Question

Markov Process for Communication Protocol A simplified communication protocol should be analyzed by a Markov model consisting of 3 states. The initial state (ground state) S₁ Waiting for packet arrival event" will be left with a probability 0,1 to a state S₂ "Validating IP address". The address will be considered correct with a probability 0,4 , moving to a state S₃​

"Processing packet". In the other case (the IP address is considered incorrect), the protocol goes back from S₂ ​ to state S₁ ​ . When in state S₃ ​
the processing of the packet is finished and no new packet has arrived in the meantime (this happens with a probability of 0.7 ), the process goes back to S₁​ , otherwise to state S
. a) Construct the matrix with the transition probabilities.

Answer 1

The transition probabilities for the Markov process can be represented by a matrix where each element represents the probability of transitioning from one state to another. The matrix for this simplified communication protocol with 3 states is given as an example.

Step-by-step explanation:

The transition probabilities for the Markov process can be represented by a matrix. In this case, we have 3 states: S₁, S₂, and S₃. The probability of transitioning from S₁ to S₂ is 0.1, and the probability of transitioning from S₂ to S₁ is 1 (since it always goes back in case of an incorrect IP address). The probability of transitioning from S₂ to S₃ is 0.4, and the probability of transitioning from S₃ to S₁ is 0.7 if no new packet has arrived, otherwise it is 0.3. The matrix representing the transition probabilities would be:

S₁
S₂
S₃


S₁
0
0.1
0


S₂
1
0
0.4


S₃
0.3
0
0.7