Expressions are derived for the mean message delay, as a function of message length, when data messages of different lengths arrive asynchronously at a trunk and are divided, as they come in, into packets of some maximum length. The packets of different messages are intermingled and are put onto the trunk either from a single first-in-first-out (FIFO) queue, or from a high-priority and a low-priority queue for single-packet and multiple-packet messages, respectively. The results are compared to the case in which messages enter service in order of arrival and each message is served to completion without interruption, so that the mean message delay is independent of message length.>