In this note we give a short and easy proof of the equivalence of Hakimi's one-median problem and the k-server-facility-loss median problem as discussed by Chiu and Larson in Computer and Operation Research. The proof makes only use of a stochastic monotonicity result for birth and death processes and the insensitivity of the M/G/k/k loss model.

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Keywords Hakimi median, stochastic location, stochastic monotonicity
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Frenk, J.B.G., Labbé, M., & Zhang, S.. (1993). A note on a stochastic location problem. Operations Research Letters, 13(4), 213–214. doi:10.1016/0167-6377(93)90042-F