Asked by Chintan Kothari on May 08, 2024
Verified
A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of λ = 7.5 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ = 10 vehicles per day with a repair time distribution that approximates an exponential distribution.
a. What is the utilization rate for this service system?
b. What is the average time before the facility can return a breakdown to service?
c. How much of that time is spent waiting for service?
d. How many vehicles are likely to be in the system at any one time?
Utilization Rate
The percentage of capacity or capability that is being used effectively at a given time.
Poisson Distribution
A probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space, assuming these events happen with a known constant rate and independently of the time since the last event.
- Ascertain the probability linked to the volume of units in the system and the latency periods in specific queue models.
Verified Answer
MR
Mario RivasMay 13, 2024
Final Answer :
(a) Utilization is ρ = 7.5 / 10 = .75 or 75%; (b) Ws = 1 / (10 - 7.5) = 1 / 2.5 = 0.4 days; (c) Wq = 7.5 / 10∗(10 - 7.5) = 0.3 days; (d) Ls = 7.5 / (10 - 7.5) = 7.5 / 2.5 = 3 units.
Learning Objectives
- Ascertain the probability linked to the volume of units in the system and the latency periods in specific queue models.