## Introduction to Queueing Theory |

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### Contents

Scope and Nature of Queueing Theory | 1 |

Review of Topics from the Theory of Probability | 9 |

BirthandDeath Queueing Models | 73 |

Copyright | |

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### Common terms and phrases

analysis arbitrary customer arrival epoch arrival rate arriving customer arriving customer's distribution assume birth-and-death process blocked customers busy period calculate Chapter conditional probability consider customers arrive customers present customers waiting defined Erlang delay system example Exercise exponential service exponentially distributed finite follows formula geometric distribution given Hence independent interarrival interval iteration Laplace-Stieltjes transform length low-priority customers M/G/l queue Markov chain Markov property mathematical mean number mean service mean waiting method number of customers Observe obtain offered load order of arrival ordered server overflow group Poisson distribution Poisson input Poisson process primary group probability-generating function quasirandom input queue discipline queueing models queueing system queueing theory random variable Riemann-Stieltjes integral right-hand side servers busy service completion service-time distribution function simulation solution solve stationary policy statistical-equilibrium stochastic processes Takacs test customer test customer's theorem tion traffic variance waiting customers waiting for service waiting positions waiting-time distribution function