Customers arrive at a coffee shop on average every 4 min. The barista can serve

Question

Customers arrive at a coffee shop on average every 4 min. The barista can serve every customer every 3 min. Find the average number of people in the system and the que, the average one in the que, and the utilization factor. Are these results acceptable to management? Should an additional server be hired? Customers arrive at a coffee shop on average every 4 min. The barista can serve every customer every 3 min. Find the average number of people in the system and the que, the average one in the que, and the utilization factor. Are these results acceptable to management? Should an additional server be hired?

Explanation / Answer

Arrival Rate (?) = 1/Arrival Time = 60/4 = 15 customers/hour

Service Rate (?) = 1/Service Time = 60/3 = 20 customers/hour

Utilization factor(?) = ?/? = 15/20 = 0.75

Average Number of people in the queue Lq = ?2/(1-?) = (0.75*0.75)/(1-0.75) = 2.25

Wq = Lq/? = 2.25/15 = 0.15

W = Wq+1/µ = 0.15+3 = 3.15

Average Number of people in the system L = ?W = 15*3.15 = 47.25

The results are acceptable to the management and additional server should not be hired as the utilization factor of the existing server is just 75%

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