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A network is modeled by a Markov chain with three states fA;B;Cg. States A, B, C...

A network is modeled by a Markov chain with three states fA;B;Cg. States A, B, C denote low,
medium and high utilization respectively. From state A, the system may stay at state A with
probability 0.4, or go to state B with probability 0.6, in the next time slot. From state B, it may
go to state C with probability 0.6, or stay at state B with probability 0.4, in the next time slot.
From state C, it may go to state B with probability 0.2, or go to state A with probability 0.3, or
stay at state C with probability 0.5, in the next time slot.
(a) Draw the Markov chain with all the states and transition probabilities.
(b) Find the transition probability matrix, P.
(c) What proportion of the time the network operates with high utilization?
(d) Assuming that this network is leased from a major network provider who charges per use as
follows: For state A (low utilization), state B (medium utilization), state C (high utilization),
the monthly cost is $1400, $2800, and $5600 respectively. Then how much would it cost for
leasing the network based on the above Markov model for one year.

Math   Statistics-And-Probability   
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