Age of Information (AoI), which measures the time elapsed since the generation of the last received packet at the destination, is a new metric for real-time status update tracking applications. In this paper, we consider a status-update system in which a source node samples updates and sends them to an edge server over a delay channel. The received updates are processed by the server with an infinite buffer and then delivered to a destination. The channel can send only one update at a time, and the server can process one at a time as well. The source node applies generate-at-will model according to the state of the channel, the edge server, and the buffer. We aim to minimize the average AoI with \emph{independent and identically distributed} transmission time and processing time. We consider three online scheduling policies. The first one is the optimal long wait policy, under which the source node only transmits a new packet after the old one is delivered. Secondly, we propose a peak age threshold policy, under which the source node determines the sending time based on the estimated peak age of information (PAoI). Finally, we improve the peak age threshold policy by considering a postponed plan to reduce the waiting time in the buffer. The AoI performance under these policies is illustrated by numerical results with different parameters.