In a production flow line with stochastic environment, variability affects the system performance. These stochastic nature of real-world processes have been classified in three types: arrival, service and departure process variability. So far, only service process - or task time - variation has been considered in assembly line (AL) balancing studies. In this study, both service and flow process variations are modelled along with AL balancing problem. The best task assignment to stations is sought to achieve the maximal production. A novel approach which consists of queueing networks and constraint programming (CP) has been developed. Initially, the theoretical base for the usage of queueing models in the evaluation of AL performance has been established. In this context, a diffusion approximation is utilised to evaluate the performance of the line and to model the variability relations between the work stations. Subsequently, CP approach is employed to obtain the optimal task assignments to the stations. To assess the effectiveness of the proposed procedure, the results are compared to simulation. Results show that, the procedure is an effective solution method to measure the performance of stochastic ALs and achieve the optimal balance.