L1 retrotransposon is a strange gene in our genome as it is one of only very few causing random DNA mutations (which apparently could be sometimes lethal to the host) . For that reason its reverse transcription mechanism is of great interest and has been extensively studied. However, in order to model L1 reverse transcription a transcription process itself needs to be modeled first. I shall briefly outline a general model of gene transcription and indicate how it can be represented and analyzed using a system of coupled stochastic equations. I will further give an outline of the simulation algorithm for such a system as well as discuss its stationary distribution in relation to parameters estimation and model validation procedures using M/M/Infinity queues and L1 gene data.