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This paper discusses the methods available to find transient solutions for huge, but sparse Markov processes, as they arise in connection with queueing systems. The methods discussed include Runge-Kutta, Liou's method and randomization. It is shown that all these methods are closely related, but that the method of randomization is superior to the other two methods. Our own experience and experience of others clearly indicate that all the methods mentioned above are viable for finding transient solutions in problems having 600 states or more.