## Mathematical Methods for Construction of Queueing Modelsto the English edition Many processes that describe the operation of engineering, economic, organiza tional, and other systems are represented as sequences of operations performed on material, information, or other types of flows. Typical examples are processes of connection of telephone users, data transmission and processing, calculation at multi user computer centers, and queueing at service centers. The models studied by the theory of service systems, or queueing theory, are used to describe such processes. The more pessimistic term "queueing theory" is used more often in the non-Soviet literature. Random arrivals (requests for service), probability distributions defining queueing processes (distributions of service times and acceptable waiting times), and structure parameters (customer priorities, parameters that delimit acceptable queues, parameters that define paths of customers, etc.) are characteristic com ponents of queueing models. Typical output characteristics of queueing models are the probability distributions of queue lengths, waiting times, lengths of busy periods, and so forth. |

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### Contents

Substantive Formulation of the Problem | 1 |

The Concept of Characterization as a General Mathematical Schema | 17 |

Characterization of the Components of Queueing Models | 125 |

Copyright | |

8 other sections not shown

### Other editions - View all

Mathematical Methods for Construction of Queueing Models Vladimir Kalashnikov No preview available - 2013 |

### Common terms and phrases

According analogous apply approximation assertion assume bound Chapter characteristics characterization closeness concept Consequently consists construction continuity convergence COROLLARY corresponding customers defined definition determine distance distribution function equation estimate evaluation examine example exists exponential fact finite flow formulate identically identification independent inequality input data intervals introduce Kalashnikov known lemma Markov chain mathematical means measure methods metric minimal natural nonnegative obtain Obviously output data P₁ parameters particular perturbed model possible presented probability metric problem proof prove quantity queueing models Rachev random variables reference relation renewal replaced representation respect satisfy sequence side simple solution space specific stability statistical subset theorem theory tion transform valid values vector write