The operation of replenishment at sea is investigated for three
supply ships and L combatants using queueing theory concepts and a
random walk model in three dimensions. The distribution for total
replenishment time given the initial number of combatants to be
replenished by each supply ship and a specified cyclic order of
replenishment is expressed in terms of its Laplace transform under
the assumption of independent, exponential service times for each
supply vessel. A method for counting all possible sequences of
replenishment is not found, but some preliminary counting techniques
are developed which may be useful in its eventual determination.http://www.archive.org/details/schedulingthrees00huliLieutenant, United States NavyApproved for public release; distribution is unlimited
