Simulation Optimization is acquiring always more interest within the simulation community. In this field, Mathematical Programming Representation (MPR) has been applied for both simulation and sample path-based optimization of production systems performance. Although in the traditional literature these systems have been represented by means of Integer Programming (IP) models, recently, approximate Linear Programming (LP) models have been proposed to optimize and evaluate the performance of a category of production systems. This work deals with LP models developed based on the Time Buffer (TB) variable whose concept, applicability and structural properties will be presented. Moreover the models convergence, within the Sample Average Approximation (SAA) framework, will be characterized.