jMarkovManual.pdf

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{X(t), t 0} S Q

qij = limt0

P{X(t) =j |X(0) =i} i, j S.

qii i qij i j

P(t)

pij(t) =P{X(t + s) =j |X(s) =i} i, j S.

P(t) =eQt t >0.

= [1, 2, . . . , ]

Q= 0

1= 1,

1
http://localhost/var/www/apps/conversion/tmp/scratch_1/copa.uniandes.edu.cohttp://localhost/var/www/apps/conversion/tmp/scratch_1/copa.uniandes.edu.co


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Q Q=

eEQ(e)

Q(e)

e E

i0 U S

U

S=,U={i0} E U =

e E (i, e)

D:= (i, e) j D

j / S U U :=U {j}

Rij :=Rij+ (i,j,e)

r r(i) i S

r(i) i t

E

r(X(t)

= aP(t)r,

a

ai = P{X(0) =i} , i S

limt

1

t

t0

E

r(X(s)

ds= r.


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MarkovProcessSimpleMarkovProcessGeomProcess

Build Package

JMarkovElement

PropertiesElementEvent PropertiesEvent

State GeomState GeomRelState PropertiesState

Basics Package

SolverSteadyStateSolverGeometrixtSolverTransientSolverJamaSolver

JamaTransientSolver

MtjSolverMtjLogRedSolver

Solvers Package


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MarkovProcess SimpleMarkovProcess

GeomProcess

JMarkovElement

PropertiesStateGeomRelState

EventState

PropertiesEventGeomState

PropertiesElement


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Solver

SteadyStateSolverTransientSolver

JamaSolverJamaTransientSolver MtjSolver

GeometrixtSolver

MtjLogRedSolver

1 2 N N

X(t) = (X(t), Y(t), Z(t)) X(t) Y(t) Z(t) N 2 2 2 N 2 X, Y Z (0, 1, 2)

S={(0, 0, 0), (0, 1, 0), (1, 0, 0)} {(1, 1, k) :k = 0, 1, . . . , N 2}


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. . . (1 ) 2 1 1 2 1+ 2

1+ 2


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K 1, 2, . . . , K N K N k k

k = k

I, k I

I

X(t) = (S(t), Q(t)) S(t) = (S1(t), . . . , S K(t)) Sk(t) = 1 k


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{X(t) : t 0} S = {(n, i) : n 0, 0 i m} n i m

(n, i) (n, i) n =n n =n 1 n =n + 1 n 1 n Q

Q=

B00 B01B10 A1 A0

A2 A1 A0

,

m0 = m m0 B00 m0 m0 B01 B10 (m0 m) (m m0)

Q = 0 1 = 1 Q

= [0, 1, . . .].

n+1= nR, n > 1,

R

m R

A0+ RA1+ R2A2= 0.

R

R0 Rk

Rk+1= (A0+ R2kA2)A

11 .

A1

R

0 1

0 1

B00 B01B10 A1+ RA2

=

0 0

01 + 1(I R)11= 1.


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ri i n 1

n=1

nr= 1(I R)1r,

r m ri nri i n

n=1

nnr= 1R(I R)2r.

B00 B01 B10 A0 A1 A2

A0 A1 A2

R

0 1

n

i

i

i

i

0 i n

M/G/1

x= (x1, x2) x1 0 0 x2 n


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x2 x1

0 i n E={a, c1, c2, . . . , cn} a ci i

a ci, 0 i n i

a

n

n

i

i i

ci

0, 0

n i

a

ci

i


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http://math.nist.gov/javanumerics/jama/http://rs.cipr.uib.no/mtj/


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http://www.java.sun.com/


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Documents

jMarkovManual.pdf