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Mathematical Modelling


We develop a method for determining the optimal size and placement of parking spaces and approach aisles for an automobile parking lot. In particular, our solution concerns a parking lot of size 100' x 200' located at the corner of an intersection of two streets in a New England town. We begin by arguing the superiority of driver operation over attendant operation of vehicles to be parked. Then a statistical analysis is performed on a sampling of 160 1987 model automobiles to determine upper bounds and ideal values for the length and width of a parking space and for the turning radius required to navigate entrance into said space. Using this data, we show that the optimal degree for diagonal parking which minimizes necessary lot area for a particular space can be expressed as a function of the turning radius of the automobile and the width of the parking space. However, concerning our particular lot, right-angle parking is established as the method by which optimal use of space can be achieved by showing that to minimize wasted area using the diagonal parking scheme requires a greater number of spaces than can be accommodated in the given dimensions. Using these preliminary results, a computer program which utilizes a 12-way tree structure and recursion is employed to generate possible lot designs. Next, other considerations not so conducive to programming-such as snow removal, lot use fees and effects of our design on the adjacent intersection-are discussed.

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