k-workers in a Circular Warehouse -- A random walk on a circle, without passing

Details k-workers in a Circular Warehouse -- A random walk on a circle, without passing k-workers in a Circular Warehouse -- A random walk on a circle, without passing

2003-09-02

arxiv.org/abs/math/0309039v1

Mathematics

Probability

11 pages, 6 figures

Scientific paper

We consider the problem of stochastic flow of multiple particles traveling on a closed loop, with a constraint that particles move without passing. We use a Markov chain description that reduces the problem to a generalized random walk on a hyperplane (with boundaries). By expressing positions via a moving reference frame, the geometry of the no-passing criteria is greatly simplified, with the resultant condition expressible as the coordinate system planes which bound the first orthant. To determine state transition probabilities, we decompose transitions into independent events and construct a digraph representation in which calculating transition probability is reduced to a shortest path determination on the digraph. The resultant decomposition digraph is self-converse, and we exploit that property to establish the necessary symmetries to find the stationary density for the process.

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