The queue theory is based on the assumption that most system are normally assigned to stay under steady state. Therefore, the initial problem can be represented by a symbolic model but such a representation does not permit analysis of all the interesting alternatives. When the solution to the problem is thus restricted to a particular subclass of available alternatives, the symbolic model can be solved by mathematics to deduce which alternative is optimal. However, when be consider slightly more complicated alternatives, the analytic procedures become interactable. The purpose of this study is to show how a simulation model enable us to handle the more complicated system after examining the characteristics of the complications that negate more complicated system. Then construct a simulation model and compare the solution of simulation models with analytic methods.