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In this paper, we study large multi-server loss models under power-of-$d$routing scheme when service time distributions are general with finite mean.Previous works have addressed the exponential service time case when the numberof servers goes to infinity giving rise to a mean field model. The fixed pointof limiting mean field equations (MFE) was shown to be insensitive to theservice time distribution through simulation. Showing insensitivity to generalservice time distributions has remained an open problem. Obtaining the MFE inthis case poses a challenge due to the resulting Markov description of thesystem being in positive orthant as opposed to a finite chain in theexponential case. In this paper, we first obtain the MFE and then show that theMFE has a unique fixed point that coincides with the fixed point in theexponential case thus establishing insensitivity. The approach is via ameasure-valued Markov process representation and the martingale problem toestablish the mean-field limit. The techniques can be applied to other queueingmodels.

Insensitivity of the mean-field Limit of Loss Systems Under Power-of-d Routing