As most waiting queue problem can be simulated with Normally Distribution Model or Poisson Distribution Model, the processing time for a immigration petition case waiting till its approval comes without any exceptions. It has been found that the model characterizes the processing time distribution quite well for the year where a significant amount of cases have been approved. For the year where most case are pending for approval, the Log Normally Distribution Model and Poisson Distribution Model have been founded more accurate for the so-called developing random situation. All the three models mentioned above can be characterized with two parameters μ, the average and σ, the standard deviation. If you do not want dive into the math world to burn your brain, you can just simply view μ as a median value and σ as a judgment of how good μ is. Mathematically, if the ratio of σ over μ is less than 0.5 (σ/μ<0.5), the simulation is considered as "trustworthy" and it is quite safe to conclude that most (>60%) events (approval) happened within the interval from μ-σ to μ+σ. If σ/μ>0.5, either the distribution was too noisy to be simulated with any model or the modeled used just failed for the specific situation considered. But no matter what, the following statement is always true: 50% cases have been waiting longer than μ for their approvals and 50% shorter.