Path-wise performance in a tree-type network: Per-stream loss probability, delay, and delay variance analyses

This paper deals with path-wise performance analysis rather than a nodal one to enrich results previously obtained in the literature under simple but unsatisfactory assumptions, e.g., Poisson processes. First deriving the per-stream loss probability, delay, and delay variance of an isolated queue with multi-class input streams modeled by heterogeneous two-state Markov-modulated Poisson processes (MMPPs), we then propose simple and novel decomposition schemes working together with an input parameter modification scheme to (approximately) extract the per-stream output process for a lossy queue receiving MMPPs under a general service time distribution. The novelty of the decompositions is that they can be easily implemented based on a lossless queueing model. Through numerical experiments, we show that the accuracy in estimating the per-stream output process using such schemes is good. These decomposition schemes together with the input parameter modification scheme and a moment-based fitting algorithm used to fit the per-stream output as a two-state MMPP make analysis of path-wise performance viable by virtually treating each node in isolation along a path to get performance measures sequentially from the source node en route to the destination node.