# Simulate 200 arrivals at the bank, specifying the

## Simulate 200 arrivals at the bank, specifying the type of each customer. Simulate the corresponding service-times, and calculate the total waiting and service times for each customer. Explain carefully the meaning of each value you calculate

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Individual Coursework Assignment 2

Coursework Brief

For this coursework you are required to solve a simulation problem using SAS. Your solution should be word-processed and submitted electronically. Your solution should include any SAS code used to process the data, any output produced from the analysis, and a detailed account of the methods you have used, the reasons you have chosen those particular methods, and the conclusions you have drawn.

The problem:

A sub-branch of a major bank has only one service point. The inter-arrival times of customers have an exponential distribution with mean 5 minutes, and for each customer there is a probability 0.7 that the customer is a business customer, and a probability 0.3 that the customer is a private customer. Service times for business customers have an exponential distribution with mean 5 minutes. Service times for private customers have an exponential distribution with mean 2 minutes.

(i) Simulate 200 arrivals at the bank, specifying the type of each customer. Simulate the corresponding service-times, and calculate the total waiting and service times for each customer. Explain carefully the meaning of each value you calculate.  [30 marks]

(ii) Calculate the size of queue each customer finds on arrival. [20 marks]

(iii) What are the minimum, maximum and mean waiting time? What are the minimum, maximum and mean queue length encountered?  [15 marks]

(iv) Produce suitable graphs and summary statistics of the waiting times and the queue lengths encountered, in order to investigate how queues build up, and whether the service regime is adequate to deal with them. Give a detailed report on your results, considering any changes that may be desirable (e.g. opening a separate service point for business customers) and the effect such changes may have. [35 marks]

Key Marking criteria will include:

• Accuracy of the SAS coding and the calculations

• Appropriateness of the methodology

• Clarity and conciseness of the descriptions of the methodology

• Evidence of understanding how the simulation relates to the practical application