A many-state Markov model for the estimation and prediction of computer software performance parameters

A many-state Markov model has been developed for the purpose of providing various performance criteria for computer software. The software system under consideration is assumed to be fairly large, of the order of 10 5 words of code, so that statistical deductions become meaningful, and is assumed to initially contain an unknown number of unknown bugs. The model provides estimates and predictions of the most probable number of errors that will have been corrected at a given time t in the operation of this software package based on preliminary modeling of the error occurrence rate λ as well as the error correction policy μ. The model also provides predictions for the availability A(t) and for the reliability R(t) of the system. The differential equations corresponding to the Markov model are solved for the case when λ and μ are constant using an exact (closed-form) solution. The numerical solution is also obtained for this case for verification and demonstrative purposes. The more interesting and important case, from an applications point of view, is that when λ and μ are not constant, but rather functions of the state of debugging achieved. This case is solved numerically only, since the exact solution is cumbersome. It is also demonstrated that the numerical solution is superior to the so-called exact solution. Finally, some extensions and modifications of the basic Markov model are briefly discussed.