Answer:
11.11
Explanation:
λ=1/100/day
K=10,000
Therefore the expected length of time for replacing a burned-out lamp is equally the expected waiting time in the system which is W.
L= 1,000 (average number of burned-out lamps)
Effective arrival rate:
¯λ=λ(K-L) =1/100(10,000-1,000) = 90/day
Average length of time it takes to replace a burned-out lamp is:
W=L/¯λ= 1,000/90 =11.11
Mafia, Inc. is not living up to the contract since the company is supposed to replace the burned-out street lamp in an average of 7 days.
Answer:
This means that Mafia, Inc. is NOT living up to the contract (
Explanation:
We can relate this question to machine repair problem M/M/1.
Using the formula λ*=λ(K-L)
Where λ is average days of usage = 1/100 per day
K is Total sample of streetlights = 10000
L is the average number of burned-out lamps = 1000
The expected length of time for replacing a burned-out lamp is the expected waiting time given by W= L/λ*
Therefore the effective arrival rate λ*=λ(K-L) =1/100(10000-1000)
= 90/day
Thus, the average length of time it takes to replace a burned-out lamp is
W=L/λ* = 1000/90≈11.11 days
This means that Mafia, Inc. is NOT living up to the contract (contract states that the company is supposed to replace a burned-out street lamp in an average of 7 days).
