Probabilistic Network Loads with Dependencies and the Effect on Queue Sojourn Times

For the dimensioning of shared resources, the latency and utilization of the service is a vital design characteristic. The throughput and latency is as important for e.g. network streaming applications as in e.g. (small-scale) distributed embedded systems interacting with physical processes. Calculating latencies of a system involves the analysis of the queue sojourn times. The analysis of queue sojourn time depends on the model of the load. While for fixed and known load, natural and deterministic worst-case models are a good choice, highly variable loads are more appropriately modeled in a stochastic fashion. For the analysis of stochastic load models, the load is often assumed to be stochastic independent and time-invariant. Analysis of loads with auto-correlation or modelling of different streams that are correlated (or dependent in general) requires a highly tuned and specialized model to capture all effects. In this work we apply a queuing sojourn time analysis of streams with stochastic load models with upper and lower bounds guaranteed under any stochastic dependency. The experimental results show how big the effect of dependencies really is and that stochastic load dependency is vital to the calculation of resource utilization and response times (or transmission delays). We propose the use of Fréchet bounds and probability boxes to allow real-time analysis of stochastic models with unknown dependencies.