Abstract

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.

Keywords: Performance analysis; Decomposition scheme; Markov-modulated Poisson process

Article Outline

1. Introduction

2. Model description

2.1. Traffic model

2.2. System model

3. Performance analysis for an isolated node

3.1. Preliminaries

3.2. Overall and per-stream loss probabilities

3.3. Overall and per-stream delay moments

4. Decomposition schemes and the input parameter modification scheme

4.1. Decomposition schemes

4.2. Input parameter modification scheme

5. Performance of an individual path in a tree-type network

6. Numerical examples and discussions

6.1. Per-stream output statistics through a finite-buffer queue

6.2. Per-path performance in tree-type networks

7. Conclusions

Appendix A. Formulas for and

Appendix B. Overall output process of an MMPP/G/1 queue

Appendix C. Formulas for and

Appendix D. Computation of γ_n

Appendix E. The moment-based fitting algorithm

References

Vitae

This work was supported in part by the National Science Council, Taiwan, R.O.C. under Contracts NSC 90-2213-E-011-096, NSC 93-2219-E-011-007, and NSC 94-2219-E-011-006.