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Error analysis of burst level modeling of active-idle sources

It is often not feasible to simulate high-speed networks at the packet level. One common technique for simulation speedup is to model traffic at coarser timescales, which we refer to as the abstract simulation. In this article, we analyze the sources for the accuracy degradation in abstract simulation. Specifically, we consider burst level modeling of active-idle sources and study a queue fed by such sources. The arrival rates vary during active periods. The burst level model assumes constant rates during each active period. Therefore, it can not track queue-length variations within an active period, which leads to the queue-length evaluation error. We study two scenarios. In the first scenario, the queue is always busy whenever the source is on. During each active period, the evolution of the queue length can be viewed as an integration process of the arrival rate. In this case, the error in the mean queue length shows nice properties. It is only determined by the traffic characteristics and does not change with the utilization. In the multiple-flow case, the error is the sum of the errors caused by abstraction on individual flows. We also show that the error does not propagate for tree-like networks or networks with probabilistic routing. In the first scenario, under very general conditions, burst level modeling does not cause significant underevaluation of the queue length. In the second scenario, the queue may empty during on periods of the source. We call these empty periods E intervals. We quantify the error in the mean queue length, which depends on the numbers, lengths, and positions of the E intervals. The burst level model significantly underevaluates the queue length if such intervals occur often. High utilizations, strong traffic burstiness at the active-idle level, and small arrival granularity tend to reduce such occurrences and the error in the mean queue length. This explains why these conditions favor traffic modeling at coarser timescales. Our findings are not limited to the specific traffic sources and the time-abstraction techniques. Instead, they shed light on the conditions needed for abstract models to deliver evaluation fidelity in a general context.