ABSTRACT
This chapter provides the mathematical tools commonly used in simulation. It briefly reviews important concepts in probability and statistics relating to simulation modeling, including: probability functions, random numbers generation, random variate generation from distribution functions, and error estimation. Exponential distribution is frequently used in simulations of queueing systems to describe the interarrival or interdeparture times of customers at a server. Poisson distribution is a discrete distribution widely used in modeling arrival distributions and other random events. It is particularly important in the analysis of queueing systems. Normal distribution also known as the Gaussian distribution, is heavily used in probability and statistics. Lognormal distribution is a distribution of a variable whose natural logarithm follows the normal distribution. Just as the normal distribution models an additive process, the lognormal distributiom models a multiplicative process. The Erlang distribution is widely used in queueing theory to model an activity that occurs in phases, with each phase being exponentially distributed.
