The Crowded Checkpoint Queue
It is 07:40 on a Monday at a highway checkpoint. Two officers are on duty. A queue of 36 vehicles is waiting. Each vehicle takes an average of 90 seconds to process under the current full-search procedure. A senior officer radios that a suspect vehicle matching a description (a dark blue saloon with a dented rear bumper) is expected to pass through within the next 30 minutes. The officers are told to keep the queue moving but also to identify the suspect vehicle. Processing time cannot be reduced below 45 seconds per vehicle without skipping the document check, which is mandatory. A third officer is available but would take 12 minutes to arrive.
1. Calculate whether the two officers can clear the current 36-vehicle queue before the suspect is expected, and recommend whether to call the third officer.
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Processing rate: 90 s per vehicle ÷ 2 officers = 45 s per vehicle handled in parallel (each officer handles one vehicle at a time, so combined throughput is 1 vehicle per 45 s).
Time to clear 36 vehicles: 36 × 45 s = 1,620 s = 27 minutes.
So the queue clears at about 08:07, which is within the 30-minute window but leaves almost no margin. The mandatory document check cannot be skipped.
Third officer: arrives in 12 minutes. From minute 12 onward there are 3 officers, cutting per-vehicle time to 30 s. By minute 12 the two officers have processed 12 min ÷ 45 s = 16 vehicles, leaving 20. With 3 officers those 20 take 20 × 30 s = 10 min, finishing at minute 22 (about 08:02).
Recommendation: Call the third officer. It buys roughly 5 minutes of buffer and lets the officers slow down slightly for the suspect-vehicle check without letting the queue grow. The gain is modest but the margin matters because a single slow vehicle (e.g., a lorry with paperwork issues) could otherwise push clearance past the 30-minute mark.
2. The officers decide to keep the full 90-second search but add a visual pre-scan of each approaching vehicle for the dented bumper. Explain the trade-off and one risk of this approach.
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Trade-off: The visual pre-scan adds no processing time at the booth because it happens while vehicles are still queuing, so it preserves the 27-minute clearance. It lets officers flag a likely match early and pull that vehicle aside for a focused search rather than slowing every vehicle.
Risk: A visual pre-scan is unreliable at distance and in poor light; a dented bumper may be hidden, dirty, or the description may be incomplete. Officers could become over-focused on the bumper and miss a vehicle that matches on other features, or wrongly flag innocent drivers and add delay. The pre-scan should be a supplement to, not a replacement for, the document check and a quick consistent look at each vehicle.