GATE 2026 MN – Question 42
Dumpers arrive exponentially at5/hour and loading times are exponential. Waiting cost is₹200 per dumper-hour. Shovels S1,S2,S3,S4 have operating costs₹800,850,920,1000/hour and loading rates8,9,10,11 dumpers/hour respectively. Ignore hiring cost. Which minimises operating plus queue-waiting cost?
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Correct answer: (B) S2
Explanation
For an M/M/1 queue, Lq=λ²/[μ(μ−λ)]. At λ=5 the four queue lengths are1.0417,0.6944,0.5 and0.3788. Add200Lq to each operating cost: approximately1008.33,988.89,1020 and1075.76 rupees/hour. The smallest is S2, B. Waiting here excludes the dumper actually being loaded.