456 The UMAP Journal 28. 3(2007) The boarding technique is modeled in a matrix identical in size to the matrix presenting the layout of the plane. This matrix is full of positive integers, one for each passenger, assigned to a specific submatrix, representing each ssenger's boarding group location. within each of these submatrices, seat- ng is assigned randomly to represent the random order in which passengers line up when their boarding groups are called. Interferences are counted in every location where they occur within the ma- trix representing the plane layout. These interferences are then cast into our probability distribution defined above, which gives a measurement of time Passengers wait for interferences around them before moving closer to their assigned seats; if an interference is found, the passenger will wait until the time delay has finished counting down to O The simulation ends when all delays caused by interferences have counted down to O and all passengers have taken their assigned seats Strengths and Weaknesses of the Model Strengths It is robust for all plane configurations and sizes. The boarding algorithms that we design can be implemented on a wide variety of planes with minimal effort. Furthermore, the model yields reasonable results as we adjust the parameters of the plane; for example, larger planes require more time to board, while planes with more aisles can load more quickly than similarly sized planes with fewer aisles. It allows for reasonable amounts of variance in passenger behavior. While with more thorough experimentation a superior stochastic distribution de scribing the delays associated with interferences could be found our simu- lation can be readily altered to incorporate such advances It is simple. We made an effort to minimize the complexity of our simula- tion, allowing us to run more simulations during a greater time period and minimizing the risk of exceptions and errors occurring. It is fairly realistic. Watching the model execute, we can observe passengers to each other taking time to load their ba gage, and waiting around as passengers in front of them move out of the way. Its ability to incorporate such complex behavior and reduce it are key456 The UMAP Journal 28.3 (2007) "* The boarding technique is modeled in a matrix identical in size to the matrix representing the layout of the plane. This matrix is full of positive integers, one for each passenger, assigned to a specific submatrix, representing each passenger's boarding group location. Within each of these submatrices, seat￾ing is assigned randomly to represent the random order in which passengers line up when their boarding groups are called. "* Interferences are counted in every location where they occur within the ma￾trix representing the plane layout. These interferences are then cast into our probability distribution defined above, which gives a measurement of time delay. "* Passengers wait for interferences around them before moving closer to their assigned seats; if an interference is found, the passenger will wait until the time delay has finished counting down to 0. "* The simulation ends when all delays caused by interferences have counted down to 0 and all passengers have taken their assigned seats. Strengths and Weaknesses of the Model Strengths "* It is robust for all plane configurations and sizes. The boarding algorithms that we design can be implemented on a wide variety of planes with minimal effort. Furthermore, the model yields reasonable results as we adjust the parameters of the plane; for example, larger planes require more time to board, while planes with more aisles can load more quickly than similarly￾sized planes with fewer aisles. "* It allows for reasonable amounts of variance in passenger behavior. While with more thorough experimentation a superior stochastic distribution de￾scribing the delays associated with interferences could be found, our simu￾lation can be readily altered to incorporate such advances. "* It is simple. We made an effort to minimize the complexity of our simula￾tion, allowing us to run more simulations during a greater time period and minimizing the risk of exceptions and errors occurring. "* It is fairly realistic. Watching the model execute, we can observe passengers boarding the plane, bumping into each other, taking time to load their bag￾gage, and waiting around as passengers in front of them move out of the way. Its ability to incorporate such complex behavior and reduce it are key to completing our objective