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In this paper, we propose an analytical approach for performance evaluation of the classic tree/stack splitting algorithm in an interference-dominating wireless access network with random traffic and finite nodes. In an interference-dominating wireless access network, a receiver could simultaneously receive multiple packets from a variety of transmitters, as long as the signal-to-interference-plus-noise ratio exceeds a predetermined threshold. We use discrete-time Markov chains and regenerative processes to derive the throughput curve, the packet blocking probability, the average system size, and the average packet delay. We show that the exact performance of the splitting algorithm depends on the total number of nodes in the network. We verify our numerical results by rigorous mathematical proof and computer simulations.