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GATE 2024 MN – Question 19

Mineral Economics, Mine Planning, Systems Engineering · Systems Engineering · 1 mark · Multiple choice

An M/M/1 shovel queue has arrival rate 9 dumpers/hour and service rate 12/hour. Find probability that exactly one dumper is in the system.

  1. 1/16
  2. 3/16
  3. 3/4
  4. 1/4

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Correct answer: (B) 3/16

Explanation

Utilisation isρ=λ/μ=9/12=3/4<1. The stationary count distribution is P(N=n)=(1−ρ)ρⁿ. At n=1 this is(1/4)(3/4)=3/16, B. The phrase is interpreted as one dumper in the system, including service.

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