A guide to simulation (2nd ed.)
A guide to simulation (2nd ed.)
Introduction to Algorithms: A Creative Approach
Introduction to Algorithms: A Creative Approach
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
Monte Carlo summation and integration applied to multiclass queuing networks
Journal of the ACM (JACM)
Output-sensitive generation of random events
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Speeding up call center simulation and optimization by Markov chain uniformization
Proceedings of the 40th Conference on Winter Simulation
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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 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.