Conclusions

We have shown how transient analysis for network control (Section 5) and design (Sections 6 & 7) can be carried out for multi-level sources with general, possibly long-tailed, level-holding-time distributions. In Section 2 we analyzed the transient behavior of a general source traffic model composed of a semi-Markov level process and a zero-mean piecewise-stationary within-level variation process. We approximated the conditional aggregate demand from many sources given system state information by the conditional aggregate mean given level values and ages. The within-level variation process plays no role in this approximation. We showed that the conditional mean can be effectively computed using numerical transform inversion (Section 2) and developed several approximations to it (Sections 3 & 7). We showed how the model can be exploited to study the value of information (Section 4). We applied our techniques to examples in network control (Section 5) and design (Section 7).

Even though our approach is to focus on offered load, unaltered by loss and delay associated with finite capacity, we can apply the conditional mean approximation in Section 2 to develop an approximation to describe loss and delay from a finite-capacity system, just as described in Section 5 of [10] for the M/G/$\infty$ arrival process.