## Introduction to queueing theory |

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### Contents

PROBLEMS OF THE THEORY OF QUEUEING PROCESSES | 1 |

THE INCOMING STREAM | 54 |

SOME TYPES OF STOCHASTIC PROCESSES | 114 |

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### Common terms and phrases

absolutely continuous analytic arbitrary assumption busy period characteristics completely component constant converges corresponding customer arrives customer is served customer stream cycle death processes defined determined distribution function ergodic distribution ergodic theorem event exists exponentially distributed failure finite given instant Hence incoming stream integro-differential equations interval of length Khinchin L-process Laplace transform Laplace-Stieltjes transform large number Lemma Let us assume Let us consider Let us denote Let us introduce machines Markov chain Markov process mathematical expectation method Monte Carlo method nonnegative notation number of customers obtain Obviously occur orderly parameter Poisson process Poisson stream problem proof proved queueing systems queueing theory reliability theory renewal process renewal theory satisfied semi-Markov process sequence server is free servers are busy serving system simple stream single-server system solution stationary stream stochastic process stream without aftereffects subsection system with waiting tion total probability formula transition units Veroyatnostei zero