Before revision:  Moreover, when the degree of the prolonged service time is pre-specified, we show that the pooling system with prolonged service time at non-dedicated servers is not preferred when the work load in the systemis greater than a certain threshold .
After revision:  Moreover, when 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 not preferred when the work load in the systemis greater than a certain threshold .