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.
- What is the average number of customers in Comet? Draw the rate diagram, clearly defining the states and label all transition rates.