## 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 157

now divide the real line into intervals of fixed

sequence of states such that je - a - (j + 1)e denotes that X(t) e E,. We now

consider the transition probabilities of the process defined on the set of intervals {

E}}.

now divide the real line into intervals of fixed

**length**e and denote by {E,} asequence of states such that je - a - (j + 1)e denotes that X(t) e E,. We now

consider the transition probabilities of the process defined on the set of intervals {

E}}.

Page 431

In this case there is complete balking for queues of

than n. An examination of (9.192) and (9.193) shows that, associated with any

equilibrium distribution of queue

In this case there is complete balking for queues of

**length**equal to or greaterthan n. An examination of (9.192) and (9.193) shows that, associated with any

equilibrium distribution of queue

**length**satisfying (9.193), there is a balking ...Page 433

where tro(s) denotes to with p replaced by ps, and from (9.195) and (9.198) we

have G(s) = #| - o (9.199) 0 Hence the equilibrium queue

balking distribution are uniquely determined if tro, as a function of p, is known.

where tro(s) denotes to with p replaced by ps, and from (9.195) and (9.198) we

have G(s) = #| - o (9.199) 0 Hence the equilibrium queue

**length**X and thebalking distribution are uniquely determined if tro, as a function of p, is known.

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### Contents

Introduction | 1 |

Processes Discrete in Space and Continuous in Time | 57 |

Processes Continuous in Space and Time | 129 |

Copyright | |

9 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 |

### Common terms and phrases

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