Question 1198579
**a. Effect of Tellers Handling Both Transactions**

* **Current Situation:**
    * Two separate queues: One for deposits, one for withdrawals. 
    * Each teller specializes in one type of transaction.
    * This can lead to uneven queues and longer wait times for customers in the longer queue, even if the average arrival rates are similar.

* **Effect of Combined Handling:**
    * **Reduced Wait Times:** By allowing both tellers to handle both deposits and withdrawals, customers can be served in the order they arrive (e.g., FIFO - First In, First Out). This would significantly reduce wait times, as customers won't be stuck in a long queue while the other teller remains idle.
    * **Improved Efficiency:** Both tellers can be utilized more effectively, minimizing idle time and ensuring smoother customer flow.

**b. Effect of Increased Service Time**

* **Increased Service Time:** If the service time increases to 3.5 minutes per customer for both tellers, it will likely increase the average waiting time for both depositors and withdrawers. 
* **Potential Impact:** 
    * Longer queues: Increased service time can lead to longer queues forming, even if both tellers handle both types of transactions.
    * Reduced throughput: The number of customers served per hour will decrease, potentially leading to longer overall wait times.

**Key Considerations:**

* **Customer Satisfaction:** Reduced wait times generally lead to increased customer satisfaction.
* **Resource Utilization:** Allowing both tellers to handle both types of transactions improves resource utilization and efficiency.
* **Training:** Tellers may require additional training to handle both types of transactions effectively.

**In Summary:**

* Allowing both tellers to handle both deposits and withdrawals would likely significantly reduce average waiting times for customers.
* Increasing the service time to 3.5 minutes per customer would likely have a negative impact on waiting times and overall efficiency.

**Note:**

This analysis assumes that the arrival rates and service times remain constant. In reality, these factors can fluctuate throughout the day. 

To accurately assess the impact of these changes, more detailed analysis using queuing theory models (e.g., M/M/1, M/M/2 queues) would be necessary. These models can help predict wait times, queue lengths, and system utilization under different scenarios.