## 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 29

The satisfy the equations "i = Z"iPtl [1-60] <=o with = I. and the distribution {77 1}

is uniquely determined. i-o Proof: By hypothesis, the states j have

recurrence times Ms. Let 7r, = Mf1. Nowpj"} —>□ n,; hence, (1.61) holds for 00 *

= j.

The satisfy the equations "i = Z"iPtl [1-60] <=o with = I. and the distribution {77 1}

is uniquely determined. i-o Proof: By hypothesis, the states j have

**finite**meanrecurrence times Ms. Let 7r, = Mf1. Nowpj"} —>□ n,; hence, (1.61) holds for 00 *

= j.

Page 395

The general queueing process considered in telephone traffic theory can be

described as follows: Consider a telephone exchange (or center) with m (to

or infinite) available trunks or channels, and assume that calls arrive at the ...

The general queueing process considered in telephone traffic theory can be

described as follows: Consider a telephone exchange (or center) with m (to

**finite**or infinite) available trunks or channels, and assume that calls arrive at the ...

Page 399

infinite arid

only to calls are being handled, and we have in this case px = mn, for x > to.

Hence, for x < to the Kolmogorov equations in the

by ...

infinite arid

**finite**channel cases. However, if the system is in state x with x > to,only to calls are being handled, and we have in this case px = mn, for x > to.

Hence, for x < to the Kolmogorov equations in the

**finite**channel case are givenby ...

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### Contents

Introduction | 1 |

Processes Discrete in Space and Time | 9 |

Processes Discrete in Space and Continuous in Time | 57 |

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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