Results of kinetic modelling of an X-ray preionised, discharge-pumped ArF excimer laser, operating with a spikersustainer circuit are presented. The parallel-resistor model includes the complete ArF laser kinetics and calculations of the Boltzmann equation in each layer taking into account the effects of electron-electron and super-elastic collisions. The model further includes a detailed description of the electrical circuit and the formation of filaments with a realistic electrode profile. This model shows a good correspondence with the experimental results in predicting laser energy and optical behaviour. Neglecting the formation of filaments and the electron-electron and super-elastic collision processes yields remarkably poorer results. Parametric studies on the electrode profile, the formation of micro-arcs and on the electrical circuit parameters were performed numerically.