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Analysis of Random Scheduling Policy of Multi-Server Parallel System with Redundancy: Quality of Exponent
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: Received: 25 December 2019 / Approved: 26 December 2019 / Online: 26 December 2019 (10:51:23 CET)
How to cite: Zhang, J. Analysis of Random Scheduling Policy of Multi-Server Parallel System with Redundancy: Quality of Exponent. Preprints 2019, 2019120353 Zhang, J. Analysis of Random Scheduling Policy of Multi-Server Parallel System with Redundancy: Quality of Exponent. Preprints 2019, 2019120353
Abstract
A multi-server parallel system dispatches the incoming job, which contains kn tasks into n servers. A job is considered to be computed if all the tasks associated with the job are processed. One job’s tasks can be encoded into at least kn “replicas” such that the job is considered to be served if any kn replicas finishing computation. In this paper, we analyze the random scheduling policy of a multi-server computing system under discrete time model in terms of Quality of Exponent (QoE), which is defined as the probability exponent that a typical job can be computed within a given number of time slots. We let kn/n be a constant. Assuming that any task of any job can be randomly dispatched by a “scheduler” to any server, and computing each task takes exactly one time slot. We divide the calculation of probability exponent into two parts, exponent of numerator and exponent of denominator. For the denominator, we give the almost exact exponent using Lagrange multiplier method, while for the numerator, an upper bound of the numerator’s exponent is provided. In addition, we also express the exponent in terms of information theoretical quantities and reconsider both of exponents in the context of large deviation theory.
Keywords
probability exponent; multi-server parallel system; discrete time model; arrangement of multiple sets; large deviation theory
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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