In prior packet transmission systems and/or switching systems information being transmitted was classified as being either statistical, i.e., bursty information or periodic, i.e., so-called circuit type information.  An example of the statistical information is data transfer between computers or the like.  An example of periodic information is PCM encoded voice signals.  In the prior packet systems, packets including periodic information (periodic packets) were given priority over packets including statistical information (statistical packets) for transmission in order to minimize any possible delay variation.  Statistical packets were transmitted only when there were no periodic packets to be transmitted.  Consequently, the statistical packets either experienced long delays in transmission or were dropped.  Both of these results are undesirable. 
More recently, it has been suggested to assign a small portion of the transmission bandwidth for the transmission of statistical packets whether or not higher priority periodic packets are present for transmission.  Specifically, an interval T.sub.1 of a frame is assigned for transmission of periodic packets and a much smaller interval T.sub.2 of the frame is assigned for transmission of statistical packets.  A limitation of such a packet transmission arrangement is that there is no way to know or estimate the delay in transmission experienced by the statistical packets.