The essence of efficient scheduling and data transmission techniques lies in providing the web-applications with advanced data processing capabilities. In this paper we have efficiently combined the push and the pull scheduling to develop a new, practical, dynamic, hybrid scheduling strategy for heterogenous, asymmetric environments. The proposed algorithm dynamically computes the probabilities and the optimal cutoff-point to separate the push and the pull data sets. The data items are also assumed to be of variable lengths. While the push strategy uses the flat, roundrobin scheduling, the pull items are determined by stretch-optimal (max-request min-service time) scheduling policy. In order to make the scheduling more practical, we have considered the impact of the impatience of the clients waiting to get the service of a particular data item. The effects of this impatience can lead to departure of specific client(s) from the system. Our proposed hybrid scheduling strategy takes care of these effects to capture a real portrayal of the system dynamics. These scenarios are modelled by suitable birth and death process to analyze the overall expected delay of the system. Subsequently, simulation results corroborate the average system performance and points out significant improvement over existing hybrid systems in terms of average waiting time spent by a client.