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We present an example of a single-server polling system with two queues andan adaptive service policy where the stability region depends on the expectedvalues of all the primitives and also on a certain exponential moment of theservice-time distribution in one of the queues. The latter parameter can not bedetermined, in general, in terms of any finite number of power moments. Itfollows that the fluid approximation approach may not be an appropriate toolfor the stability study of this model.

A polling system whose stability region depends on a whole distribution of service times