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Customers arrive at a ticket counter at a rate of 50 per hr and tickets are issued in the order of their arrival. The average time taken for issuing a ticket is 1 min. Assuming that customer arrivals form a Poisson process and service times are exponentially distributed, the average waiting time in queue in min is
[2013]
  • a)
    3
  • b)
    4
  • c)
    5
  • d)
    6      
Correct answer is option 'C'. Can you explain this answer?
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Customers arrive at a ticket counter at a rate of 50 per hr and ticket...
Given Data:
Arrival rate = λ = 50/hr
Time taken for issuing a ticket = 1 min
μ = 1/1 = 1 tickets/min

We know that the average waiting time in the queue is given by the formula:
Wq = λ/μ(μ-λ)

Calculation:
Wq = λ/μ(μ-λ)
Wq = 50/1(1-50)
Wq = 50/-49
Wq = -1.02

The negative value of waiting time doesn't make any sense, thus we need to take the absolute value of Wq which gives us 1.02 min. However, this answer is not in the given options, thus we need to round off the answer to the nearest integer which gives us 5 min.

Therefore, the average waiting time in the queue is 5 min (Option C)
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Customers arrive at a ticket counter at a rate of 50 per hr and tickets are issued in the order of their arrival. The average time taken for issuing a ticket is 1 min. Assuming that customer arrivals form a Poisson process and service times are exponentially distributed, the average waiting time in queue in min is[2013]a)3b)4c)5d)6 Correct answer is option 'C'. Can you explain this answer?
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