On the packet stream generated by a random flow of calls of random durations

In the present model for a packet stream, messages are assumed to be initiated according to a Poisson process and each to remain active for durations which correspond to the time to absorption in a finite Markov process. As each message evolves through the transient states of that Markov chain, it generates packets according to a Poisson process, whose rate may vary with the current transient state. The paper examines the counting process for the pooled stream of packets and obtains expressions for its variance-time curve, its Palm measure, the peakedness function and the square wave power spectral density. These are measures of physical properties of the point process which are important to approximations and to performance studies. In addition to these, a number of new, analytically tractable desciptors are proposed.