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Dynamic Bandwidth Allocation (DBA) is an important problem for upstream transmission in Fiber-to-the-Home (FTTH) systems. We propose a generalized scheduling mechanism for bandwidth allocation with a view to dissolution of the paradox between efficiency (utilization) and dynamism. Our scheme is shown to work for both TDM PONs as well as hybrid TDM/WDM PONs and pure WDM PONs as well as Next Generation PONs (NGPONs). While conventional bandwidth scheduling schemes pose efficiency as well as fairness issues, our proposed algorithm overcomes these. Three extensions as part of our scheduling technique include: 1) a K-out-of-N scheme to increase efficiency, with a general choice of K being a performance driven parameter; 2) strategic scaling to promote dynamism and reduce bandwidth starvation; and 3) a valuation based strategy that is uniquely tailored to reflect different service requirements. A thorough stochastic analysis based on a Markov-model is presented to compute the network-wide parameters such as delay, optimality and throughput. A detailed simulation model measures the performance of our scheme for latency, dynamism, efficiency and blocking comparing the analytical results with other techniques for dynamic bandwidth allocation in PONs.