圆形仓库中的k-工人--在圆上的随机游动，不经过
k-workers in a Circular Warehouse -- A random walk on a circle, without passing
摘要：
我们考虑多个粒子在一个封闭的回路上运动的随机流问题，其中粒子运动而不通过。我们使用马尔可夫链的描述，减少了问题的广义随机游动超平面（边界）。通过移动参考系来表示位置，极大地简化了不通过准则的几何形状，结果条件可表示为限制第一正交线的坐标系平面。为了确定状态转移概率，我们将转移分解为独立事件，并构造一个有向图表示，其中计算转移概率减少到最短路径的有向图的确定。由此产生的分解有向图是自逆的，我们利用该属性来建立必要的对称性，以找到该过程的稳态密度。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
