Question

Jobs arrive at a facility at an average rate of 5 in an 8 hour shift. The arrival of the jobs follows Poisson distribution. The average service time of a job on the facility is 40 minutes. The service time follows exponential distribution. Idle time (in hours) at the facility per shift will be _______.

• A. (A) 57
• B. (B) 143
• C. (C) 75
• D. (D) 103

Answer 1

Answer: (B)

(B) 143

Answer 2

Explanation:
Given:Arrival rate (λ)=58 Jobs Hour Service time for one job is 40 minTherefore, Service rate (μ)=32 Jobs Hour Utilization factor ρ=λμIdle time =1−ρλ=58 Jobs Hour μ=32 Jobs Hour ρ=λμ=5832=512 Idle time =1−ρ=1−512=712 hourTherefore, Idle time for 8 hour shift =712×8=143 hours.Hence, the correct option is (B).