This paper presents a statistical characterization of on-line service traffic. The traffic is parameterized by the call holding times, the aggregate number of bytes and the number of packets transferred during the call. Particular attention is paid to modeling the stochastic rate function describing the call arrivals. The time of day and day of the week seasonal features produce long term correlations in the arrival process. In addition, short term correlations are found to exist within the hourly time scale. The arrival rates are in general nonstationary in the mean rate. This is attributed to the daily influx of new subscribers and other exogenous influences such as promotions and advertisements that trigger increased usage. A time series modeling methodology is used to identify and quantify these features. Under suitable transformations, a stationary rendition of the arrival process is derived and characterized by the short and long term correlation coefficients. The second order characterization of the arrival process is used to predict resource usage.

In many applications certain parameters of a system should be set on the basis of some large percentiles of a delay random variable, for which the characteristics may not be known or may change slowly with time. Assuming that sample values of delays are available sequentially, the authors obtain a simple algorithm to track two key statistical characteristics of the delay. Any high percentile then may be approximated as a simple linear function of these parameters. The approach is based on a quasi-exponential assumption concerning the delays.>

Broadband packet switches handling an asynchronous-time-division-multiplexing type protocol format, e.g. Starlite, can achieve buffer efficiencies by sharing buffers between output ports. It is shown that the number of buffers required with sharing, for random traffic, would be overestimated by as much as 30% at 90% traffic load if the negative correlations that naturally exist, for this type of traffic, between packet streams destined for different output ports were not taken into account. In general, the discrepancy increases as the traffic load increases, and decreases as the switch size increases. A general approach is developed for the analysis of set of queues to which the arrival streams are correlated, which could be used to assess the impacts on shared buffer requirements due to other types of stream correlation (e.g. positive correlations) that may result from other traffic assumptions.>