A packet processing device that achieves stable operation by alleviating the workload of packet processing. A packet buffer checks a packet length flag and a processing time flag to observe the device's operating condition for a first connection. When neither of the two flags are on, the packet buffer keeps buffering first packets on the first connection. When either or both flags are on, the packet buffer changes focus to a second connection and begins buffering second packets on the second connection. A packet length monitor turns on the packet length flag if a new cumulative packet length is greater than a packet length threshold. A processing time monitor turns on the processing time flag if a new cumulative processing time estimate is greater than a predetermined processing time threshold.