Abstract: In a queueing network with overtaking, the probabilistic effects entailed by a customer propagate in such a manner that the sojourn time of the same customer in a node visited later is affected. The main effect of overtaking is the dependency of node sojourn times on non-overtake-free paths: the sojourn time distribution of a non-overtake-free path is not simply the convolution of the sojourn time distributions of the nodes belonging to the considered path. Overtaking arises in manufacturing systems with rework, where defective parts are processed several times until the required quality is met or if sequences of processing steps of different product types intersect (re-entrant lines). Since the influence of overtaking is limited to higher moments of sojourn time distributions (the mean is not affected), and since the influence increases with larger overtaking, the variability of sojourn times can be reduced by diminishing the magnitude of overtaking. For the purpose of reducing the variance of sojourn times, we investigate several queueing disciplines and derive analytical results for basic queueing networks with overtaking. Numerical results comparing the considered scheduling policies are presented and open problems are discussed. Revised: October 1.
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