Summary form only given. A hybrid scheduling is introduced that effectively combines broadcasting of more popular data (push data) and dissemination upon-request for less popular data (pull data), for asymmetric environments where the clients outnumber the servers having higher downlink communication (server to client) bandwidth than the uplink communication (client to server) bandwidth. We do not assume prior knowledge of the data access probability; in fact data access probabilities and thereby the cut-off-point to separate the push and the pull set are computed dynamically. In our scheme all the data items are assumed to be of variable length arranged in descending order of their access probabilities. The clients send their requests to the server, which queues them up for the pull items. At any instant of time, the item to be broadcast is designated applying a pure-push scheduling; whereas the item to be pulled is the one stored in the pull-queue, which has accumulated, so far, the highest number of pending requests with minimum service time requirement. The expected waiting time spent by a client in the hybrid schedule is evaluated analytically, and the cut-off point between push and pull items is chosen to minimize waiting time.