Worst-case performance of ATM multiplexer with GCRA-conforming arrival processes

The worst-case performance of an asynchronous transfer mode (ATM) multiplexer, in which each multiplexed connection sends cells so as to conform to a generic cell-rate algorithm (GCRA), has been examined. Specifically, the concept of large-deviation ordering is introduced to find the ‘worst’ cell-arrival process, i.e. the one yielding the worst performance of the ATM multiplexer. Several interesting results are obtained. First, the cell-loss ratio (CLR) of a bufferless model does not always give the worst CLR when the buffer size per connection is less than c/M, where c is the capacity of the outgoing link per connection, and M is the peak rate of the connection. Second, the cell-delay variation tolerance does not affect the worst-case performance if the buffer size is sufficiently large. Finally, theoretical support is derived for Yamanaka's conjecture that the greedy on–off pattern is not always the worst cell-arrival pattern among those conforming to the dual GCRAs.