## 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. |

### Contents

Substantive Formulation of the Problem | 4 |

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

7 | 91 |

Copyright | |

17 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

analogous assertion characterization problem condition construction continuity COROLLARY defined by equation definition distribution functions estimate example exists exponential distribution finite following bound formulate fulfilled function F hyper-Erlang ideal metric identically distributed independent inequality input data input flow intervals Kalashnikov lemma Let us consider Let us define Let us write Lévy metric Lévy-Prokhorov metric Markov chain Markov process Math Mathematical measures method metric space minimal metrics nonnegative obtain output data P₁ P₂ parameter perturbed model probability metric proof quantity quasimetric quasimetric space queueing models queueing theory random variables relation renewal processes right side S. T. Rachev Section semi-Markov process sequence simple metric stability of characterization Statistics stochastic subset theorem Theory Prob tion unperturbed V. M. Zolotarev V. V. Kalashnikov valid values vector weak convergence