### 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}/(a_{1} + ... + a_{n}), where the 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.

Original language | English (US) |
---|---|

Pages (from-to) | 1-19 |

Number of pages | 19 |

Journal | ACM Transactions on Modeling and Computer Simulation |

Volume | 3 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1993 |

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### ASJC Scopus subject areas

- Software
- Modeling and Simulation

### Cite this

*ACM Transactions on Modeling and Computer Simulation*,

*3*(1), 1-19. https://doi.org/10.1145/151527.151529

**Fast algorithms for generating discrete random variates with changing distributions.** / Rajasekaran, Sanguthevar; Ross, Keith.

Research output: Contribution to journal › Article

*ACM Transactions on Modeling and Computer Simulation*, vol. 3, no. 1, pp. 1-19. https://doi.org/10.1145/151527.151529

}

TY - JOUR

T1 - Fast algorithms for generating discrete random variates with changing distributions

AU - Rajasekaran, Sanguthevar

AU - Ross, Keith

PY - 1993/1

Y1 - 1993/1

N2 - 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) = ai/(a1 + ... + an), where the ai'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 ai'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.

AB - 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) = ai/(a1 + ... + an), where the ai'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 ai'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.

UR - http://www.scopus.com/inward/record.url?scp=0027189274&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027189274&partnerID=8YFLogxK

U2 - 10.1145/151527.151529

DO - 10.1145/151527.151529

M3 - Article

AN - SCOPUS:0027189274

VL - 3

SP - 1

EP - 19

JO - ACM Transactions on Modeling and Computer Simulation

JF - ACM Transactions on Modeling and Computer Simulation

SN - 1049-3301

IS - 1

ER -