Show transcribed image text Problems Related to Markov Chains 1 Problenm Consider a memory system which only allows you to do sequential search. For example a read/write tape drive. If you want to look for a file you have to search sequentially looking at the first file, then the second file and so on until you find the file. A reasonable strategy would be place the most recently retrieved file at the front (imagine that the tape system can magically do this). This way the files that are accessed more often will be "at the front" and require less searching time in the long run. Consider the case with only 3 files A, B, and C. ordered A and then B followed by C, then Xo = Î› BC. Enumerate the state space. 2. If Xo = Î› BC, list all possible states of X1. 3. If p,1,pB, and PC, = 1-PA-pB are the probabilities with which files A, B, and C are accessed, respectively, determine the one-step state transition matrix. 4. If pA-06, pB = 0.10, PC 0.3, determine the steady state probability for the file order ABC. 5. In general show that the steady state probability of the state ABC is given by PAPB PB PC

Problems Related to Markov Chains 1 Problenm Consider a memory system which only allows you to do sequential search. For example a read/write tape drive. If you want to look for a file you have to search sequentially looking at the first file, then the second file and so on until you find the file. A reasonable strategy would be place the most recently retrieved file at the front (imagine that the tape system can magically do this). This way the files that are accessed more often will be "at the front" and require less searching time in the long run. Consider the case with only 3 files A, B, and C. ordered A and then B followed by C, then Xo = Î› BC. Enumerate the state space. 2. If Xo = Î› BC, list all possible states of X1. 3. If p,1,pB, and PC, = 1-PA-pB are the probabilities with which files A, B, and C are accessed, respectively, determine the one-step state transition matrix. 4. If pA-06, pB = 0.10, PC 0.3, determine the steady state probability for the file order ABC. 5. In general show that the steady state probability of the state ABC is given by PAPB PB PC