1. Each year, an average of 10 upscale restaurants open in Cary, NC. The average time that one of these restaurants stays open for business is 2 years. Assume the time a restaurant stays open is exponentially distributed while the time between openings follows a 2-stage, special Erlang distribution.

a. Assuming this trend continues, how many of these restaurants would you expect to find open in the future?

b.Assume that the Town of Cary is considering passing an ordinance forbidding more than 5 of these restaurants to be open one time. Build a model that could be used to answer the questions of parts c and d, below. Your model must include (1) a state definition, (2) a list of possible events, and (3) a state transition rate diagram.

c.Write down any three balance equations for your model.

d.Assume that you have solved for the steady state probabilities ('s).(Subliminal hint: Don't forget about the Law of Total Probability.)Using these 's as needed, give a mathematical expression for each of the below questions.

i)What fraction of the time are there none of these restaurants open?

ii)What is the effective rate that restaurants go out of business?