A Class of Data Traffic Processes - Covariance Function Characterization andRelated Queuing Results

In this paper, our interest is in calculating delay information when packets resulting from a collection of calls in progress contend for a data network resource; e.g., transmission delays experienced by packets resulting from the collectioh of virtual circuits on a trunk in a packet switching network. Since the number and types of calls in progress are stochastically varying, the resulting packet process is doubly stochastic. To do an exact analysis when this class of processes is offered to a queuing system, e.g., representing a trunk or packet switch, can be quite intractable. The approach we take is to obtain queuing results by approximating the packet process by a simpler doubly stochastic 897 process that captures the important statistical properties and that is amenable to analysis when offered to a queuing system. In this paper, we (i) characterize the overall packet arrival process in terms of the covariance function of the packet rate, which is itself a stochastic process, and its moments, (11) approximate it by a simpler process which matches the above characterization, and (iii) analyze the performance of the queuing system whose input is the resulting packet process. The characterization depends on the statistics of the call origination process, call durations, the rate of packet arrivals per call, and the discipline for limiting the number of calls in progress. The approximating process is a simple doubly stochastic Poisson process1 where the intensity of a Poisson process varies with the state of a continuous-time Markov chain.