The GATE Grind

GATE 2017 ME (ME2) – Question 33

Operations Research · Simple queuing models · 1 mark · Multiple choice

A single server has Poisson arrivals and exponential service times. Arrival rate is 12 per hour. Which service rate permits a steady-state finite queue?

  1. 6 per hour
  2. 10 per hour
  3. 12 per hour
  4. 24 per hour

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Show answer and explanation

Correct answer: (D) 24 per hour

Explanation

Queue stability requires utilisation ρ=λ/μ<1. With arrival rate12 per hour, service rate must exceed12. Among6,10,12 and24, only **24 per hour, D** qualifies. Equalityρ=1 does not give a finite stationary queue length.