My morning rush is chaos. Customers are walking out. Do I need another person, or is something else broken?

The situation

Sarah owns an independent coffee shop in a mid-sized city. During the 7–9am rush she handles orders, makes drinks, and manages the register — with one other barista. She's been thinking about hiring a third person but isn't sure whether that would help or whether the problem is something else entirely. She's losing customers she can't see.

The analysis

The bottleneck isn't order-taking (30 sec) — it's drink assembly (3–4 min). A dedicated order-taker wouldn't help; only another full barista does.

Without data, the default move is to hire and hope. But hiring costs $18/hr for a 2-hour rush slot — around $800/month — and if the bottleneck is the queue itself rather than the service rate, another barista might not move the needle.

The Process Map models the flow: customer arrives → joins queue → barista takes order and makes drink → customer picks up and leaves. Arrivals follow an exponential distribution (average: one customer every 2 minutes during peak). Service time is normal (mean: 3.5 minutes, std dev: 0.8 minutes). With 2 baristas, the simulation shows an average wait of 4.2 minutes — acceptable. But the 90th percentile is 8.7 minutes, and the worst-case runs push past 12. Roughly 1 in 8 customers waits long enough that the research on customer abandonment says they'll leave.

Adding a third barista drops the 90th percentile to 2.3 minutes. The model estimates the abandonment rate falls from ~12% to ~2%, recovering ~6 customers per rush hour. At $7.50 average ticket and 22 operating days per month, that's approximately $1,485/month in recovered revenue — nearly double the cost of the hire.

The non-obvious finding: the bottleneck isn't the order-taking step (30 seconds) — it's drink assembly (3–4 minutes). That means a dedicated order-taker wouldn't help at all. Only another full barista changes the outcome.

The decision

Sarah hires a third barista for rush hours and saves her arrival and service-time distributions to her library, with Monitoring watching live wait times against them. Two months later, Monitoring flags that arrivals have drifted — a write-up in a local newsletter pushed rush-hour traffic up 20%. She re-fits the arrival distribution and confirms three baristas still hold, instead of finding out from a line out the door.