G. Hasslinger, D. Fausten: Analysis of the Workload in Communication Systems Analysis of the Workload in Communication Systems including Data Transfers over Arbitrary Time Scales

We show how results known for discrete time GI/GI/1 systems with service time distributions of finite support can be generalized to include arbitrary, especially long-tailed distributions of the service time. Therefore we prove and exploit the property, that the tail of the service time distribution beyond a certain bound has negligible effect on the idle times. This enables to compute the idle time distribution in a modified system with appropriately truncated service time. Knowledge of the idle time distribution represents one factor and thus the decisive part of the Wiener-Hopf factorization method to obtain the steady state distribution of the workload. We apply the workload analysis to Pareto distributed service demands, which are observed for the size of files transmitted over the Internet and which generate self-similar traffic pattern. Although difficulties remain in order to evaluate extremely large workload percentiles from the obtained generating functions e.g. for GI/Pareto/1 systems, we can derive lower bounds being confirmed in the special case of M/Pareto/1 by known similar results.