November 2006 B
High Productivity Computing Systems and the Path Towards Usable Petascale Computing
Andrew Funk, MIT Lincoln Laboratory
John R. Gilbert, UC Santa Barbara
David Mizell, Cray Inc.
Viral Shah, UC Santa Barbara

2. Timed Markov Processes

Figure 1

Figure 1. A timed Markov process.

The process of software development is iterative and probabilistic. It is iterative in the sense that a programmer often repeats a sequence of steps in the software development process; edit, compile, launch test run, for example. It is probabilistic in that the times in each of the steps of the process can vary, and the number of times a cycle will be repeated before the programmer can move on to the next phase is unpredictable. A timed Markov process can model both aspects.

A timed Markov process is a Markov process, augmented with dwell times for state transitions. Each state transition has both a probability of transition and a dwell time associated with it. Timed Markov processes closely resemble signal flow graphs, 6for which well known methods exist to estimate time to completion. Iterative design processes and software development processes have been studied using similar techniques.7 8

In Figure 1, prob(B|A) is the probability of transitioning to state B given that the process is now in state A. time(A|B) is the dwell time spent in state A given that the next state transitioned to is B. prob(C|A), which would equal 1-prob(B|A) in this example, is the probability of transitioning to state C given that the process is now in state A.

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Reference this article
"Modelling Programmer Workflows with Timed Markov Models ," CTWatch Quarterly, Volume 2, Number 4B, November 2006 B. http://www.ctwatch.org/quarterly/articles/2006/11/modelling-programmer-workflows-with-timed-markov-models/

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