## Analytic Methods in Applied Probability: In Memory of Fridrikh KarpelevichThis volume is dedicated to F. I. Karpelevich, an outstanding Russian mathematician who made important contributions to applied probability theory. The book contains original papers focusing on several areas of applied probability and its uses in modern industrial processes, telecommunications, computing, mathematical economics, and finance. It opens with a review of Karpelevich's contributions to applied probability theory and includes a bibliography of his works. Other articles discuss queueing network theory, in particular, in heavy traffic approximation (fluid models). The book is suitable for graduate students, theoretical and applied probabilists, computer scientists, and engineers. |

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### Contents

Karpelevichs Contribution to Applied Probability | 1 |

A Note on an MG1 Queue with a Waiting Server Timer and Vacations | 25 |

Asymptotics for the Maximum of a Modulated Random Walk with HeavyTailed Increments | 37 |

Stochastic Networks and Activity Analysis | 53 |

Stability Bounds for Queueing Models in Terms of Weighted Metrics | 77 |

Contextfree Evolution of Words | 91 |

The Maximum of a TreeIndexed Random Process with Applications | 115 |

Stochastic Bounds for Fast Jackson Networks | 133 |

Markov Chains in a Wedge with Excitable Boundaries | 141 |

Selecting the Shortest of Two Queues Improved | 165 |

Stability of Global LIFO Networks | 177 |

The Exponential Rule | 185 |

New Ratio Limit Theorems for Markov Chains | 203 |

Stability of PatchworkJSQ Feedback Networks | 213 |

### Common terms and phrases

Appl applied approximations assume assumptions asymptotics boundaries branching processes Brownian motion buffer channel component condition consider constant convergence d-left scheme d-left system d-random system defined denote distribution function drift dynamic E-mail address equation ergodic example exists exogenous exponential F. I. Karpelevich fast Jackson network finite fixed point flow fluid limit fluid model follows functions f Hence independent inequality input interarrival Jackson network Kreinin Lemma limit theorems linear Lyapunov function Markov chain Markov processes Math Mathematics Subject Classification matrix mean multiclass queueing networks node nonnegative paper parameters PC boards Poisson positive recurrent Prob probability problem proof of Theorem queue length queueing models queueing systems queueing theory random variables random walk regenerative Rybko satisfies sequence server shortest queue space stationary stochastic matrix stochastic networks stochastic processing stochastic processing network Stolyar subexponential subset Suhov task vacation vector waiting X-small function