In queueing network analysis, the Markovian arrival process, MAP, can be used as approximating arrival or departure processes. While the renewal processes such as Poisson process can be generated based on the marginal moments, the Markovian arrival process requires lag-1 joint moment or joint distribution function. In fact, the Markovian arrival process can be simulated by two transition rate matrices, (D0, D1), which is called the Markovian representation. However, finding a Markovian representation of higher order involves a numerically iterative procedure due to redundancy in the Markovian representation. Since there is one-to-one correspondence between joint moments and the coefficients of the joint Laplace transform, generating a MAP based on joint distribution can be much less complicated. In this paper, we propose an approach to generate a MAP based on joint distribution function which can be quickly obtained from joint moments and joint Laplace transform. Closed form formula and streamlined procedures are given for the simulation of MAP of order 2.
