Case Analysis

1. Eugene is a business analyst at Burger King. He was assigned a task where he needs to analyze data on consumer arrivals and concluded that the arrival rate is 15 customers per hour.

He also found out that the cashier can process an average of 18 customer orders per hour.

a. Calculate λ and μ per 10 minutes period.

b. Plug the value of λ and μ into the arrival rate and service rate cell of Case_Data.xlsm file, and calculate the value of P₀, L_q, L, W_q, W, P_w. And create a column (name it ‘Baseline') in a new tab (name it ‘scenario'), showing the value of P0, L_q, L, W_q, W, Pw. Interpret each value
using at least 20 words.

c. Suppose the service rate increases from its original value (value of μ in part A) to μ=4, but the arrival rate stays the same as in part a. Calculate the value of P₀, L_q, L, W_q, W, Pw based on the original value of λ and the updated values of μ. Create a column (name it ‘Scenario 1') in a scenario tab, showing the updated value of P₀, L_q, L, W_q, W, Pw.

d. Suppose the arrival rate increases from its original value (value of λ in part A) to λ =2.8, but the service rate stays the same as in part a. Calculate the value of P₀, L_q, L, W_q, W, Pw based on the updated values of λ and the original value of μ. Create a column (name it ‘Scenario 2') in a scenario tab, showing the updated value of P₀, L_q, L, W_q, W, P_w.

e. Now you have three columns in the scenario tab. Compare the values of P₀, L_q, L, W_q, W, P_w across Baseline, Scenario 1(‘Service rate increase' option), and Scenario 2(‘Arrival Rate increase' option), and discuss how the change in service rate or arrival rate would affect the following based on the results from part b-d using at least 200 words (This is an essay question, but the answer must be based on the results to receive full credits):

- Probability that no customers are in the system, P₀
- Average number of customers waiting in line, L_q
- Average number of customers in the system, L
- Average time a customer spends waiting in line, W_q
- Average time a customer spends in the system, W
- Probability an arriving customer has to wait, P_w

f. This is an open-ended question, and there is no definite answer. "Waiting" is a core concept of the "queueing model". What is your biblical perspectives on this core concept? Explain this by quoting at least three bible verses. (Minimum words requirement: 100 words)

Attachment:- case_data.rar