The design and operation of high volume conveyor systems in distribution centers are important due to its high cost, large footprint and critical role in the system. However, there is no analytical model available. In this paper, we study the characteristics of the conveyor sortation system, develop a genetic model of a complex conveyor network. We then use the Delay and Stock abstraction to develop an approximate analytical method using sample path analysis and dynamic network flow model. The decision variables include length of accumulation segments and the speeds of conveyor components aforementioned decision variables. This analytical solution provides faster analysis,insights and useful subgradient with respect to the decision variables.