Both counters are 80% busy. Why do customers wait differently?
Same total work, different arrival and service patterns.
The question
Rill Works observes a service desk for ten minutes, starting empty. Ten jobs need 48 seconds each. Smooth arrivals come at minutes 0 to 9. Bursty arrivals put five jobs at minute 0 and five at minute 5. All jobs finish inside the window.
| Smooth | Bursty | |
|---|---|---|
| Jobs | 10 | 10 |
| Service time | 48 seconds | 48 seconds |
| Servers | 1 | 1 |
First in, first out. No priority jobs, breaks or random arrivals.
“Calculate utilization and waiting. Would a second server or smoother release help?”
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A strong answer, step by step
Open each step in turn. This is one strong answer, not the only one.
Step 1: Calculate busy time
What would you do here? Open the move you’d make.
Treat 80% as proof of equal waits.
Tempting, but it misses something. Equal busy time says nothing about when the work arrives.
Calculate load, then inspect arrival timing.
The strong move. Both traces have equal work and available staff time.
See how a strong candidate says it
“Ten times 48 seconds is eight minutes of work: 80% of one server’s ten-minute window.”
Why it works: Both traces have equal work and available staff time.
Step 2: Trace the burst
What would you do here? Open the move you’d make.
Follow each job until the server is free.
The strong move. Work arrives sooner than one server can clear it.
Average the arrival times only.
Tempting, but it misses something. Mean arrival time hides five jobs arriving together.
See how a strong candidate says it
“Smooth arrivals wait zero. The burst waits 1.60 minutes on average and at most 3.20 minutes.”
Why it works: Work arrives sooner than one server can clear it.
Step 3: Price the extra server
What would you do here? Open the move you’d make.
Call lower waiting a free gain.
Tempting, but it misses something. The second server doubles available labor time.
Compare the wait benefit with staff time.
The strong move. The improvement uses twice the available staff time.
See how a strong candidate says it
“A second server cuts burst average wait to 0.64 minutes and maximum wait to 1.60 minutes. Utilization falls to 40%.”
Why it works: The improvement uses twice the available staff time.
Step 4: Test variation in work
What would you do here? Open the move you’d make.
Measure arrival and service-time variation separately.
The strong move. A long job can create a queue even with smooth arrivals.
Assume smooth arrivals remove all waiting.
Tempting, but it misses something. Long service times can block later jobs even with smooth arrivals.
See how a strong candidate says it
“With smooth arrivals and service times 144,24,24,24,24 seconds repeated, average wait is 0.48 minutes at the same 80% utilization.”
Why it works: A long job can create a queue even with smooth arrivals.
The answer, in short
- Decision
- Smooth controllable releases first; price extra staffing when arrivals cannot be controlled.
- Because
- Average utilization alone hides both burst queues and long jobs.
- What would change it
- If customer arrivals cannot be moved, test the extra server against the actual waiting target.
The customers choose when to arrive. What evidence would justify a second server?
Common traps
- Treating average load as a wait guarantee.
- Ignoring the cost of a second server.
Check your answer
- I used the same ten-minute window.
- I distinguished service and queue time.
- I traced bursts and long jobs.
- I stated the staff-time tradeoff.
Last reviewed Nov 10, 2026