scholarly journals Scheduling independent stochastic tasks under deadline and budget constraints

2019 ◽  
Vol 34 (2) ◽  
pp. 246-264 ◽  
Author(s):  
Louis-Claude Canon ◽  
Aurélie Kong Win Chang ◽  
Yves Robert ◽  
Frédéric Vivien
Keyword(s):  
Probability Distributions ◽  
Problem Instance ◽  
Cloud Platform ◽  
Expected Number ◽  
Asymptotically Optimal ◽  
Discrete Probability ◽  
Distribution Laws ◽  
Scheduling Strategies ◽  
Discrete Probability Distributions ◽  
Deadline Constraint

This article discusses scheduling strategies for the problem of maximizing the expected number of tasks that can be executed on a cloud platform within a given budget and under a deadline constraint. The execution times of tasks follow independent and identically distributed probability laws. The main questions are how many processors to enroll and whether and when to interrupt tasks that have been executing for some time. We provide complexity results and an asymptotically optimal strategy for the problem instance with discrete probability distributions and without deadline. We extend the latter strategy for the general case with continuous distributions and a deadline and we design an efficient heuristic which is shown to outperform standard approaches when running simulations for a variety of useful distribution laws.

scholarly journals Remote Sampling with Applications to General Entanglement Simulation

Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 92
Author(s):  
Gilles Brassard ◽  
Luc Devroye ◽  
Claude Gravel
Keyword(s):  
Initial Phase ◽  
Communication Protocol ◽  
Probability Distributions ◽  
Expected Number ◽  
Trade Off ◽  
Discrete Probability ◽  
Rejection Algorithm ◽  
Distributed Sampling ◽  
Discrete Probability Distributions ◽  
Projective Measurements

We show how to sample exactly discrete probability distributions whose defining parameters are distributed among remote parties. For this purpose, von Neumann’s rejection algorithm is turned into a distributed sampling communication protocol. We study the expected number of bits communicated among the parties and also exhibit a trade-off between the number of rounds of the rejection algorithm and the number of bits transmitted in the initial phase. Finally, we apply remote sampling to the simulation of quantum entanglement in its essentially most general form possible, when an arbitrary finite number m of parties share systems of arbitrary finite dimensions on which they apply arbitrary measurements (not restricted to being projective measurements, but restricted to finitely many possible outcomes). In case the dimension of the systems and the number of possible outcomes per party are bounded by a constant, it suffices to communicate an expected O ( m 2 ) bits in order to simulate exactly the outcomes that these measurements would have produced on those systems.

scholarly journals A Neyman-Pearson Proper Way to Universal Testing of Multiple Hypotheses Formed by Groups of Distributions

2020 ◽  
pp. 18-33
Author(s):  
Evgueni Haroutunian ◽  
Aram Yesayan
Keyword(s):  
Error Probability ◽  
Probability Distributions ◽  
Single Letter ◽  
Asymptotically Optimal ◽  
Discrete Probability ◽  
Multiple Hypotheses ◽  
Universal Testing ◽  
Error Probabilities ◽  
Discrete Probability Distributions ◽  
The Given

The asymptotically optimal Neyman-Pearson procedures of detection for models characterized by M discrete probability distributions arranged into K, 2 ≤ K ≤ M groups considered as hypotheses are investigated. The sequence of tests based on a growing number of observations is logarithmically asymptotically optimal (LAO) when a certain part of the given error probability exponents (reliabilities) provides positives values for all other reliabilities. LAO tests sequences for some models of objects, including cases, when rejection of decision may be permitted, and when part, or all given error probabilities decrease subexponentially with an increase in the of number of experiments, are desined. For all reliabilities of such tests single-letter characterizations are obtained. A simple case with three distributions and two hypotheses is considered.

scholarly journals Classroom note: An inductive derivation of Stirling numbers of the second kind and their applications in statistics

1997 ◽  
Vol 1 (2) ◽  
pp. 151-157 ◽  
Author(s):  
Anwar H. Joarder ◽  
Munir Mahmood
Keyword(s):  
Probability Distributions ◽  
Stirling Numbers ◽  
Higher Order ◽  
Inductive Method ◽  
Higher Order Moments ◽  
Discrete Probability ◽  
Discrete Probability Distributions

An inductive method has been presented for finding Stirling numbers of the second kind. Applications to some discrete probability distributions for finding higher order moments have been discussed.

INTERACTIVE SIMULATIONS OF DISCRETE PROBABILITY DISTRIBUTIONS

2019 ◽  
Author(s):  
Rubén Darío Santiago Acosta ◽  
Ernesto Manuel Hernández Cooper ◽  
Faustino Yescas Martinez
Keyword(s):  
Probability Distributions ◽  
Discrete Probability ◽  
Discrete Probability Distributions ◽  
Interactive Simulations
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