## Computer Communications, Volume 31B. Gopinath, American Mathematical Society This is the proceedings of the 1983 AMS Short Course given at Denver, Colorado. Computer communications is characterized by rapid technological advances presenting problems of a theoretical nature that are often very difficult to solve. They range from those that arise on a single chip, where communication among thousands of elements on a chip is influenced by electrical properties, to those that arise when human beings communicate with databases where the logical aspects of communications play a more important role. A variety of mathematical methods is needed to attempt to solve such problems; they vary from partial differential equations to temporal or modal logic. The article on ``Diffusion Approximation'' is probably one of the best reviews of this field. The book is unique in having contributors from a variety of different fields of computer communications. All of the articles are of high research value and are self-contained. |

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### Contents

3 | |

SOME PROBABILISTIC ASPECTS OF NETWORK FLOW | 15 |

MODELLING CONCURRENT PROCESSES | 45 |

THE COMMUNICATION COMPLEXITY OF VLSI CIRCUITS | 59 |

DIFFUSION APPROXIMATIONS FOR COMPUTER COMMUNICATIONS NETWORKS | 83 |

### Common terms and phrases

arrival stream assume behavior Boolean predicate buffer central limit theorem channel chip computing circuit communication complexity complexity measure computer communications computer networks condition consider customer arrives customer of type defined Definition delay denote deterministic algorithm diffusion approximation Edited exponentially distributed finite functional central limit GI/G/1 queue heavy traffic limit identity predicate independent initial selection input bits interarrival and service intersymbol interference Jackson network label Las Vegas algorithms Lemma limit process limiting diffusion lower bounds Markov process matrix method metric space non-deterministic normalized number of customers obtained operative starvation output bits overtake-free parameters problem proof queue-length process queueing network queueing systems random variables reflected Brownian motion Reiman 33 Section separator theorem server sojourn space station stationary distribution stochastic processes switching energy theory throughput traffic intensity traffic limit theorems vector VLSI VLSI computations weak convergence when-oblivious