A donuts shop has a queue length, on average, of 6 customers and each customer has to wait 3 minutes to get their donuts from the time they enter the store. How many customers are being served every hour?

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BlackTom AI · Accepted Answer

To tackle this problem, first note two givens: the average queue length is 6 customers, and each customer requires 3 minutes of service time once they reach the counter.

Step 1: Determine the service capacity per hour. If each customer takes 3 minutes to be served, the service facility can handle 60 minutes / 3 minutes per customer = 20 customers completed per hour at the service point.

Step 2: Relate queue length to throughput. A common reading (and the one implied by the provided answer) is that the number of customers being served per hour can be estimated by multiplying the service rate by the number in the queue, i.e., throughput = (service rate per hour) × (average number in queue). Here, that would be 20 × 6 = 120 customers per hour.

Step 3: Interpret the result carefully. This approach blends the per-customer service time with the average number waiting, yielding a higher hourly throughput figure than the pure service rate alone. It reflects the idea that, on average, as the queue length grows, more customer handoffs occur across the hour if the line feeds continuously through the serving station.

Step 4: Consider alternative interpretations and common misunderstandings. If one assumes throughput must equal only the number that can be served in 60 minutes (i.e., 20 per hour), that would ignore the fact that multiple customers in the queue are cycling through the service point over the hour. Conversely, treating the 6 as the total number in the system (queue plus being served) and dividing by the 3-minute service time would give a different (and likely inconsistent) hourly rate. The problem’s stated answer aligns with multiplying the service rate by the average queue length to reflect the flow through the system.

Step 5: Synthesize the result. Therefore, using the given data and the implied interpretation, the estimated number of customers served per hour is 20 customers/hour × 6 = 120 customers/hour.

Note: If your course or problem intended a different interpretation (for example, using Little’s Law L = λW with L as total in system and W as average time in system), you might get a different value. Always check which quantities are labeled as “in queue” vs “in service” and whether you’re calculating throughput (λ) or total in the system (L).

4510_COMMGMT_2511 Quiz 5 (Week 6) Ch6 Little's Law

A donuts shop has a queue length, on average, of 6 customers and each customer has to wait 3 minutes to get their donuts from the time they enter the store. How many customers are being served every hour?

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