An analytical model for application to the operation of replenishment at sea
Waggoner, Mark Harvey
Milch, Paul R.
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An analytical model for replenishment at sea is formulated for two supply ships and L combatants using queueing theory concepts and a random walk model in the plane. Exponential distributions are assumed for replenishment times, and, given the initial number of combatants to be replenished by each supply ship, the distribution for total time to complete the finite operation is obtained in terms of Laplace transforms. All possible sequences for finishing the replenishments of the combatants have been considered in the model, and the techniques which were developed to count the number of sequence possibilities are presented as an appendix. Although this model involves only two supply ships, it is believed that the methods used may be generalized for application to more complicated models.
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