The ammount of waste, in tonnes, at a recycling depot can be modelled as a CTMC, where the state of the system represents the amount of waste. Trucks arrive as a Poisson process with rate A = 3 per hour, and each truck dumps 1 tonne of waste. Each tonne of waste is processed by the facilicty in an exponentially distributed amount of time with mean = = 1 = - hours. Assume that the size of the yard is infinite and define lim P (() = *; [-+00 (a) What is the condition for an equlibrium solution to exit? OXCH OX= H (b) If the system is in equlibrium and the yard is visited at a random time, what is the probability there will be 1 tonnes of waste in the yard? (a number) (c) If the system is in equilibrium, what is the proportion of time the system will be in state k ? O TK O time is independent of k O ATE (d) Calculate the expected amount of waste in the yard at equilibrium. [a number)