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We consider a stationary Markov process that models certain queues with abulk service of a fixed number $m$ of admitted customers. We find an integralexpression of its transition probability function in terms of certainmulti-orthogonal polynomials with respect to a system of distributions thatcontain measures supported on starlike subsets of the complex plane. We alsostudy the corresponding steady state.

A multi-orthogonal polynomials' approach to bulk queueing theory