A class of data traffic processes — covariance function characterization and related queuing results

While the “call” or “session” is the basic entity that is set up in many data traffic applications, the performance analysis of data network elements depends on the internal units of traffic into which calls are decomposed. In a packet-switching network, the packet represents the basic internal unit of traffic, and packets from different calls time-share facilities and contend for network resources, giving rise to queuing delays. In this paper, we consider the problem of characterizing the doubly stochastic packet process resulting from a superposition of call types, each type having a stochastically varying number of calls in progress. We obtain statistical properties of the process and use them to obtain an approximating process, based in part upon time constants associated with the packet-rate covariance function. We discuss existing queuing models dealing with this approximating class of inputs and present results showing the effect of call and packet traffic parameters on queuing performance.