The Comet is a very small coffee shop, in the Nichols Arcade, with great coffee and room for at most five customers. That is, if Comet is full, no...

The Comet is a very small coffee shop, in the Nichols Arcade, with great coffee and room for at most five customers. That is, if Comet is full, no other customer can even enter. Suppose that customers arrive according to a Poisson Process with rate 30 per hour and that there is only one server with a service time that can be modeled as an independent exponential random variables with a mean of three minutes. Assume that once served, customers leave.

1. (b) How many customers enter Comet per hour?
2. (c) If the server could work twice as fast, how much more business would be done? (That is, on average, how many more customers would be able to enter Comet per hour with respect to (b)?) Draw the rate diagram, clearly defining the states and labelling all transition rates.
3. (d) Now, if the server was working at the original rate, but she could hire an additional worker with the same service rate, how much more business would Comet do. (That is, on average, how many more customers would be able to enter Comet per hour with respect to (b)?) Draw the rate diagram, clearly defining the states and labelling all transition rates.