One Clerk or Two at the Counter? The Arrival Rate at Which a Second Server Pays for Itself in Waiting Time

A small post office counter is staffed by habit until the queue becomes a local scandal. This paper computes the staffing threshold from queueing theory: customers arrive at random, service averages four minutes, and the service standard is a mean queue wait of at most ten minutes. One clerk meets that standard only up to 10.7 arrivals per hour; at 12 arrivals an hour the mean wait with one clerk is 16.0 minutes against 0.76 minutes with two, and at 14 per hour it is 56.0 minutes against 1.11. Pricing the second clerk at USD 2.20 per hour and customer waiting at USD 0.90 per customer-hour, the second clerk becomes the cheaper option in total cost at 11.56 arrivals per hour — close to, but above, the rate at which the standard breaks, so an office that waits for the financial signal alone will already have breached its standard: the service promise is the earlier warning. SIMULATED, NOT MEASURED.