If the average arrival rate in a queue is 13/hr and the average service rate is 20/hr, then the average number of customers in the line (including the customer being served) will be:

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HPCL Engineer Mechanical 04 Nov 2022 Official Paper (Shift 2)
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  1. 1.857
  2. 1.908
  3. 1.946
  4. 1.880

Answer (Detailed Solution Below)

Option 1 : 1.857
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Detailed Solution

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Concept:

The probability that there are k customers in the system = (ρ)k(1 - ρ) = 

No. of customers in the  system or length of the system  

No. of customers in the queue or length of the queue 

Average arrival time and the time spent in the queue (before being served) (Waiting time in queue) = 

Calculation:

Given:

average arrival rate, λ = 13/hr, average service rate, μ = 20 / hr

No. of customers in the  system or length of the system 

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