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MathGroup Archive 2007

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equation solving in a markov model

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75204] equation solving in a markov model
  • From: omur.tosun at gmail.com
  • Date: Fri, 20 Apr 2007 00:41:04 -0400 (EDT)

sorry for the previous massage ....

shortly i prepare a markov availability model....and i'm a bit
confused, hope someone help me...

a = Lambda[d]/(Lambda[d] + Lambda[in]);


P(0, 0)  = 1/(k + (Lambda[in] / Mu[in]) * (k - 1) +
                          (Lambda[in] / Mu[m]) * (k - 1) +
                          a* ((1 - a^(n - k)) / (1 - a)) +
                          (Lambda[in] / Mu[in])* a * ((1 - a^(n -
k)) / (1 - a)) +
                         (Lambda[in] / Mu[M]) * a * (( 1 - a^(n -
k)) / (1 - a)) +
                         (Lambda[d] / Mu[D]) * a^(n - k));

> Availability (A)  = P(0,0)*(k + (a * (1-a^(n-k))))

> i want to find the optimal Lambda[in] which max. the availability.. is there
> any way to solve without giving any numerical values? i use D[A, Lambda[in]]
> but without numerical values i couldn't achieve any solution
>
> and i want to plot A-Lambda[in] from the equation, what should i do for it?
>
> best regards...



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