Analytic comparison results for communication networks

Abstract

Queueing networks are known to provide a useful modelling and evaluation tool in computer and telecommunications. Unfortunately, realistic features like finite capacities, link failures, dynamic routing and non-exponentiality usually prohibit analytic solutions. Numerical and approximate computations as well as simplifications and performance bounds for queueing networks therefore become of practical interest. These are usually based on some form of a system modification or rather a comparison of a system under different conditions. This tutorial will outline and survey a technique to conclude comparison results and error bounds for comparing performance measures of a system under different circumstances. Most notably, this includes: • perturbations • system comparisons • state space truncations or extensions • modifications to obtain simple performance bounds The advantages and disadvantages of this technique, which is based on recursive or dynamic Markov reward structures, compared to the standard stochastic comparison or sample path approach will also be outlined. To illustrate and support the results a number of practical queueing network applications will be presented. These applications cannot be solved analytically, but simple performance bounds will be provided. The applications include simple expressions for: • Jackson networks subject to breakdowns • Jackson networks with large finite buffers • a performability front-end database system • a communications example with alternate routing • a circuit-switch telecommunications model with link failures