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Fast algorithms for generating discrete random variates with changing distributions

Authors:

Sanguthevar Rajasekaran,

Keith W. RossAuthors Info & Claims

ACM Transactions on Modeling and Computer Simulation (TOMACS), Volume 3, Issue 1

Pages 1 - 19

https://doi.org/10.1145/151527.151529

Published: 02 January 1993 Publication History

Abstract

One of the most fundamental operations when simulating a stochastic discrete-event dynamic system is the generation of a nonuniform discrete random variate. The simplest form of this operation can be stated as follows: Generate a random variable X that is distributed over the integers 1,2,…,n such that P(X=i) = a_i/(a₁ +…+a_n), where a_i's are fixed nonnegative numbers. The well-known “alias algorithm” is available to accomplish this task in O(1) time. A more difficult problem is to generate variates for X when the a_i's are changing with time. We present three rejection-based algorithms for this task, and for each algorithm we characterize the performance in terms of acceptance probability and the expected effort to generate a variate. We show that, under fairly unrestrictive conditions, the long-run expected effort is O(1). Applications to Markovian queuing networks are discussed. We also compare the three algorithms with competing schemes appearing in the literature.

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Cited By

Maurer P(2024)Discrete random variates with finite support using differential search treesSIMULATION10.1177/00375497241235199Online publication date: 15-Mar-2024
https://doi.org/10.1177/00375497241235199
D’Ambrosio FBodlaender HBarkema G(2022)Dynamic sampling from a discrete probability distribution with a known distribution of ratesComputational Statistics10.1007/s00180-021-01159-337:3(1203-1228)Online publication date: 1-Jul-2022
https://dl.acm.org/doi/10.1007/s00180-021-01159-3
Maurer P(2017)Finite random variates using differential search treesProceedings of the Summer Simulation Multi-Conference10.5555/3140065.3140093(1-12)Online publication date: 9-Jul-2017
https://dl.acm.org/doi/10.5555/3140065.3140093
Show More Cited By

Index Terms

Fast algorithms for generating discrete random variates with changing distributions
1. Computing methodologies
  1. Modeling and simulation
    1. Simulation theory
    2. Simulation types and techniques
      1. Discrete-event simulation
2. Mathematics of computing
  1. Probability and statistics
    1. Probabilistic reasoning algorithms
      1. Random number generation

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Published In

cover image ACM Transactions on Modeling and Computer Simulation

ACM Transactions on Modeling and Computer Simulation Volume 3, Issue 1

Jan. 1993

79 pages

ISSN:1049-3301

EISSN:1558-1195

DOI:10.1145/151527

Editor:
Richard E. Nance
Virginia Tech, Blacksburg

Issue’s Table of Contents

Copyright © 1993 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 02 January 1993

Published in TOMACS Volume 3, Issue 1

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Cited By

Maurer P(2024)Discrete random variates with finite support using differential search treesSIMULATION10.1177/00375497241235199Online publication date: 15-Mar-2024
https://doi.org/10.1177/00375497241235199
D’Ambrosio FBodlaender HBarkema G(2022)Dynamic sampling from a discrete probability distribution with a known distribution of ratesComputational Statistics10.1007/s00180-021-01159-337:3(1203-1228)Online publication date: 1-Jul-2022
https://dl.acm.org/doi/10.1007/s00180-021-01159-3
Maurer P(2017)Finite random variates using differential search treesProceedings of the Summer Simulation Multi-Conference10.5555/3140065.3140093(1-12)Online publication date: 9-Jul-2017
https://dl.acm.org/doi/10.5555/3140065.3140093
Lang K(2014)Practical Algorithms for Generating a Random Ordering of the Elements of a Weighted SetTheory of Computing Systems10.1007/s00224-013-9496-654:4(659-688)Online publication date: 1-May-2014
https://dl.acm.org/doi/10.1007/s00224-013-9496-6
Ramaswamy RSbalzarini I(2011)Exact on-lattice stochastic reaction-diffusion simulations using partial-propensity methodsThe Journal of Chemical Physics10.1063/1.3666988135:24Online publication date: 23-Dec-2011
https://doi.org/10.1063/1.3666988
Buist EChan WL'Ecuyer PJefferson TFowler JIngalls R(2008)Speeding up call center simulation and optimization by Markov chain uniformizationProceedings of the 40th Conference on Winter Simulation10.5555/1516744.1517034(1652-1660)Online publication date: 7-Dec-2008
https://dl.acm.org/doi/10.5555/1516744.1517034
Buist EChan WL'Ecuyer P(2008)Speeding up call center simulation and optimization by Markov chain uniformization2008 Winter Simulation Conference10.1109/WSC.2008.4736250(1652-1660)Online publication date: Dec-2008
https://doi.org/10.1109/WSC.2008.4736250
Slepoy AThompson APlimpton S(2008)A constant-time kinetic Monte Carlo algorithm for simulation of large biochemical reaction networksThe Journal of Chemical Physics10.1063/1.2919546128:20Online publication date: 23-May-2008
https://doi.org/10.1063/1.2919546
Bernstein D(2005)Simulating mesoscopic reaction-diffusion systems using the Gillespie algorithmPhysical Review E10.1103/PhysRevE.71.04110371:4Online publication date: 8-Apr-2005
https://doi.org/10.1103/PhysRevE.71.041103
Jaeyong Lim Rajasekaran S(2003)Parallel cache management protocol and algorithm for cooperative Web serversIEEE International Conference on Communications, 2003. ICC '03.10.1109/ICC.2003.1204473(918-922)Online publication date: 2003
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