Question

1. National Bank (see previous problem: pasted down below) is considering adding a second teller to the lunch-time situation to alleviate congestion. If the second teller is added, find the following:
   1. The average teller utilization
   2. The probability that there are 0 customers in the system
   3. The average number of customers in line
   4. The average time a customer waits before it seeing the teller
   5. The average time a customer spends in the service system
   6. If the tellers are paid $15/hour, is it worth adding the second teller (Hint: answer the question by only looking at the single hour by comparing 1 vs. 2 people)

To help answer the question, here is the "previous problem":

1. National Bank currently employs a single teller to assist customers over their lunch breaks. The typical arrival rate of customers is 11 people per hour where the teller can service people at a rate of 12 customers per hour. Assuming the standard assumptions of queuing models are met, find the following:
   1. The utilization of the teller
   2. The probability that there are 0 customers in the system, 8 customers in the system.
   3. The average number of customers in line
   4. The average time a customer waits before it seeing the teller
   5. The average time a customer spends in the service system

Answer 1

After adding the second teller, now this is the problem of the Multi-Server Queuing Model.

Given Information:

The arrival rate of the customer (ʎ) = 11 people per hour

The Service rate of the customer (µ) = 12 people per hour

Number of tellers (s) = 2

A. The average Teller Utilization:

B. The probability that there are 0 customers in the system:

C. The average number of customers in the line

D. The average time a customer waits before seeing the teller

E. The average time a customer spends in the service system

F. The average waiting time of a customer in the line when 2 tellers are used:

The average waiting time of a customer in the line when one teller is used:

Since the waiting time for the customer when one teller is used is much more than in 2 teller systems. Also, the system has some idle time which can be used when there will be high traffic.

Therefore, to improve customer satisfaction, it will be worth to add the second teller.

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