Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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**Week Question: 13-04 In an M/M/1 Queueing System**

In an M/M/1 queueing system, the arrival rate is 3 customers per hour and the service rate is 6 customers per hour. If the service process is automated (resulting in no variation in service times but the same service rate), what will be the resulting performance measurements?

**Note:** Round your answers to 3 decimal places.

---

**a. What is the utilization?**

- **Utilization:** 0.500
  - **Answer:** Complete and correct.

**b. What is the expected number of customers in the system (L)?**

- **Number of customers:** 1.000
  - **Answer:** Complete but not entirely correct.

**c. What is the expected waiting time (in hours) for the system (W)?**

- **Waiting time (in hours):** 0.333
  - **Answer:** Complete but not entirely correct.

---

The image contains three questions related to an M/M/1 queueing system. Each part provides a calculation related to utilization, the expected number of customers, and expected waiting time, with feedback on the completeness and correctness of the solutions.
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Transcribed Image Text:**Week Question: 13-04 In an M/M/1 Queueing System** In an M/M/1 queueing system, the arrival rate is 3 customers per hour and the service rate is 6 customers per hour. If the service process is automated (resulting in no variation in service times but the same service rate), what will be the resulting performance measurements? **Note:** Round your answers to 3 decimal places. --- **a. What is the utilization?** - **Utilization:** 0.500 - **Answer:** Complete and correct. **b. What is the expected number of customers in the system (L)?** - **Number of customers:** 1.000 - **Answer:** Complete but not entirely correct. **c. What is the expected waiting time (in hours) for the system (W)?** - **Waiting time (in hours):** 0.333 - **Answer:** Complete but not entirely correct. --- The image contains three questions related to an M/M/1 queueing system. Each part provides a calculation related to utilization, the expected number of customers, and expected waiting time, with feedback on the completeness and correctness of the solutions.
**Queue Analysis Questions**

**d. What is the expected number of customers in the queue (Lq)?**

- Answer: The submitted answer indicates that the expected number of customers in the queue is 0.500. However, it is noted that the answer is complete but not entirely correct. 

**e. What is the expected waiting time (in hours) in the queue (Wq)?**

- Answer: The submitted answer indicates an expected waiting time of 0.167 hours in the queue. Similarly, this answer is complete but not entirely correct. 

**Explanation:**
The questions relate to queuing theory, focusing on calculating the expected number of customers in a queue and their waiting time. The answers are partially correct, suggesting a need for further refinement or error checking in the calculations.
expand button
Transcribed Image Text:**Queue Analysis Questions** **d. What is the expected number of customers in the queue (Lq)?** - Answer: The submitted answer indicates that the expected number of customers in the queue is 0.500. However, it is noted that the answer is complete but not entirely correct. **e. What is the expected waiting time (in hours) in the queue (Wq)?** - Answer: The submitted answer indicates an expected waiting time of 0.167 hours in the queue. Similarly, this answer is complete but not entirely correct. **Explanation:** The questions relate to queuing theory, focusing on calculating the expected number of customers in a queue and their waiting time. The answers are partially correct, suggesting a need for further refinement or error checking in the calculations.
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