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1. For this problem you should use hand calculation, not a software package. Consider the following two Markov models. (a) (b) A. Assuming $λ=0.01$, what is the system availability of (a) in the steady state? B. Assuming $λ=0.01$ and $μ=0.1$, what is the system availability of (b) in the steady state? C. Assuming $λ=0.01$, what is the MTTF of (a)? Also, if you were asked to describe the meaning of MTTF for (a) and (b), how would you distinguish them from each other?

To solve this problem, we need to analyze the given Markov models and calculate the system availability and mean time to failure (MTTF) for each model. Let's go step by step. (a) Markov model: 1-47 42 31 1(F) 1 1-3/ In this model, the states are represented by the numbers and letters. The transitions between states are indicated by arrows. The numbers inside parentheses represent the failure (F) rates. A. System availability of (a) in the steady state: The system availability (A) is the probability that the system is operational at any given time. In this model, we need to find the steady-state availability. To calculate the system availability in the steady state, we can use the following equation: A = ? / (? + ?µ) Where ? is the total arrival rate (sum of incoming rates) and ?µ is the sum of the service rates. In this case, ? = 0.01 (given) and ?µ = 1 + 3 = 4 (sum of service rates). A = 0.01 / (0.01 + 4) = 0.01 / 4.01 ? 0.002494 So, the system availability of (a) in the steady state is approximately 0.002494.

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