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. Average time a customer spends in the system (waiting time + service time). b. Probability that the server is idle (not serving any customer). c. 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?
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. Average time a customer spends in the system (waiting time + service time).
b. Probability that the server is idle (not serving any customer).
c. 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?
d. Discuss how the probability in part f above might change if the average service
time per customer increases or decreases.
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