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Question 4 - Suppose a company has two servers and two employees who are capable of repairing them if they break down. The servers each break down at rate and each repairer can fix a broken down server at a rate of u. Only one repairer will work on a server at any one time. The states, including the rates of arrival and service are depicted in the diagram below and indicate the number of broken servers. For the questions that follow, assume that the system is in a steady state. a) By equating the rate out of state with the rate into state 0 find an expression for Pin terms of p = A/p and P (5 marks) b) Similarly, first find an expression for B, in terms of p and P, and then use your answer to part (a) to find the expression in terms of pand P. (5 marks) c) Using the fact that P+P+P = 1, solve for P, so that you have an expression for P, that depends only on p (5 marks) d) Suppose that the servers break down at a rate of 1 per week. In order to ensure that there are no broken servers for at least half of the time, what is the smallest acceptable service rate? (5 marks) Question 4 - Suppose a company has two servers and two employees who are capable of repairing them if they break down. The servers each break down at rate and each repairer can fix a broken down server at a rate of u. Only one repairer will work on a server at any one time. The states, including the rates of arrival and service are depicted in the diagram below and indicate the number of broken servers. For the questions that follow, assume that the system is in a steady state. a) By equating the rate out of state with the rate into state 0 find an expression for Pin terms of p = A/p and P (5 marks) b) Similarly, first find an expression for B, in terms of p and P, and then use your answer to part (a) to find the expression in terms of pand P. (5 marks) c) Using the fact that P+P+P = 1, solve for P, so that you have an expression for P, that depends only on p (5 marks) d) Suppose that the servers break down at a rate of 1 per week. In order to ensure that there are no broken servers for at least half of the time, what is the smallest acceptable service rate