Null message algorithm (NMA) is one of the efficient conservative time management algorithms that use null messages to provide synchronization between the logical processes (LPs) in a parallel discrete event simulation (PDES) system. However, the performance of a PDES system could be severely degraded if a large number of null messages need to be generated by LPs to avoid deadlock. In this paper, we present a mathematical model based on the quantitative criteria specified in  to optimize the performance of NMA by reducing the null message traffic. Moreover, the proposed mathematical model can be used to approximate the optimal values of some critical parameters such as frequency of transmission, Lookahead (L) values, and the variance of null message elimination. In addition, the performance analysis of the proposed mathematical model incorporates both uniform and non-uniform distribution of L values across multiple output lines of an LP. Our simulation and numerical analysis suggest that an optimal NMA offers better scalability in PDES system if it is used with the proper selection of critical parameters.