Triage in a Two-Person Queue
You manage a two-person support queue for a payment platform. At 09:00 on a Monday, 480 tickets are open; the 8-hour first-response target covers 92% of them. One agent is the only person trained on suspected fraud escalations, and 37 tickets are tagged possible fraud. The other agent can handle general tickets but cannot clear fraud. Your workforce model says two agents clear about 55 tickets per day each, and new tickets arrive at roughly 70 per day. The fraud-trained agent can either work fraud (about 12 minutes each) or general tickets (about 8 minutes each). The fraud team will not be available until 14:00.
1. Set a prioritization rule for 09:00–14:00 and show the arithmetic that makes it feasible or infeasible.
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Rule for 09:00–14:00: the fraud-trained agent handles only high-risk fraud first; the general agent handles general tickets plus any fraud triage that does not require the specialist.
Arithmetic:
- The fraud-trained agent has 5 hours = 300 minutes. At 12 minutes per fraud ticket, the maximum is 25 fraud tickets. There are 37, so full clearance before 14:00 is impossible.
- Split fraud by harm: account takeover, confirmed unauthorized transactions, and amounts over $500 are high-risk. Assume that subset is 11 tickets: 11 × 12 = 132 minutes, leaving 168 minutes for about 21 general tickets.
- General agent: 300 minutes ÷ 8 = 37 general tickets.
- Total first-touch capacity in five hours is roughly 58 tickets, against 70 daily arrivals plus a 480 backlog. A first-in-first-out rule would miss both fraud and the response target.
Priority order: high-risk fraud by 11:30 → remaining fraud triage → general tickets already past 6 hours or involving vulnerable customers → all other general tickets. Low-risk general tickets are explicitly deferred, not silently queued.
2. What do you tell the business about the 92% first-response target, and what do you refuse to promise?
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What I tell the business: the 92% eight-hour first-response target is not achievable today with two agents and a 480-ticket backlog. The math: 92% of 480 is 442 tickets; two agents clear about 110 tickets per day, and 70 new tickets arrive, so only about 40 tickets per day reduce the backlog. Clearing 480 takes roughly 12 working days before new arrivals. Promising 92% would be a false commitment.
What I commit to:
- 100% of high-risk fraud triaged within 2 hours until 14:00, then handed to the fraud team with a complete record.
- A named owner and timestamp for every ticket touched.
- A revised first-response estimate for general tickets, updated at 11:00 and 14:00.
What I refuse to promise: the 92% target, same-day clearance of the backlog, or that deferred low-risk tickets will receive an eight-hour response. I would request overtime or a third agent, and document the capacity gap rather than distort the queue to hit a metric.