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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.

Fast algorithms for generating discrete random variates with changing distributions