Business

[25 points] Fresh Sub hires three workers during the peak hours. When customers arrive, one worker is dedicated to order taking and preparing the bread and the meat; then the customer is passed to the second worker, who asks the customer about the vegetable selection and specializes in assembly; finally, the customer is passed to the third worker, who is a cashier. The service time for the first worker (order taker) follows a normal distribution with mean equals to 3 minutes and a standard deviation equals to 2 minutes. The service time for the second worker (assembler) is uniformly distributed between 2.2 minutes to 2.6 minutes. The service time for the third worker (cashier) is exactly 2.2 minutes. Customers arrive following a Poisson process with a rate of 15 customers per hour (i.e., the inter-arrival time is exponential).
[6 points] Does Fresh Sub have enough capacity (on average) to serve the customers? [Hint: This problem is designed to show that we can view a queuing system as a process. Note that we have 3 steps (activities) associated with the process of making a sandwich, and each step has a single worker (or resource).]
[3 points] What are the utilization rates of the three workers?
[7 points] On average, how many customers will wait for the first worker (order
taker)? And how long on average will a customer wait?
[3 points] As the customers finish order taking and bread/meat selection and move onto the second worker (assembler), from the assembler’s view, does the arrival rate still follows a Poisson process?
[6 points] Will customers ever wait for the second worker (assembler)? Will customers ever wait for the third worker (cashier)?

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