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We introduce and evaluate the performance of penalty-based resource management (PRM) based on mathematical analysis. In PRM, the penalties associated with connections/sessions and packets facilitates efficient differentiation on delay, blocking/handoff-rejection rates, and utilizations between applications with different QoS requirements, lending itself to an effective tool for DiffServ in the next-generation wireless networks and Internet. An important advantage and unique characteristic of PRM is that such differentiated QoS provisioning is under the control of network operators, in contrast to previous approaches for QoS adaptation. We introduce several Markov fluctuated arrival rate (M-FAR) processes for realistic modeling and feasible analysis of heterogeneous wireless networks. We then present two approaches for the generation of arrival events and service times based on the proposed M-FAR Poisson processes. We derive the PRM theorem, which can provide the exact blocking rates for PRM as well as their closed-form upper and lower bounds. Our analytical results validate our previous simulation results for PRM, and show that PRM can achieve considerably lower blocking rates as compared to previous resource management schemes without PRM mechanisms.