We present a dynamic inter-RAT handover decision mechanism that allocates network resource for UEs over heterogeneous cells considering UE's mobility, QoS, and cell transition for overload situations. It aims to minimize access failure and handover signalling, while prioritizing UEs with high QoS level for differentiated cell selection. We formulate the problem of dynamic cell selection over a period of time into an optimization problem consisting of step-wise binary integer programs according to UE's moving speed. Simulation results show that our dynamic scheme achieves low access failure ratio in a highly overloaded network. More importantly, the proposed algorithm remarkably diminishes cell handover rate by 20% compared to a counterpart algorithm based on static optimization. We demonstrate that our algorithm successfully controls cell acceptance and connected cell types by prioritizing with UE's QoS and moving speed.