Transient Analysis of Asynchronous Markovian Production Lines by Quasi Product Form

Analytical models have been extensively used to analyze the performance of production systems. Due to their enormous state spaces, the analysis of such models is very often approximated and limited to stationary first moment performance measures. However, in presence of randomness, the system performance observed in the short-medium run can be significantly different from the long term average performance. Moreover, modern systems often never reach the steady state due to the continuous product and process modifications that take place over time. Therefore, the analysis of higher order system performance measures in the short run has recently attracted more and more attention both by scientist and practitioners. This paper proposes an approximate model to analyze the performance of asynchronous production lines with finite capacity buffers. The transient probabilities of such model are analyzed by assuming a \emph{quasi product form}. This assumption simplifies the dependency structure of the model and leads to a relatively small set of ordinary differential equations (ODE) that can be used to compute an approximation of the transient probabilities. The accuracy of this approximate method is studied by comparing the numerical results with those provided by simulation.