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In this paper, we investigate the impact of transmission opportunity (TXOP), arbitration interframe space (AIFS), and contention window on the performance of an IEEE 802.11e cluster with four traffic classes under Poisson frame arrivals. We derive an analytical model of the cluster using queuing model of individual nodes, discrete time Markov chain, and probabilistic modeling of the backoff process. The analytical model demonstrates the complex interaction between TXOP, on one side, and AIFS and contention window, on the other. We derive saturation and stability points for all traffic classes and discuss their dependency on TXOP allocations. Our results indicate that use of nonzero TXOP parameter under Poisson frame arrivals improves performance slightly by separating points of saturation and instability. More substantial performance improvements should be expected by deploying TXOP differentiation under bursty traffic. Since all traffic classes need to operate in stable, nonsaturated regime, this work has important implications for the design of congestion control and admission control schemes in IEEE 802.11e clusters.