## Elements of the theory of Markov processes and their applicationsGraduate-level text and reference in probability, with numerous scientific applications. Nonmeasure-theoretic introduction to theory of Markov processes and to mathematical models based on the theory. Appendixes. Bibliographies. 1960 edition. |

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Page 58

For the continuous time parameter case, we say that {X(t), t > 0} is a Markov

process if P(E,t;lr) = &{Xf) e E \ X(n), 0 < tj < t} = 0>{X(t)eE\X(T) = l;} i.e., the

probability distribution of X(t) is completely

knowledge of the ...

For the continuous time parameter case, we say that {X(t), t > 0} is a Markov

process if P(E,t;lr) = &{Xf) e E \ X(n), 0 < tj < t} = 0>{X(t)eE\X(T) = l;} i.e., the

probability distribution of X(t) is completely

**determined**for all t > t by theknowledge of the ...

Page 313

... 1 - <D(f) + S(t — u) d<b{u) (6.83) Jo Application of the Laplace transformation

to (6.83) gives f"[l— ®(t)]e-<dt co(s) = &{S(t)} = -± ^ (6.84) 1— er"dO(t) Jo Given <

D(<), the Laplace transform of S(t) can be

.

... 1 - <D(f) + S(t — u) d<b{u) (6.83) Jo Application of the Laplace transformation

to (6.83) gives f"[l— ®(t)]e-<dt co(s) = &{S(t)} = -± ^ (6.84) 1— er"dO(t) Jo Given <

D(<), the Laplace transform of S(t) can be

**determined**; the inversion of it gives S(t).

Page 433

Hence the equilibrium queue length X and the balking distribution are uniquely

= 1, we obtain m = <f{X} = _ £— [1 - G'(l) - 2G(1)] (9.200) 1 — p By differentiating ...

Hence the equilibrium queue length X and the balking distribution are uniquely

**determined**if it0, as a function of p, is known. If we differentiate (9.196) and put s= 1, we obtain m = <f{X} = _ £— [1 - G'(l) - 2G(1)] (9.200) 1 — p By differentiating ...

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### Contents

Preface | 1 |

Processes Continuous In Space and Time | 3 |

Processes Discrete in Space and Time | 9 |

Copyright | |

10 other sections not shown

### Other editions - View all

Elements of the Theory of Markov Processes and Their Applications A. T. Bharucha-Reid Limited preview - 2012 |

Elements of the Theory of Markov Processes and Their Applications Albert T. Bharucha-Reid Limited preview - 1997 |

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