The critical path provides a lower bound on the execution time of a distributed discrete event simulation. The optimal execution time can be achieved by immediately executing each event on the critical path. A solution is to preferentially schedule an LP, called a critical parent, which probably has a critical event. Critical parent preferential scheduling has been experienced as a viable solution of conservative LP scheduling. In this paper, we introduce a mathematical analysis to show the quantitative benefit of critical parent preferential scheduling in terms of speed-up of execution time. The analysis shows the benefit of the critical parent preferential scheduling with the acceleration of earliest incoming time update and with the reduction of non-critical null messages. The effectiveness of analytical model has been validated with experiments.