1 Problem: 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 S₂. a) Construct the matrix with the transition probabilities. b) Draw the Markov model. c) What is the probability of the system being in the ground state S₁?
1 Problem: 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 S₂. a) Construct the matrix with the transition probabilities. b) Draw the Markov model. c) What is the probability of the system being in the ground state S₁?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:1 Problem: 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 S₂.
a) Construct the matrix with the transition probabilities.
b) Draw the Markov model.
c) What is the probability of the system being in the ground state S₁?
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