Operations research
Why?
Why Queues Explode Near Full Capacity
Why does a queue explode when the server is only 90% busy?
Quick check · tap an answer to continue
Lesson notes
Key points
- Because arrivals are random, customers often bunch together even when the average rate is below capacity.
- Because a busy server has little idle slack, each bunch leaves a backlog that clears only slowly.
- Because in M/M/1 the average number in the system is ρ divided by one minus ρ, it rockets as ρ approaches one.
Takeaway: So designing systems near 100% utilisation guarantees long waits.
Quick check: In an M/M/1 queue with ρ = 0.75, what is the average number in system?
- 0.75
- 3
- 1.33
L = ρ/(1−ρ) = 0.75/0.25 = 3 customers.
Random arrivalsLittle slackL = ρ/(1−ρ)
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