This paper deals with the problem of the computation of the optimal routing sequence in a queuing system made of two parallel queues with exponential service times. The optimal policy (minimizing the expected waiting time) is a Sturmian sequence. An algorithm to compute the optimal routing sequence is proposed together with an extensive set of experiments which show several interesting features of the optimal policy with apparent discontinuities and a fractal behavior. Several good approximations using fast heuristics are given at the end.
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