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One of the key challenges in the design of bandwidth allocation schemes (BAS) and call admission control (CAC) algorithms for adaptive multimedia services in wireless cellular networks is to balance user satisfaction and fairness among all users, while at the same time ensuring that the scarce bandwidth be utilized efficiently. The inherent nature of the adaptive multimedia services allows some of the ongoing calls to undergo degrading and release some bandwidth which could be used to accommodate new calls, however, at the cost of user satisfaction. We propose a novel bandwidth allocation scheme (BAS) and CAC algorithms which could solve the conflicting relationship between user satisfaction and fairness, which could be more imperative while employing degradation policies. Specifically, we utilize a modified two-dimensional Markov chain model to analyze the proposed BAS and detail the proposed CAC algorithms integrated with a compensation mechanism based on the type of adaptive multimedia services. Moreover, in order to evaluate the performance of our proposed algorithms, we measure metrics such as blocking probability of incoming calls and bandwidth utilization rates through extensive computer simulations. The simulation results show that our proposed algorithms outperform other schemes that assign all the requested channels to incoming adaptive multimedia calls.