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jobs arrive at a facility at an average rate of 5
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 _______.
MHT CET
Updated On:
Jun 23, 2024
(A)
5
7
(B)
14
3
(C)
7
5
(D)
10
3
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The Correct Option is
B
Solution and Explanation
Explanation:
Given:Arrival rate
(
λ
)
=
5
8
Jobs
Hour
Service time for one job is
40
minTherefore, Service rate
(
μ
)
=
3
2
Jobs
Hour
Utilization factor
ρ
=
λ
μ
Idle time
=
1
−
ρ
λ
=
5
8
Jobs
Hour
μ
=
3
2
Jobs
Hour
ρ
=
λ
μ
=
5
8
3
2
=
5
12
Idle time
=
1
−
ρ
=
1
−
5
12
=
7
12
hourTherefore, Idle time for
8
hour shift
=
7
12
×
8
=
14
3
hours.Hence, the correct option is (B).
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