An asynchronous mode transfer (ATM) switch conducting switching based upon the calculation of weights for entries corresponding to cells in an input queue to achieve a high throughput rate which avoids head of line blocking. The switch includes a cell scheduler driven by the iterative resolution of a traffic matrix formed by highest priority entries for each of a plurality of output ports queued in each of a plurality input queues each having separate virtual queues corresponding to the output ports. Conflicts in the matrix are resolved according to weight so that one entry per one row is chosen to be transmitted in parallel. Selection of winning entries from among a group of conflicting entries during any step are resolved by selecting the heaviest weighted entry and leaving the remaining ports maximum satisfactory transmission opportunities. The input queue communicates with the cell scheduler to assign priority level entries corresponding to highest priority cells which are queued in the input queue for each output port. The calculated weight for each entry during an iteration is a function of its priority level and the priority level of all other entries in a common row and column. A subsequent iteration is conducted without the winner and without all other entries in the same row and column as the winner.