Question

The goal of this assignment is to demonstrate your ability to understand the basics of simple queueing models as solved using a simulation approach:

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 average number of customers in line
   3. The average time a customer waits before it seeing the teller
   4. The average time a customer spends in the service system

Please remember to answer using a simulation approach

** For each problem, you should run at least 10 iterations of 50 simulations to ensure your results are correct. You can report the answers as the aggregation of your trials.

Answer 1

Solution:

Please find the formula below that is used for calculating average queuing metrics. Since it is required to conduct 50 simulations we can assume the below formula still holds because we are averaging the queuing metrics over 50 simulations.

Hence,

Hence,

Hence,

a) Utilization.

b) An average number of customers in the line.

c) The average waiting time in the line

d) The average time a customer spends in the system.