## Scheduling Divisible Loads in Parallel and Distributed SystemsThis book provides an in-depth study concerning a claqss of problems in the general area of load sharing and balancing in parallel and distributed systems. The authors present the design and analysis of load distribution strategies for arbitrarily divisible loads in multiprocessor/multicomputer systems subjects to the system constraints in the form of communication delays. In particular, two system architecture-single-level tree or star network, and linear network-are thoroughly analyzed. The text studies two different cases, one of processors with front-ends and the other without. It concentrates on load distribution strategies and performance analysis, and does not cover issues related to implementation of these strategies on a specific system. The book collates research results developed mainly by two groups at the Indian Institute of Science and the State University of New York at Stony Brook. It also covers results by other researchers that have either appeared or are due to appear in computer science literature. The book also provides relevant but easily understandable numerical examples and figures to illustrate important concepts. It is the first book in this area and is intended to spur further research enabling these ideas to be applied to a more general class of loads. The new methodology introduced here allows a close examination of issues involving the integration of communication and computation. In fact, what is presented is a new "calculus" for load sharing problems. |

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### Contents

INTRODUCTION | 1 |

THE SYSTEM MODEL | 13 |

LOAD DISTRIBUTION IN LINEAR NETWORKS | 22 |

LOAD DISTRIBUTION IN TREE AND BUS NETWORKS | 57 |

Networks | 84 |

OPTIMALITY CONDITIONS FOR LOAD DISTRIBUTION | 93 |

ANALYTICAL RESULTS FOR LINEAR NETWORKS | 130 |

OPTIMAL SEQUENCING AND ARRANGEMENT | 147 |

LINEAR AND TREE | 162 |

EFFICIENT UTILIZATION OF FRONT ENDS IN LINEAR | 182 |

Bibliographic Notes | 201 |

MULTIINSTALLMENT LOAD DISTRIBUTION IN SINGLELEVEL | 202 |

MULTIINSTALLMENT LOAD DISTRIBUTION IN LINEAR | 226 |

MULTIJOB LOAD DISTRIBUTION IN BUS NETWORKS | 260 |

FUTURE RESEARCH DIRECTIONS | 275 |

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### Common terms and phrases

algorithm arbitrarily divisible loads assume asymptotic analysis boundary bus network Chapter child processors closed-form expressions closed-form solution communication delay computational load consider control processor defined denote diagram Equa equipped with front equivalent processor example finish Front End function given by Equation given load distribution Hence homogeneous network homogeneous tree instant Lemma linear network link speeds load distribution equations load distribution strategy load fractions load origination minimum processing multi-installment strategy multi-job scheme Nonterminal Nodes normalizing equation Note number of installments number of processors obtain optimal load distribution optimal sequence parent processor problem processing load processor-link pairs processors and links processors stop computing proof prove recursive equations reduced network Robertazzi root processor scheduling sequence of load shown in Figure single-job scheme single-level tree network speed parameters speedup subtree terminal nodes th processor Theorem tion violate Equation 5.28 wTcp zkTcm zTcm