Mining Engineering > GATE 2026 > Systems Engineering - Queueing Theory
A shovel needs to be selected from four models of different capacities, S1 to S4, for loading of dumpers. The operational data for the shovel-dumper combination are provided. The mean arrival rate of the dumpers at the loading point is 5 per hour and the waiting cost of dumper is ₹ 200 per hour. The inter-arrival time of dumpers and loading time of shovel follows exponential distribution. Ignoring the shovel hiring cost, the shovel type that will have minimum total cost (waiting and operating cost) is
| Model | Operating cost (₹/hr) | Mean loading rate (dumpers/hr) |
|---|---|---|
| S1 | 800 | 8 |
| S2 | 850 | 9 |
| S3 | 920 | 10 |
| S4 | 1000 | 11 |
Correct : b
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