## Communication nets: stochastic message flow and delay |

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### Contents

summary of results | 19 |

the problems of an exact | 35 |

U some new results for multiple | 57 |

Copyright | |

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### Common terms and phrases

alternate routing procedure Appendix average arrival rate average message delay average number average path length behavior bits/sec channel capacity assignment Chap circulant matrix communication nets conservation law consider constraint define delay-dependent priority system described destination equation expected number expected value exponential distribution first-come first-served fixed routing procedure fixed-priority system fully connected function independence assumption interarrival ith channel l)st late-arrival system Markov processes message arrives message enters message lengths message spends message traffic minimizes network topology node Note nth message number of messages number of steps obtain Poisson priority discipline priority group priority structure probability probability density function problem Proof Theorem quantities queue discipline queueing process queueing theory random routing procedures root channel capacity service facility shown in Fig simulation solution square root assignment square root channel switching centers tagged unit tion total capacity total channel capacity total number traffic matrix transmission transmitted waiting line