Question

A technician monitors a group of computers that run an automated manufacturing facility. It takes an...

  1. A technician monitors a group of computers that run an automated manufacturing facility. It takes an average of 15 minutes (exponentially distributed) to adjust a computer that develops a problem. The computers run for an average of 85 minutes (Poisson distributed) without requiring adjustments. What is the:
  1. Average number of computers waiting for adjustment?
  2. Average number of computers not in working order?
  3.   Probability the system is empty?
  4. Average time in the queue?
  5. Average time in the system?
Math   Statistics-And-Probability   
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Answer #1
arrivals/time period = λ=    1/85 /minute
served/time period= μ=    1/15 /minute

a)

average number in queue Lq = λ2/(μ(μ-λ))= 0.0378

b)

average number in system L = λ/(μ-λ)= 0.2143

c)

probability of 0 wating in system = (1-λ/μ)*(λ/μ)0      = 0.8235

d)

average time spend in queue Wq                   = λ/(μ(μ-λ))= 3.21 minute

e)

average time spend in system W                   = 1/(μ-λ)= 18.21 minute
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