Customers in a Small Retail Store Arrive at the Single

question 38

Essay

Customers in a small retail store arrive at the single cashier at the rate of 10 per hour. The average service time for the cashier is five minutes. Arrivals tend to follow a Poisson distribution, and service times follow an exponential distribution.
a. What is the average utilization of the cashier?
b. What is the average number of customers in the system?
c. What is the average number of customers in line?
d. What is the average time spent in the system?
e. What is the average time spent in line?

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Definitions:

Vestibular Sense

The sensory system that contributes to balance and spatial orientation by sensing gravity and motion.

Kinesthesis

The sense of movement and body position, allowing individuals to be aware of their limbs and body parts in space without having to see them.

Audition

Audition, or hearing, is the sense and process by which sound waves are detected by the ear and transmitted to the brain for interpretation, enabling sound perception.

Smell

The sense that allows the detection of odors or scents, also known as olfaction.