class19 - remember U_c=1 n^0 = 1 so U_s^0 + U_f^0 = 1 P_200=

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Sheet1 Page 1 pairing the arcs -Equate the flow into "A" from "B" to the flow into "B" from "A" see previous example 1) _f*P_110 = _c*p*P_200 2) _s*P_101 = _c(1-P)*P_101 3) _f*P_020 = _c*p*P_110 4) _s*P_011 = uc*(1-p)*P_110 5) _f*P_011 = uc*p*P_101 6) _s*P_002 = uc*(1-p)*P_101 solve for P_110 P_110 = (uc*P / uf) * P_200 P_101 = (uc*(1-P) / uf) * P_200 P_020 = (uc*P / uf) * P_110 = (uc*P / uf)^2 *P_200 ... ... meanwhile back at the lair Relitive utilization assume CPU = 100% +-----------------------+ | fastDisk ( f)| |lambda p queue | +queue-------< >----+ CPU (1-p) queue ( s) c slowDisk U_c= back now(U means Utiliazation) 1)P_110=U_f*P_200 2)P_101=U_s*P_200 3)P_020=U_f*P_110 = U_f^2*P_200 4)P_011=U_s*P_110 = U_s*U_f *P_200 5)P_011=U_F*P_101 = U_s*U_f *P_200 6)P_002=U_s*P_101 = U_s^2*P_200 use Pi = 1 P_200*[1+Uf + U_s + U_f^2 + U_s*U_f + U_s^2]=1
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Sheet1 Page 2 P_200 = 1/[1+Uf + U_s + U_f^2 + U_s*U_f + U_s^2] its called a changeover. and noone in the audience has any idea.
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Unformatted text preview: remember U_c=1 n^0 = 1 so U_s^0 + U_f^0 = 1 P_200= U_c^2*Uf^0*U_s^0-----------------------------------[U_c^2*Uf^0*U_s^0 + U_c^1*U_f^1*U_s^0 + U_c^1*U_f^0*U_s^1 + U_c^0*U_f^2*U_s^0 + U_c^0*U_f^1*U_s^1 + U_c^0* U define terms of the denomenator G(2) P_200 = U_c^2*Uf^0*U_s^0----------------G(2) G(2) is the normalization constant such that Pi = 1 the number of terms in G() is equal to the number of states in the system therefore it is dependant on the number of devices and the multiprograming level usually written as G(MPL) hence G(2) P_110 = U_c^1 U_c^1 U_s^0-----------------G(2) P_101 = U_c^1 U_c^0 U_s^1-----------------G(2) P_020 = U_c^0 U_c^2 U_s^0-----------------G(2) P_011 = U_c^0 U_c^1 U_s^1-----------------G(2) P_002 = U_c^0 U_c^0 U_s^2-----------------G(2) P_200 = U_c^2 U_c^0 U_s^0-----------------G(2)...
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class19 - remember U_c=1 n^0 = 1 so U_s^0 + U_f^0 = 1 P_200=

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