Summary: This paper deals with an enhanced hitless-prediction router system that has the hitless-restart capability with forecasting. Hitless-restart means that the router can stay on the forwarding path and the network topology remains stable. But the major difficulty of the current hitless-restart is that the router is always active to take the action, such as non-stop forwarding (upgrade, maintenance and capacity expansion may be included as third party activities). Stochastic hitless-prediction model gives the decision making factors that manage a router system more efficiently. An analogue of the first exceed level theory is applied for the restriction of the number of buffer size that is the router capacity. Analytically, tractable results are obtained by using a first exceed level process that enables us to determine the decision making factors such as recycle periods of the hitless-prediction point to prevent a router shutdown.