaiting collection, an offered load of 30.0 compartment-days per day. To keep turned-away parcels at or below two percent requires 39 compartments, at which the average occupancy is 29.4 compartments (75.4 percent utilisation) — the bank must stand with about a quarter of its compartments empty on average to absorb arrival bunching. Removing five compartments raises blocking to 6.63 percent. A sizing table for arrival rates from 6 to 30 parcels per day and dwell times from 1.5 to 3 days is provided, together with the rule that compartments must exceed the offered load by a margin that shrinks, in percentage terms, as the bank grows. SIMULATED, NOT MEASURED.