2, Operations Research Models and Methods. See the Excel help file topic 'About add-ins' before continuing. 5, rate (lambda), 0.2, Queue Station, SimQ1, Number, TBA RN, TFS RN, TBA, TFS, 0, 0, 0, Start, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 10000. Insight to system Hands-on Helps with programming Complex systems not amenable to spreadsheet. 16 Single Server & Queue What are the state variables?
Simulation Models A simulation model is a mathematical model that calculates the impact of uncertain inputs and decisions we make on outcomes that we care about, such as profit and loss, investment returns, environmental consequences, and the like. Such a model can be created by writing code in a programming language, statements in a simulation modeling language, or formulas in a Microsoft Excel spreadsheet.
Regardless of how it is expressed, a simulation model will include:. Model inputs that are uncertain numbers - we'll call these uncertain variables. Intermediate calculations as required. Model outputs that depend on the inputs - we'll call these uncertain functions It's essential to realize that model outputs that depend on uncertain inputs are uncertain themselves - hence we talk about uncertain variables and uncertain functions. When we perform a simulation with this model, we will test many different numeric values for the uncertain variables, and we'll obtain many different numeric values for the uncertain functions.
We'll use statistics to analyze and summarize all the values for the uncertain functions (and, if we wish, the uncertain variables). Creating Models in Excel or Custom Programs An Excel spreadsheet can be a simple, yet powerful tool for creating your model - especially when paired with Monte Carlo simulation software such as. If your model is written in a programming language, Monte Carlo simulation toolkits like the one in Frontline's provide powerful aids. An example model in Excel might look like this, where cell B6 contains a formula =PsiTriangular(E9,G9,F9) to sample values for the uncertain variable Unit Cost, and cell B10 contains a formula =PsiMean(B9) to obtain the mean value of Net Profit across all trials of the simulation. A portion of an example model in the C# programming language might look like this, where the array Var receives sample values for the two uncertain variables X and Y, and the uncertain function values are computed and assigned to the Problem's FcnUncertain object Value property: Choosing Samples for Uncertain Variables We must also choose what random sample values to use for the uncertain variables. During a simulation, a new sample value will be drawn for every uncertain variable on each trial.
Provides state-of-the-art and for your simulation needs. In the simplest case, we might generate random numbers between 0 and 1, and use these as sample values.
But in most cases, the range of values, and chance that different values in the range will be drawn on each trial, must be tailored to the uncertain variable. To do this, we normally choose a probability distribution and appropriate parameters for the uncertain variable. As discussed next, selecting appropriate probability distributions is a key step in building a simulation model.
. Part of the book series (RELIABILITY) Abstract Simulation is widely used to study model for balancing congestion and security of a screening system. Security network is realistic and used in practice, but it is complex to analyze, especially when facing strategic applicants. To our best knowledge, no previous work has been done on a multi-stage security screening network using game theory and queueing theory.
This research fills this gap by using simulation. For multi-stage screening, the method to determine the optimal screening probabilities in each stage is critical. Potential applicants may have access to information such as screening policy and other applicants’ behaviors to adjust their application strategies. We use queueing theory and game theory to study the waiting time and the strategic interactions between the approver and the applicants.
Arena simulation software is used to build the screening system with three major components: arrival process, screening process, and departure process. We use Matlab Graphic User Interface (GUI) to collect user inputs, then export data through Excel for Arena simulation, and finally export simulation from the results of the Arena to Matlab for analysis and visualization. This research provides some new insights to security screening problems. This research was partially supported by the United States National Science Foundation (NSF) under award numbers 1200899 and 1334930. This research was also partially supported by the United States Department of Homeland Security (DHS) through the National Center for Risk and Economic Analysis of Terrorism Events (CREATE) under award number 2010-ST-061-RE0001.
However, any opinions, findings, and conclusions or recommendations in this document are those of the authors and do not necessarily reflect views of the NSF, DHS, or CREATE. Cen Song and Jun Zhuang are the corresponding authors.