In this thesis work, the problem of scheduling deadline constrained traffic is studied. The problem is explored in terms of Weighted Round Robin (WRR) service discipline in input queued packet switches. Application of the problem may arise in packet switching networks and Satellite-Switched Time Division Multiple Access (SS/TDMA) systems. A new formulation of the problem is presented. The main contribution of the thesis is a ’’backward extraction” technique to schedule packet forwarding through the switch fabric. A number of heuristic algorithms, each based on backward extraction, are proposed, and their performances are studied via simulation. Numerical results show that the algorithms perform significantly better than earlier proposed algorithms. The experimental results strongly assert Philp and Liu conjecture.