Efficient matrix-exponential random variate generation using a numeric linear combination approach

Matrix Exponential (ME) probability distributions form a versatile family of distributions and enable an accurate description and simulation of a wide variety of situations where a positive distribution is required. In queueing theory they are used for arrival and service processes. Random Number Generators (RNG) for ME's are not commonly available. In this work, we create a new ME RNG by scaling a uniform random number using a weighting function, which is then converted to the ME random variate using an inverse transformation. The weighting function is obtained by arranging the distribution as a linear combination (allowing negative and/or complex components) of exponentials and numerically solving the cumulative distribution function (CDF) for e−x. Of the proposed techniques to generate ME random variables, our method is more efficient and can be applied to a wider sub-class of ME distributions. Additionally, we have incorporated our RNG into OPNET and it can readily be integrated into other simulation packages as well. Distributions are specified through their moments, by a matrix representation (include Phase Type), or by selecting from a palette of common distributions (hyper-, hypo-, exponential). The accuracy of the RNG is determined by analyzing the first three moments of the generated random numbers. Finally, the performance of our RNG is compared to other methods to generate ME random variates.