Abstract: This paper discusses two theoretic issues in the verification of discrete time system specification (DTSS) simulation in the context of widely used superposed alternative renewal process. Firstly, a quantitative measure of the simulation accuracy at the I/O level is given based on the variance of key simulation variables. Secondly, because the quantitative measure is generally difficult to solve analytically, an approximate expression is given under Zeigler's theoretic framework of simulation, by proving the equivalence of DTSS and discrete event system specification (DEVS) system representations.