Recently, a number of empirical studies have demonstrated the existence of long-range dependence (LRD) or self-similarity in VBR video traffic. Since previous LRD models cannot capture all short- and long-term correlation and rate-distribution while still retaining mathematical tractability, there exist many doubts on the importance of SRD, LED, and rate-distribution on traffic engineering. In this paper, we present a video traffic model based on the shifting-level (SL) process with an accurate parameter matching algorithm for video traffic. The SL process captures all those key statistics of an empirical video trace. Also, we devised a queueing analysis method of SL/D/1/K, where the system size at every embedded point is quantized into a fixed set of values, thus the name quantization reduction method. This method is different from previous LRD queueing results in that it provides queueing results over all range not just an asymptotic solution. Further, this method provides not only the approximation but also the bounds of the approximation for the system states and thus guarantees the accuracy of the analysis. We found that for most available traces their ACF can be accurately modeled by a compound correlation (SLCC): an exponential function in short range and a hyperbolic function in long range. Comparing the queueing performances with C-DAR(1), the SLCC, and real video traces identify the effects of SRD and LRD in VBR video traffic on queueing performance.

In this paper we introduce a general class of level-dependent quasi-birth-and-death (QBD) processes and their stationary solution. We obtain the complete characterization of their fundamental matrices in terms of minimal non-negative solution of the number of matrix quadratic equations. Our results provides a mixed-geometric solution for the stationary solution of level-dependent chains. Applications in overload control in communication networks are also discussed.