The ever-increasing popularity of web services, growing demand for wireless multimedia and introduction of new, feature-enhanced, hand-held devices has already given birth to a new set of data-centric applications. Providing such applications with enhanced data processing capability calls for an efficient scheduling and transmission technique. The goal of most scheduling strategy lies in reducing the average waiting time. However, in most practical systems the variation of waiting time often results in client?s impatience, thus provoking the clients to send repeated requests for the particular data item(s). In this paper we have developed a new hybrid scheduling framework for heterogeneous, asymmetric environments, by exploring the advantages of broadcasting very popular (push) data and dissemination of less popular (pull) data. The data access probabilities and the cut-off point used to segregate push and pull sets are dynamically computed. Packet Fair Scheduling (PFS) and stretch-optimal scheduling principle is deployed to obtain the push and pull schedule respectively. The framework explicitly takes care of the repeated requests originating from the impatient clients and minimizes the overall expected access time by obtaining an optimal cut-off point. Extensive performance analysis and simulation experiments are performed to show the efficiency of the system in reducing the overall expected access time (delay).