  The prolonged service time at non-dedicated servers has been observed in [1].
Motivated by such real problems, we propose a stylized model which
characterizes the feature of the prolonged service time at non-dedicated
servers in an asymmetric system. We study the independent system, the full
flexibility system and the partial flexibility system when the occupation rate
of the system, the degree of the prolonged service time and the degree of the
asymmetry are allowed to change. We show that under certain circumstances, the
partial flexibility scheme outperforms the full flexibility system and the
independent system in such a model. Our results also provide instructions on
how to introduce flexibility when the service time at non-dedicated servers is
prolonged in an asymmetric system.
