A hybrid scheduling algorithm is proposed that effectively combines broadcasting of more popular data (push data) and dissemination upon-request for less popular data (pull data), for asymmetric environments in which the clients outnumber the servers and the downlink (server to client) communication bandwidth is much higher than the uplink (client to server) bandwidth. Our algorithm assumes no prior knowledge of the data access probability. Instead, data access probabilities and thereby the cut-off-point to separate the push and the pull sets are computed dynamically. The data items are assumed to be of variable lengths 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 selected based on a pure-push scheduling; whereas the item to be pulled is the one from the pull-queue that has so far accumulated the highest number of pending requests with minimum service time requirement. The expected waiting time for a client in the hybrid schedule is evaluated analytically, and the cutoff point between push and pull items is chosen to the minimize waiting time.