We consider a multi-server polling system with , that is the number of servers that can attend a queue simultaneously is limited. Stability conditions are available when service policies are unlimited. The definition of stability conditions when both server limits and limited service policies apply remains an open problem. We postulate a conjecture for the stability condition in this case that is supported by our simulation results. The study of this particular variant of the multi-server polling system is motivated by the performance evaluation of next generation passive optical access networks.