A Crew of Mechanics at the Highway Department Garage Repair

question 133

Essay

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?

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Definitions:

Social Role Transitions

Changes in an individual's social positions or roles that require adjustment, often involving significant life events such as marriage, parenthood, or career changes.

Clinical Depression

A serious mood disorder characterized by persistent feelings of sadness, hopelessness, and a lack of interest or pleasure in activities, affecting a person’s daily life.

Stressful Life Changes

Significant alterations in one's life situation, such as divorce or job loss, that can lead to increased stress and may necessitate psychological support.

Psychoanalysis

A therapeutic approach developed by Sigmund Freud that emphasizes unconscious processes and past conflicts as key influences on behavior.