Deformations of asymptonic bounds and balanced job bounds

In order to reduce computational needs in evaluating queueing networks, much effort has been done to develop bounds for the most important performance measures. Thus, for large queueing networks with a large number of classes and devices, it may be worthwile to work with these bounds. This paper, however will exploit another advantage of bounds, namely that they are given by (simple) analytical formulae, as opposed to the exact solution which is given in the form of an algorithm. This paper will give examples how existing bounds can be deformed w.r.t. interesting variables and show how the characteristics of these deformed bounds can be used to gain insight in the behaviour of computer system configurations in a changing environment. This paper contains deformations of asymptotic bounds (ABA), simple balanced job bounds (SBJB) and balanced job bounds (BJB) and they will be used to study the behaviour of single class, closed queueing networks (including delay centers) and of closed queueing networks with two classes and two centers (all jobs are batch). It will also be shown (for the single class case) that under a simple workload policy, residence time temporarily can increase with a more powerful CPU. Throughput-analysis for a system with two classes also gives non-intuitive results.