In this thesis, we consider the output contention problem with the objective of both increasing the throughput and decreasing the mean cell waiting time for asynchronous transfer mode (ATM) switching systems. We consider a new cell scheduling problem and propose a new cell scheduling algorithm to achieve the objective. The time complexity of the new cell scheduling algorithm is the same as that of the existing cell scheduling algorithm. The simulation results of the new cell scheduling algorithm compared with that of the cell scheduling algorithm are that: 1) The maximum throughputs and efficiencies of the both algorithms are similar. 2) The mean cell waiting time of the new cell scheduling algorithm is less than that of the cell scheduling algorithm under heavy offered load. 3) The cell loss probability of the new cell scheduling algorithm is slightly less than that of the cell scheduling algorithm.