Introduce a mathematical model for the metro passengers waiting time

Can be say all or most people tend to do the work faster and also move faster from place to other place, and fed up with the factors which could cause things done and moving on slowly and keep aloof too waiting. In this paper, given the importance of passenger waiting time in systems of Public transport such as Metro and being an effective amount of it on the amount of the people welcomed, therefore we attempted to identify factors that can be expected over Passengers waiting time and with regard to relationship between these factors, we introduce a Mathematical model for minimizing the average waiting time. For comparison Mathematical model with the actual model, simulation was required that using simulation software Arena we achieved this goal. We also solve the Mathematical model using MATLAB software and the output was created by simulation model. To obtain the necessary parameters, sampling was done from the station of Tehran TARASHT, 8 time, an hour a day in the middle of the week. Solution of these models was done in two forms.When there is an operator at the box office and also when there are two operators. Finally After solving the Both models in two-forms and 8 time, The Obtained Output were compared.