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I'm doing a self-study of semi-Markov processes and was wondering if there are efficient methods for generating random numbers for sojourn times. For example, generating a bunch of random numbers from a given distribution might be faster than generating a single random number at each step, especially for distributions that are more expensive than the usual exponential/geometric.

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What do you mean by efficient methods? Could you also describe in more details what you mean by a semi-Markov process. Also, probably [markov-chains] and [markov-process] are not very appropriate, but a [reference-request] should likely be added. –  user40314 Jan 15 '13 at 3:41
What I mean by semi-Markov process is basically a process with a given transition matrix that is Markovian at the jump times, with sojourn times depending on the current state and the next state and specified by arbitrary distributions. –  Bhuvanesh Jan 24 '13 at 23:27
For simulation purposes, it might be better to generate several random numbers at a time from a given distribution, so I'm looking for heuristic sampling strategies that give good performance while not generating an excess of random numbers and taking up memory. –  Bhuvanesh Jan 24 '13 at 23:32
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