a. Calculate the utilisation factor for the grocery store checkout counter. Express your answer as a percentage and explain what this measure represents in the context of queue performance. Is the system operating at its optimal level? Why or why not? b. Average time a customer spends in the queue (waiting time). c. Average number of customers waiting in the queue.
A grocery store checkout counter operates with a single server to process customer
transactions. Customers arrive at the counter with an average rate of 20 customers per
hour, following a Poisson distribution. The average service time per customer is 2.5
minutes, following an exponential distribution. Calculate the following performance
measures for the checkout counter:
a. Calculate the utilisation factor for the grocery store checkout counter. Express
your answer as a percentage and explain what this measure represents in the
context of queue performance. Is the system operating at its optimal level? Why
or why not?
b. Average time a customer spends in the queue (waiting time).
c. Average number of customers waiting in the queue.
d. Average time a customer spends in the system (waiting time + service time).
e. Probability that the server is idle (not serving any customer).
f. Determine the probability that there will be exactly two customers in the system
(both in the queue and being served) at any given moment. What does this
probability indicate about the checkout counter's efficiency in handling customer
flow?
g. Discuss how the probability in part f above might change if the average service
time per customer increases or decreases.
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