GATE 2016 ME (ME2) – Question 30
In a single-channel queuing model, the customer arrival rate is 12 per hour and the serving rate is 24 per hour. The expected time that a customer is in queue is _______ minutes.
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Correct answer: 2.4 to 2.6
Explanation
For the conventional M/M/1 queue, Wq=λ/[μ(μ−λ)]. With λ12/hour and μ24/hour, Wq=12/(24·12)=1/24hour. Multiplying by60 gives **2.5minutes**. Total time in the system would additionally include service time.