Super-criticality revisited

Critical path analysis has been suggested as a technique for establishing a lower bound on the completion times of parallel discrete event simulations. A protocol is super-critical if there is at least one simulation that can complete in less than the critical path time using that protocol. Previous studies have shown that several practical protocols are super-critical while others are not. We present a sufficient condition to demonstrate that a protocol is super-critical. Also, we show that a condition used in a previous study is not sufficient but is necessary for super-criticality. It has been claimed that super-criticality requires independence of one or more messages (states) on events in the logical past of those messages (states). We present an example which contradicts this claim and examine the implications of this contradiction on lower bounds