We have studied the video packet loss due to excessive queueing delay in a single statistical multiplexer. The underlying video codec is assumed to separate its outputs into high-priority data and low-priority data so that the loss of low priority will cause a modest picture degradation. In conjunction with such hierarchical coding, the video multiplexer employs a control scheme that selectively discards low-priority data to alleviate the possibility of overload. The quality of the received pictures is measured by the expected underload period and the expected number of high-priority arrivals during an overload period. The former quantity measures the mean period that the received picture stays free of serious disturbance by packet loss due to excessive queueing delay, while the
latter is an indicator of the picture area affected. We have analyzed the performances of such a system under the given control scheme. Our analysis shows that the simple congestion control based on selective packet discarding can significantly prolong the underload period and reduce the number of high-priority losses in the overload period. To further reduce the number of high-priority arrivals in overload periods, we propose a control scheme that blocks all arrivals once they exceed the maximum delay. Moreover, the underload period can be dramatically prolonged by reducing the packetization buffer at the network input end. These results show that transporting video by the ATM technique is very promising.