Show transcribed image text 3 Problem The article "Markov Chain Model for Performance Analysis of Transmitter Power Control in Wireless MAC Protocol" 21st International Conference on Advanced Networking and Applications, 2007) describes a Markov chain model for the state of the communication channel using a particular "slotted non-persistent" (SNP) protocol. The channel's possible state are (1) idle, (2) successful transmission and (3) collision. For the particular values of the authors' proposed four parameter model, we get the following transition matrix 0.50 0.40 0.10 P=10.02 0.98 0 0.12 0.88 1. Verify that P is the transition matrix of an Ergodic (regular) Markov Chain. 2. Determine the steady state probabilities for this channel 3. What proportion of the time is the channel idle, in the long run. 4. What is the average number of time steps between successive collisions?

3 Problem The article "Markov Chain Model for Performance Analysis of Transmitter Power Control in Wireless MAC Protocol" 21st International Conference on Advanced Networking and Applications, 2007) describes a Markov chain model for the state of the communication channel using a particular "slotted non-persistent" (SNP) protocol. The channel's possible state are (1) idle, (2) successful transmission and (3) collision. For the particular values of the authors' proposed four parameter model, we get the following transition matrix 0.50 0.40 0.10 P=10.02 0.98 0 0.12 0.88 1. Verify that P is the transition matrix of an Ergodic (regular) Markov Chain. 2. Determine the steady state probabilities for this channel 3. What proportion of the time is the channel idle, in the long run. 4. What is the average number of time steps between successive collisions?