The Gate Distribution

ABSTRACT

Gates that transfer objects within their capacity, without formation of queues, are considered in a combinatorial framework. The number of different ways, I (m,n,l), n objects can pass randomly an array of m gates, each with constrained capacity l, is used to characterize its performance. Two gate distributions were formulated and their properties studied. The first, n dependent distribution was found to be symmetric, whereas the second, l dependent distribution is skew. These properties persist also in the case of multivariate gate distributions. In the latter case, the expectation and variance turn to have additive properties, respectively.