We consider a stationary Markov process that models certain queues with a bulk service of a fixed number $m$ of admitted customers. We find an integral expression of its transition probability function in terms of certain multi-orthogonal polynomials with respect to a system of distributions that contain measures supported on starlike subsets of the complex plane. We also study the corresponding steady state.

翻译：我们考虑一个稳态马尔可夫过程，该过程对固定数量$m$个被接纳客户的批量服务进行建模。我们找到了其转移概率函数的一个积分表达式，该表达式涉及关于一系统分布的多正交多项式，这些分布包含在复平面上星形子集上支撑的测度。我们还研究了相应的稳态。