While a number of scheduling policies achieve the maximum throughput region, the average delay minimization problem for cellular broadcast systems still awaits its complete solution. To this end, we introduce a scheduling policy which decomposes the cross-layer delay optimization problem into two subproblems: allocation of physical resources and user priority management. The first subproblem is translated into a weighted sum rate maximization problem that can be efficiently solved for different channel models. The solution of the second subproblem determines the weight factors in the maximization problem expressing the priorities of users. For the latter subproblem we present a so-called idle state prediction algorithm minimizing our relevant delay measure. Analytical and simulative tools are used to show that the introduced scheduling policy provides both optimal throughput and low delay performance.