The authors consider the output contention problem with a view towards increasing the throughput for asynchronous transfer mode (ATM) switching systems. A cell scheduling algorithm for increasing the throughput is proposed. The maximum throughput is increased up to 0.957. The efficiency (output trunk utilization/input trunk utilization) is almost equal to 100% and is independent of the switch size and traffic load. A switching system implemented with this cell scheduling algorithm is also proposed. The switching network usually consists of a sorting network followed by a routing network. Here, it is sufficient for a sorting network to establish input-output paths through it simultaneously without conflicts, and it is not necessary to append a routing network. In addition, a parallel mesh-connected architecture of a component of the switching system is proposed to speed up the cell scheduling of the system. Consequently, this approach can offer an effective alternative to ATM switching systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>