GATE 2026 PI – Question 44

Operations Research and Operations Management · Operations Research · 2 marks · Multiple choice

An M/M/1 queue has arrival rate three customers per minute and steady-state mean number n in the system. Utilization is below one. Find mean time in the system (minutes).

$3n$
$n/3$
$n/6$
$3/n$

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Show answer and explanation

Correct answer: (B) $n/3$

Explanation

Little’s law is $L=\lambda W$. Here L = n and arrival rate λ = 3 per minute, so **$W=n/3$ minutes, B**. This is total time in the system, including service.

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